Why don't we see more supernovae in our galaxy? I found this on the Wikipedia page on supernovae:

  The total supernova rate in our galaxy is estimated to be about 4.6 per century, or one every 22 years, although we haven't actually observed one for several centuries.

That sounds like a freak occurrence to me.

It made me curious about the numbers so I refreshed my knowledge on the Poisson distribution. It is not specified how many centuries we have not seen a supernova, but let's assume it's only two.

If on average 9.2 supernovae happen per 2 centuries then the chance of having exactly 9 in any two century period can be calculated with:

$$p(k) = {\lambda^k \times e^{-\lambda} \over k!}$$

Filling in $k=9$,

$$p(9) = {9.2^9 \times e^{-9.2} \over 9!}=0.1315$$

The chance that there is not a single supernova in a two century period is:

$$p(0) = {9.2^0 \times e^{-9.2} \over 0!}=0.00010104$$

That's about a 1 in 10,000 chance. If "several" means 3 centuries, then the chance of not having any supernova is as little as 1 in 100,000.

So from this I can only come to the conclusion that supernovae did in fact happen in the Milky Way in the last two centuries, but that we didn't see any of them.

But now I'm confused. I read about supernovae that have happened in galaxies billions of light-years from here that lit up as the brightest source of light in the sky for days. Surely we would be able to see all of the supernovae that happen in our Milky Way (no more than 100,000 light years away) with the naked eye, let alone with telescopes?

Are some supernovae so much more super than others? Are all of the Milky Way's supernovae visible to the naked eye?

So from this I can only come to the conclusion that supernovae did in
  fact happen in the Milky Way in the last two centuries, but that we
  didn't see any of them.

  But now I'm confused. I read about supernovae that have happened in
  galaxies billions of light-years from here that lit up as the
  brightest source of light in the sky for days. Surely we would be able
  to see all of the supernovae that happen in our Milky Way

One problem with estimating how many supernovae have happened in the Milky Way in the last two centuries, is that the remnant from a supernova is far dimmer than the nova itself and far harder to find. Several supernovae could have happened in the Milky Way in the last 2 centuries and remain undiscovered — and just for clarity, we define the date of a supernova by the date the light from the explosion reaches the Earth, so saying saying a nova "happened" in the last 200 years refers to the date the light from the event reached Earth, not the actual date of the event, which you probably already know, but just to clarify.

So for argument's sake, let's say that a supernova's light reached the Earth about 50 years ago, but it took place on the far side of the galaxy. To find that, we'd have to look for a nebula on the far side of the galaxy and that's a hard thing to see. Similar to looking for the theoretical Planet Nine, finding old supernova remnants on the other side of the Milky Way takes a lot of looking. Even with modern telescopes, it's still a needle in a haystack, and especially if the view is blocked by dust like much of the Milky Way is.

A Milky Way supernova remnant was discovered in 1985, supernova remnant G1.9+0.3. It was thought to have "happened" around 1868, though it went unobserved and probably wasn't visible to the naked eye at the time.   There's probably been several others more recent than that one.  G1.9+0.3 would have been visible if not for interstellar dust. From article above:

  It was a type Ia supernova believed to have exploded about 25,000
  years ago, and the signal began reaching Earth around 1868. The light
  from the supernova would have been visible to 19th century
  astronomers, had it not been obscured by the dense gas and dust of the
  Galactic Center.

I'm not sure the 4.6 supernovae per century from your article is accurate. It might be, but the number I'm used to hearing is about one per century. But regardless of which number is actually correct, it still doesn't imply high mathematical improbability because many Milky Way novae would have gone unnoticed if they were far enough away. In short, I agree with what you said here:

  I can only come to the conclusion that supernovae did in fact happen in the Milky Way in the last two centuries, but that we didn't see any of them.

Here's a related article on Milky Way visibility.

Observation of a distant galaxy nova is possible if we have telescopes looking in that direction. A nova is much more detectable at the time it goes nova.  Much less so, years later.

Today, however, with neutrino detection in 7 locations around the globe, I think it's virtually impossible that we'd miss a supernova in the Milky Way, so we have a good chance of seeing one in our lifetime and it's likely that none have occurred since somewhere around 1980. A supernova was detected in the Andromeda galaxy in 1987 by that method, and our neutrino detection has improved since then to give us early warning and pinpoint location.

As far as visibility, size matters, but what matters more is how close and how much dust is in the way. Most of the recorded supernovae were quite bright and fairly noticeable to someone who was familiar with the stars in the sky (list of known supernovae).

Eight Milky Way novae have been recorded by history and observed by the naked eye in the last 2,000 years, well below the number that should have happened in that time. Five of those eight had brightness greater than $-3$, which is brighter than Jupiter and would have been immediately noticed by anyone familiar with star charting. Two others had magnitudes around zero, which is still brighter than most stars. SN386 was less bright, but is still easily visible and recorded by Chinese astronomers. And finally, Cassiopeia A was quite dim, but it was still observable. Only about 10% (ballpark estimate) of the Milky Way is close enough and unobstructed enough to provide supernovae that would visibly get noticed.  Most would have gone unnoticed until recently.

Hope that's not too wordy, I can try to clean up if needed.

Also, you might be forgetting that the distances of the stars that exploded will cause us to see them at different times.  Say three stars exploded in a given year but one was 1,000 light years away another was 1,500 light years away and the third was 2,000 light years away.  We wouldn't see those novae here on Earth in the same year.  So, while it's quite possible that there are 2 to 3 novae a year, we may (i.e. likely will) see them many years apart.

On the flip side, a star that exploded 100 years ago that was 100 light years away and another star that exploded 500 years ago and was 500 light years away would appear to us in the same year here on Earth.


Why are telescope mirrors made of glass? Optical telescope mirrors are typically made from endlessly polished glass surfaces that have been aluminised to provide a very smooth surface of reflective aluminium.

But why the need for glass at all? Why can't mirrors be made of pure metal, or of metal deposited onto some other surface?

Is there something special about the glass grinding process that means no other surface can be made as smooth and still have aluminium deposited on the surface?

Or is it to do with the thermal expansive properties of the glass used?

you are partially correct. Glass is used for several reasons. It is a very stable material and will hold its shape well for thousands of years. Glass can also be polished to a high degree of accuracy without having defects.  Another major reason is the expansion properties are very favorable as well. Glass doesn't corrode and is easier to mold into shape than metal mirrors. Glass is relatively cheap and readily available.

Some useful references are found here ,here and here.

When we look at the thermal expansion, Zerodur is much better than glas. It was used for  GTC, Keck I, Keck II, and SOFIA mirrors.


How long does a sunrise or sunset take? From the time that the sun appears on the horizon, or meets it on its setting, to the time that it is fully visible, or no longer visible on its setting, how much time passes?
Secondly, is there a place in the world where a sunrise/sunset occurs over a period of a few days? Meaning, that from the time it begins to appear over the horizon until it is fully visible, a period of a few days pass without night intervening (and the same for the opposite with sunset)?

As noted in http://aa.quae.nl/en/antwoorden/zonpositie.html#14 the
length of sunrise/sunset varies from approximately 128/cos(latitude)
seconds at the equinoxes to approximately 142/cos(1.14*latitude) at
the solstices.

More specifically, here's the length of sunrise/sunset at various latitudes:

Beyond 65 degrees north or south latitude, the sun does not rise or
set daily, and the length of sunrise/sunset increases significantly.

The data plotted above is the length of sunrise, but the length of
sunset is very similar.

All calculations for this program were made with this program:

https://github.com/barrycarter/bcapps/blob/master/ASTRO/bc-solve-astro-12824.c

The raw output of sunrise/sunset times:

https://github.com/barrycarter/bcapps/blob/master/ASTRO/sun-rise-set-multiple-latitudes.txt.bz2

You can verify these results at:
http://aa.usno.navy.mil/data/docs/RS_OneYear.php

The longest sunrise I found for 2015 was at 89 degrees 51 minutes
south latitude, 125 degrees east longitude. There, the sun starts
rising 20 Sep 2015 at 2352, bobbles up and down a bit (but never quite
sets), and finally finishes rising 43 hours and 21 minutes later, at
22 Sep 2015 at 1913, but see caveat at the end of this answer.

You can "verify" this by first visiting
http://aa.usno.navy.mil/data/docs/RS_OneYear.php with these
parameters:

to get:

Sun or Moon Rise/Set Table for One Year
             o  ,    o  ,                                                                              Astronomical Applications Dept.
Location: E125 00, S89 51                          Rise and Set for the Sun for 2015                   U. S. Naval Observatory
                                                                                Washington, DC  20392-5420
                                                            Universal Time

       Jan.       Feb.       Mar.       Apr.       May        June       July       Aug.       Sept.      Oct.       Nov.       Dec.
Day Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set
     h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m
01  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
02  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
03  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
04  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
05  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
06  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
07  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
08  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
09  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
10  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
11  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
12  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
13  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
14  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
15  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
16  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
17  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
18  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
19  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
20  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  2352       **** ****  **** ****  **** ****
21  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
22  **** ****  **** ****  1842 1614  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
23  **** ****  **** ****       0708  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
24  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
25  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
26  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
27  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
28  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
29  **** ****             ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
30  **** ****             ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
31  **** ****             ---- ----             ---- ----             ---- ----  ---- ----             **** ****             **** ****

(**** object continuously above horizon)                                                      (---- object continuously below horizon)

Note that the sun rises at 2352 on September 20th, and doesn't set for
the rest of the year, verifying the sunrise start time.

Verifying the end time is a little tricker. To do this, visit
http://ssd.jpl.nasa.gov/horizons.cgi with the following parameters:

to get:

Revised : Jul 31, 2013                  Sun                                 10

 PHYSICAL PROPERTIES (revised Jan 16, 2014):
  GM (10^11 km^3/s^2)   = 1.3271244004193938  Mass (10^30 kg)   ~ 1.988544
  Radius (photosphere)  = 6.963(10^5) km  Angular diam at 1 AU  = 1919.3"
  Solar Radius (IAU)    = 6.955(10^5) km  Mean density          = 1.408 g/cm^3
  Surface gravity       =  274.0 m/s^2    Moment of inertia     = 0.059
  Escape velocity       =  617.7 km/s     Adopted sidereal per  = 25.38 d
  Pole (RA,DEC in deg.) =  286.13,63.87   Obliquity to ecliptic = 7 deg 15'
  Solar constant (1 AU) = 1367.6 W/m^2    Solar lumin.(erg/s)   =  3.846(10^33)
  Mass-energy conv rate = 4.3(10^12 gm/s) Effective temp (K)    =  5778
  Surf. temp (photosphr)= 6600 K (bottom) Surf. temp (photosphr)=  4400 K (top)
  Photospheric depth    = ~400 km         Chromospheric depth   = ~2500 km
  Sunspot cycle         = 11.4 yr         Cycle 22 sunspot min. =  1991 A.D.

  Motn. rel to nrby strs= apex : RA=271 deg; DEC=+30 deg
                          speed: 19.4 km/s = 0.0112 AU/day
  Motn. rel to 2.73K BB = apex : l=264.7+-0.8; b=48.2+-0.5
                          speed: 369 +-11 km/s

Results

*******************************************************************************
Ephemeris / WWW_USER Fri Jan  1 21:49:19 2016 Pasadena, USA      / Horizons
*******************************************************************************
Target body name: Sun (10)                        {source: DE431mx}
Center body name: Earth (399)                     {source: DE431mx}
Center-site name: (user defined site below)
*******************************************************************************
Start time      : A.D. 2015-Sep-22 19:00:00.0000 UT
Stop  time      : A.D. 2015-Sep-22 20:00:00.0000 UT
Step-size       : 1 minutes
*******************************************************************************
Target pole/equ : IAU_SUN                         {East-longitude +}
Target radii    : 696000.0 x 696000.0 x 696000.0 k{Equator, meridian, pole}
Center geodetic : 125.000000,-89.850000,7.057E-13 {E-lon(deg),Lat(deg),Alt(km)}
Center cylindric: 125.000000,16.7540774,-6356.730 {E-lon(deg),Dxy(km),Dz(km)}
Center pole/equ : High-precision EOP model        {East-longitude +}
Center radii    : 6378.1 x 6378.1 x 6356.8 km     {Equator, meridian, pole}
Target primary  : Sun
Vis. interferer : MOON (R_eq= 1737.400) km        {source: DE431mx}
Rel. light bend : Sun, EARTH                      {source: DE431mx}
Rel. lght bnd GM: 1.3271E+11, 3.9860E+05 km^3/s^2
Atmos refraction: NO (AIRLESS)
RA format       : HMS
Time format     : CAL
RTS-only print  : NO
EOP file        : eop.160101.p160324
EOP coverage    : DATA-BASED 1962-JAN-20 TO 2016-JAN-01. PREDICTS-> 2016-MAR-23
Units conversion: 1 au= 149597870.700 km, c= 299792.458 km/s, 1 day= 86400.0 s
Table cut-offs 1: Elevation (-90.0deg=NO ),Airmass (>38.000=NO), Daylight (NO )
Table cut-offs 2: Solar Elongation (  0.0,180.0=NO ),Local Hour Angle( 0.0=NO )
*******************************************************************************
 Date__(UT)__HR:MN     Azi_(a-appr)_Elev
****************************************
$$SOE
 2015-Sep-22 19:00 *m  128.1772  -0.3117
 2015-Sep-22 19:01 *m  127.9272  -0.3109
 2015-Sep-22 19:02 *m  127.6771  -0.3101
 2015-Sep-22 19:03 *m  127.4270  -0.3093
 2015-Sep-22 19:04 *m  127.1770  -0.3085
 2015-Sep-22 19:05 *m  126.9269  -0.3077
 2015-Sep-22 19:06 *m  126.6769  -0.3069
 2015-Sep-22 19:07 *m  126.4268  -0.3061
 2015-Sep-22 19:08 *m  126.1767  -0.3053
 2015-Sep-22 19:09 *m  125.9267  -0.3045
 2015-Sep-22 19:10 *m  125.6766  -0.3037
 2015-Sep-22 19:11 *m  125.4266  -0.3029
 2015-Sep-22 19:12 *m  125.1765  -0.3021
 2015-Sep-22 19:13 *m  124.9264  -0.3013
 2015-Sep-22 19:14 *m  124.6764  -0.3005
 2015-Sep-22 19:15 *m  124.4263  -0.2997
 2015-Sep-22 19:16 *m  124.1762  -0.2989
 2015-Sep-22 19:17 *m  123.9262  -0.2981
 2015-Sep-22 19:18 *m  123.6761  -0.2973
 2015-Sep-22 19:19 *m  123.4261  -0.2964
 2015-Sep-22 19:20 *m  123.1760  -0.2956
 2015-Sep-22 19:21 *m  122.9259  -0.2948
 2015-Sep-22 19:22 *m  122.6759  -0.2940
 2015-Sep-22 19:23 *m  122.4258  -0.2932
 2015-Sep-22 19:24 *m  122.1757  -0.2923
 2015-Sep-22 19:25 *m  121.9257  -0.2915
 2015-Sep-22 19:26 *m  121.6756  -0.2907
 2015-Sep-22 19:27 *m  121.4256  -0.2899
 2015-Sep-22 19:28 *m  121.1755  -0.2890
 2015-Sep-22 19:29 *m  120.9254  -0.2882
 2015-Sep-22 19:30 *m  120.6754  -0.2874
 2015-Sep-22 19:31 *m  120.4253  -0.2865
 2015-Sep-22 19:32 *m  120.1753  -0.2857
 2015-Sep-22 19:33 *m  119.9252  -0.2849
 2015-Sep-22 19:34 *m  119.6751  -0.2840
 2015-Sep-22 19:35 *m  119.4251  -0.2832
 2015-Sep-22 19:36 *m  119.1750  -0.2823
 2015-Sep-22 19:37 *m  118.9250  -0.2815
 2015-Sep-22 19:38 *m  118.6749  -0.2807
 2015-Sep-22 19:39 *m  118.4248  -0.2798
 2015-Sep-22 19:40 *m  118.1748  -0.2790
 2015-Sep-22 19:41 *m  117.9247  -0.2781
 2015-Sep-22 19:42 *m  117.6746  -0.2773
 2015-Sep-22 19:43 *m  117.4246  -0.2764
 2015-Sep-22 19:44 *m  117.1745  -0.2756
 2015-Sep-22 19:45 *m  116.9245  -0.2747
 2015-Sep-22 19:46 *m  116.6744  -0.2739
 2015-Sep-22 19:47 *m  116.4243  -0.2730
 2015-Sep-22 19:48 *m  116.1743  -0.2721
 2015-Sep-22 19:49 *m  115.9242  -0.2713
 2015-Sep-22 19:50 *m  115.6742  -0.2704
 2015-Sep-22 19:51 *m  115.4241  -0.2696
 2015-Sep-22 19:52 *m  115.1740  -0.2687
 2015-Sep-22 19:53 *m  114.9240  -0.2678
 2015-Sep-22 19:54 *m  114.6739  -0.2670
 2015-Sep-22 19:55 *m  114.4239  -0.2661
 2015-Sep-22 19:56 *m  114.1738  -0.2652
 2015-Sep-22 19:57 *m  113.9237  -0.2644
 2015-Sep-22 19:58 *m  113.6737  -0.2635
 2015-Sep-22 19:59 *m  113.4236  -0.2626
 2015-Sep-22 20:00 *m  113.1735  -0.2618
$$EOE
*******************************************************************************
Column meaning:

TIME

  Prior to 1962, times are UT1. Dates thereafter are UTC. Any 'b' symbol in
the 1st-column denotes a B.C. date. First-column blank (" ") denotes an A.D.
date. Calendar dates prior to 1582-Oct-15 are in the Julian calendar system.
Later calendar dates are in the Gregorian system.

  Time tags refer to the same instant throughout the universe, regardless of
where the observer is located.

  The dynamical Coordinate Time scale is used internally. It is equivalent to
the current IAU definition of "TDB". Conversion between CT and the selected
non-uniform UT output scale has not been determined for UTC times after the
next July or January 1st.  The last known leap-second is used over any future
interval.

  NOTE: "n.a." in output means quantity "not available" at the print-time.

SOLAR PRESENCE (OBSERVING SITE)
  Time tag is followed by a blank, then a solar-presence symbol:

        '*'  Daylight (refracted solar upper-limb on or above apparent horizon)
        'C'  Civil twilight/dawn
        'N'  Nautical twilight/dawn
        'A'  Astronomical twilight/dawn
        ' '  Night OR geocentric ephemeris

LUNAR PRESENCE WITH TARGET RISE/TRANSIT/SET MARKER (OBSERVING SITE)
  The solar-presence symbol is immediately followed by another marker symbol:

        'm'  Refracted upper-limb of Moon on or above apparent horizon
        ' '  Refracted upper-limb of Moon below apparent horizon OR geocentric
        'r'  Rise    (target body on or above cut-off RTS elevation)
        't'  Transit (target body at or past local maximum RTS elevation)
        's'  Set     (target body on or below cut-off RTS elevation)

RTS MARKERS (TVH)
  Rise and set are with respect to the reference ellipsoid true visual horizon
defined by the elevation cut-off angle. Horizon dip and yellow-light refraction
(Earth only) are considered. Accuracy is < or = to twice the requested search
step-size.

 Azi_(a-appr)_Elev =
   Airless apparent azimuth and elevation of target center. Adjusted for
light-time, the gravitational deflection of light, stellar aberration,
precession and nutation. Azimuth measured North(0) -> East(90) -> South(180) ->
West(270) -> North (360). Elevation is with respect to plane perpendicular
to local zenith direction.  TOPOCENTRIC ONLY. Units: DEGREES

 Computations by ...
     Solar System Dynamics Group, Horizons On-Line Ephemeris System
     4800 Oak Grove Drive, Jet Propulsion Laboratory
     Pasadena, CA  91109   USA
     Information: http://ssd.jpl.nasa.gov/
     Connect    : telnet://ssd.jpl.nasa.gov:6775  (via browser)
                  telnet ssd.jpl.nasa.gov 6775    (via command-line)
     Author     : Jon.Giorgini@jpl.nasa.gov

*******************************************************************************

The sun's angular diameter is about 32 arcminutes, so the sun's lower
limb is 16 arcminutes below the sun's center. When the center of the
sun has geometric elevation -18 arcminutes (-0.3 degrees), the lower
limb has geometric elevation -34 arcminutes. Since refraction near the
horizon is also 34 arcminutes, the sun's lower limb rises when the
sun's geometric elevation is -0.3 degrees.

In the table above, this occurs between 1914 and 1915, but my program
uses slightly more accurate data for the sun's angular diameter, and
the sun actually finishes rising between 1913 and 1914 (and closer to
1913).

You can then fly almost halfway across the world to latitude 89
degrees 51 minutes and longitude -19 degrees to see the
one-minute-shorter longest sunset, which starts at 23 Sep 2015 at 2128
and ends at 25 Sep 2015 at 1648, a length of 43 hours and 20 minutes.

In this case, you would use
http://aa.usno.navy.mil/data/docs/RS_OneYear.php to verify the ending
time of the sunset, and HORIZONS to verify the start time of the
sunset.

Polar sunrises and sunsets are considerably shorter:

At the North Pole, the sun starts rising at 18 Mar 2015 at 2015,
and finishes rising at 20 Mar 2015 at 0441, a length of 32 hours and
26 minutes.
At the South Pole, the sun starts setting at 21 Mar 2015 at 1650,
and finishes setting at 23 Mar 2015 at 0117, a length of 32 hours
and 27 minutes.
At the South Pole, the sun starts rising at 21 Sep 2015 at 0508,
and finishes rising at 22 Sep 2015 at 1400, a length of 32 hours and
52 minutes.
At the North Pole, the sun starts setting at 24 Sep 2015 at 0243,
and finishes setting at 25 Sep 2015 at 1131, a length of 32 hours
and 48 minutes.

Main caveat: Like HORIZONS and the sunrise/sunset tables above, I
assume 34 arcminutes of refraction at the horizon. That's reasonable
for most locations, but may be unreasonable close the pole, where the
longest sunrises and sunsets occur. In particular, refraction can
change rapidly at these latitudes, allowing for potentially much
longer sunrises and sunsets.

I now believe that http://what-if.xkcd.com/42/ is inaccurate, and will
ping the author to let him know.

The Sun's diameter being ½ degree out of 360, I figure it is 2 minutes.
Very even precisely two, because the division of time as into minutes, very very long ago, was designed with the movement of the Sun as its base.


Is there a way to tell the difference between earth andesite from Mars I'm curios if there is a way to test if this sample might be Martian andesite.

What type of oxygen isotope (or other) test can be done to address this in some way?

As background, any information about such tests at the University of Utah would also be helpful to know.

If this is something that you have found (rather than purchased as a meteorite) the chances are very small that it is a meteorite. Even if it is a meteorite, the chances it's a Martian one are even smaller still and none have been found in the United States.

According to the Meteorites in the US page, which draws from the Meteoritical Society database, only 1821 meteorites have been found in the US over the past 200 years. Of all meteorites found in the world, less than 0.1% are from the Moon or Mars (source statement, graphs of meteorite fractions) and none of these have been found in the US, with the vast majority (99%) found in Antarctica or the African or Arabian deserts (lunar meteorites)).

There is a long "Meteorite Realities" page and a shorter, graphical "Self-Test Check-List" that it would be good to check and go through before it gets to chemical testing.

If you are determined to get testing done, the same meteorites.wustl.edu site on its page on meteorite chemical composition recommends chemical testing by Actlabs; there is more information on what they need (a 5g sample) and the type of tests to ask for on this page. Andesite is a type of basalt formed by volcanism and while it is true that most of the Martian meteorites are basalts (as discussed here), so are a lot of Earth rocks. On the chemical composition page, in plots of chemical composition such as silicon dioxide (SiO$_2$) vs total iron and magnesium oxide content  e.g. the martian meteorites (red squares) separate from most terrestrial/Earth rocks and the "meteorwrongs" (white circles) due to having higher iron+magnesium content in the form of pyroxene, olivine and ilmenite (from 'Chemistry' section of How Do We Know That It’s a Rock from the Moon?) However as noted on the basalt page:

  Unfortunately, the only way to distinguish a terrestrial (Earth) basalt from a basaltic meteorite (Moon, Mars, asteroid) is with expensive chemical and mineralogical tests. If you find a basalt, it's probably not a meteorite.

So I would guess that these additional tests for the contents may be enough to distinguish a non-Earth basalt from an Earth one when the appearance to the eye or under a microscope is very similar (due to the similar formation mechanism via lava). However additional tests needed for trace elements may also be needed (Lunar basalts are Chromium-rich but have much lower concentrations of the alkali elements of potassium, sodium, rubidium, and cesium)

Chemical analysis for martian andesite for sio2 is 55.00 - 65.00, not anywhere close to korotevs out-dated charts. My number is sio2 59.32, the only number that brings up martian andesite when googled.
I witnessed the meteorite fall 11-15-2016.
Chemical analysis returns sio2 59.32 al203 16.62 fe203(t) 9.61 cao 1.32 mno .117 mgo 3.04 na2o 1.81 k20 5.78 tio .968
Oxygen isotope analysis results. From the ocean floor next to hydro thermal vent. 170( -0.033 1.5 mg o.o57. 1.4 mg.   0.061 1.8 mg
Can anyone help me on where I could get a noble gas analyzed or a microbe spit analysis on pyroxene?


Is there a stellar database that indicates how long ago stars in our Galaxy formed? There are several ways of determining the age of a star: its position in the HR diagram, the presence of a protoplanetary disk, it belonging to a cluster...

When did the stars in our Galaxy form? Do we know their age? Does there exists a database of stars for which we know the age, from which this average could be computed ? Is there a histogram of how long ago the stars in our Galaxy formed?

The amount of stars being formed as a function of time is shown for instance in Snaith et al 2014, but this doesn't directly translate into a histogram of the age of the stars currently in our galaxy, since the more massive ones that formed early on are gone.

There isn't really a database as you request. Finding the ages of stars is difficult. Only one star has an accurately known age - the Sun. That comes from radioisotope dating of meteorites. For other stars we must rely on models to a greater or lesser extent and we can only estimate an age if the star has a mass or is in a phase of its evolution where things are changing rapidly enough to give some handle on how old it is. For stars at the mass of the Sun or a little bit bigger, one can use evolution in the Hertzsprung-Russell diagram. Stars become more luminous as they burn through their core hydrogen and precise measurements can give an age to about $\pm 1$ Gyr. These are the data that Snaith et al. (2015) use in their paper.

So what Snaith et al. do is they attempt to constrain the star formation history of our Galaxy (or at least stars in the disk of our Galaxy) by making a Galactic Chemical Evolution model that predicts how the abundances of silicon and iron change with time and compare the results of their model with the observed silicon and iron abundances in this set of solar-type stars with reasonably well-estimated ages. Iron and silicon are used because they provide differing constraints. Iron is produced during the evolution of relatively low-mass ($1.5 - 4 M_{\odot}$) stars that live their long(ish) lives (1-10 Gyr), become white dwarfs and then some of the white dwarfs explode as type Ia supernovae. Silicon is produced by massive stars with short lives ($<0.1$ Gyr) and spread promptly into the interstellar medium by core-collape type II supernovae.

A representative lot from Snaith's paper is shown below. The star forming rate is shown in plot (a) and the match of the model to the observational data (they are trying to match the solid green points here) on chemical abundance is shown in the other plots.

They test a number of models and different assumptions, but it appears to be quite a robust result (found in other studies also) that there was a burst of star formation 10-12 billion years ago, a lull at 8-9 billion years ago and then a more constant, lower rate over the last 7 billion years. The very low rate in their model over the last 2 billion years is unlikely to be true and is probably an artefact of the age uncertainties in their data points (e.g. stars with age of $1 \pm 1$ billion years) and we certainly see plenty of star formation in the disk of the Galaxy today.

Contrary to what you say in your question this does (almost) represent the age distribution of stars in the Galaxy. That is because the vast majority of stars (90+%) are of a solar mass or lower. Such stars have main sequence life times of 11+ billion years, such that almost every one of them that was born is still a main sequence star now.

There will be a small reduction in the numbers of the oldest stars, because a small fraction of those ($<10$%) will have lived and died and also because a small fraction of the oldest stars may have escaped the Galaxy entirely (due to various kinematic processes that cause their orbital speeds to change). There is also an effect whereby if you take a volume close to the Sun, the oldest stars will be under-represented because they are distributed more broadly around the disc midplane for the same reason.

But by an large, the upper left plot in the picture is roughly what we expect the age distribution of stars to be in the Galactic disk.

There are a small population of very old stars ($12+$ bilion years), perhaps 1%, that are distributed more widely in the Galactic halo.

I don't know about stars in general, but for giant stars, the following histogram shows the age distribution of those in our Galaxy based on their location in the Galaxy.

This means that most stars are between 7 and 8 billion years old.


Why do we we even exist? It came to my mind one day that why does this universe even exist and why do we even exist and like we are enclosed in the so called atmosphere and a floating rock in space called the Earth, so is there any possibility that the universe is also enclosed in something and if it is, then what is outside that enclosure?

That's an interesting question, but as the comments say might be a better place to ask this question in the Philosophy SE site, but the question about the universe being englobed maybe by another much bigger 'space' is something we might never be able to prove right or wrong. This 'existential' question might refer to the holograph theory, the multiverse theory. The thing is, at the moment the only possible explanation of whats beyond the 'observable universe' boundary is nothing, neon, an infinite multi-dimensional plane of nothingness.


Why the Milky Way appears to be arching across the sky? The Milky Way galaxy is disc-shaped and earth is in its plane:
 (source)

In the following image the milky way appears to be arcing across the sky:
 (source)

This looks like an out of plane view of the milky way... How is it possible? Why an arch and not a thick straight line?

The Earth is a sphere (or is nearly a sphere). So to make a map of the whole Earth you would need to project it onto a flat surface. When you do this you create distortions. For example, on many maps, the straight line between New York and Japan looks like a long curve. It is not actually a curve, but when you stretch the surface of Earth to make it flat, some straight lines become curved.

The sky is also a sphere. If you ignore distance and just think of the direction of each point in the sky it would be a huge sphere that surrounds you. When we take a picture of the sky we must project that sphere onto a flat surface. That causes distortions, and it means that what is a straight line on the sphere of the sky is distorted by the projection into a curve.

If you choose a projection in which the milky way goes straight across the middle, you can see that the milky way goes straight across the sky.

The appearance of an "arch" is a distortion caused by stretching the image to fit on your flat screen. It is not real.

The appearance of an "arch" is a distortion caused by stretching the
  image to fit on your flat screen. It is not real.

I have seen a number of explanations of this that claim it is due to lens distortions or projections on the flat plane of the image/screen.  I don't think either one is correct.  If you are ever in a dark-enough place to actually see the MW with your own eyes, it looks like an arc any time the band is lower than 45 degrees or so above the horizon.  If you take an image of the MW at that point with a strictly rectilinear lens, mounted with nodal slide to conrtrol for paralax, and then stitch it together it will still look like an arc. Yes, the arc can be exaggerated by lens distortion, but that is not the primary reason the MW looks like an arc.

A number of apps that predict the position of the MW exist today, and they clearly show the COMPUTED position of the MW in the sky as an arch (see for example PhotoPills or Stellarium).  The appearance of an arch is due to the projection of the MW on the curved sky, not on "your flat screen".  The solid angle subtended by the MW is very small, and when you view it from a point on the Earth's surface that is substantially out of the projection plane it looks like a curve.  As pointed out above, when the MW projection plane directly intersects a large circle of the Earth AT THE POINT WHERE YOU ARE STANDING the band is directly overhead and it looks like a flat plane.

The closest analogy I can come up with is to think of a LARGE hoop.  Place your head in the center of the hoop and look at it edge-on.  It looks like a straigt line.  Now rotate the hoop slowly around an inplane axis  while maintaining your head in the center.  It starts to look like an arc.


Can a planet's changing tilt be aligned with the rotation around its star? What I'm asking is if the tilt of a planet can "follow" the rotation around its star so that, for example, its north pole would always lean towards the star, and thus always be under daylight. The planet could have a tilt similar to earth's 23.5°. And can that planet have a rotation around its axis, allowing for day/night cycles closer to the equator? Hopefully this image will explain what I mean. The tilt (red line) stays the same, but the pole is leaning toward the star throughout the whole year, while the planet rotates around its axis.

No, or at least not for a planet of any size. To change the absolute direction of the axis of rotation of a planet needs a large force acting in some way asymmetrically. In the case of the Earth this comes from the gravity of the sun and the moon acting on the Earth's equatorial bulge and it takes 26000 years to rotate the Earth's axis around a cone 46 degrees wide. To rotate the axis in a full circle (a cone 180 degrees wide) in a single year would only be imaginable for a very irregular planet (which means a small one, since big ones collapse into spheres under their own gravity) probably with a very large and close moon to pull on it.

Kinda. Uranus has an axial tilt of 98$^\circ$, which means that it is only 8$^\circ$ off of having a pole that faces exactly the Sun. However, it wasn't formed that way. We predict that large objects, probably protoplanets, struck Uranus early in its life, which caused its axial tilt to be shifted almost sideways. Uranus definitely has day night cycles (since the 8$^\circ$ give some leeway), but, just like the Earth has midnight days and polar nights close to the poles, Uranus will have the same, but with a much larger range. In fact, only the equator and places near the equator would be spared from this, just as you described.

However, the pole is not locked to face the star, so I guess the answer is no because of angular torque, there's more to this here.


What is the exact mass of the Sun? I am having trouble finding data on this. So far, I have found at least seven values:

1: 1.9885  e30 kg
2: 1.98855 e30 kg
3: 1.9891  e30 kg
4: 1.991   e30 kg
5: 1.989   e30 kg
6: 1.99    e30 kg
7: 2       e30 kg

The first value can be found from NASA GSFC.
The second value can be found from Wikipedia in (at least) two places.

The first Wikipedia occurence references the GSFC page--which is erroneous since that value does not occur there.
The second Wikipedia occurence references USNO's 2014 Astronomical Constants, which appear to themselves be copy-pasted from data in 2009 or 2012.  The second Wikipedia occurrence also sources NIST (presumably this table).  I couldn't find the cited mass from either reference.

The third (and also the fifth) value (which, it is interesting to note, are both outside the error bound given in the second Wikipedia occurrence) can be found on this generic NASA site.
The fourth value occurs in the book Handbook of Chemistry and Physics (Robert C. Weast, 1980)
The fifth value apparently also occurs in the book Astrophysical Data (Kenneth R. Lang, 1990ish).
The sixth value occurs in the book Physics--3rd Edition (Cutnell et al. 1995).  This site lists several of the values and does a calculation to obtain the sixth value.
Occurs in many places and is pretty clearly rounded.

The fifth, sixth, and seventh values (also) occur in various non-primary sources online, and I assume are rounded values of others.

My question: what is the most recent, best estimate, to the greatest precision, of the Sun's mass?  Obviously, citable, primary sources only!

The mass of the Sun is determined from Kepler's laws:

$$\frac{4\pi^2\times(1\,\mathrm{AU})^3}{G\times(1\,\mathrm{year})^2}$$

Each term in this component contributes to both the value of the solar mass and our uncertainty. First, we know to very good precision that the (sidereal) year is 365.256363004 days. We have also defined the astronomical unit (AU) to be 149597870700 m. Strictly speaking, the semi-major axis of the Earth's orbit is slightly different, but by very little in the grand scheme of things (see below).

At this point, we can solve for the product $GM$, known as the gravitational parameter, sometimes denoted $\mu$. For the Sun,
$$\mu_\odot=132712440018\pm9\,\mathrm{km}^3\cdot\mathrm{s}^{-2}$$

So solve for $M_\odot$, we need the gravitational constant $G$, which, as it turns out, is by far the largest contributor to the uncertainty in the solar mass. The current CODATA value is $6.67384\pm0.00080\times10^{-11}\,\mathrm{N\cdot m}^2\cdot\mathrm{kg}^{-2}$, which all combines to give
$$M_\odot=1.98855\pm0.00024\times10^{30}\,\mathrm{kg}$$
where my uncertainty is purely from the gravitational constant.

The value $1.9891\times10^{30}\,\mathrm{kg}$ (and nearby values) probably come from an older value of the gravitational constant of $6.672\times10^{-11}\,\mathrm{N\cdot m}^2\cdot\mathrm{kg}^{-2}$, which is still supported by some measurements of $G$.

The answer to your question is a very simple one but, a good one at that. The exact mass is 1.9891×1030 kg. Math and new advances in solar exploration have given us so much more information about our Sun. We have been able to see solar eruptions, (CMA's), and gained information about the Sun never known.


Bright pulsating light Was looking at the sky and I see a satellite , turned around and saw another light , but this light was pulsating like a strobe light , definitely not a plane , next thing I know the light goes out and was not seen again , could this be a dying star , I know what satellites and planes look like in the sky , but I have never seen anything like this , it just went dark after being super bright

This might be it:
Astronomers Say Giant Disco Ball in Space Is Bad for Science

Three foot diameter faceted mirror ball launched late January 2018.
I don't know either designation or orbit.


Can we see the color of nebulae? Someone asked me this question:

  To see the color of the Great Nebula in Orion, how large the aperture of the telescope should be.

I don’t even know whether this is possible. I understand that the colorful patterns of the nebulae are from the cameras. Besides, my own experience shows that when I target the telescope at them, I see nothing but some white blur.

So is this possible when we watch the deep sky objects with a really huge telescope, under the finest conditions?

Very large (for amateur) scopes in very dark places, with healthy eyes on a good night have credibly reported seeing color in nebula. The Orion is about as good as it gets,
lots of photons, my eyes are not particularly good, but have been out with others who claim noticing color in the Trapezium in a thirty-ish inch reflector

Yes, it is, and that is the reason why telescope has been getting larger and larger. You need a good telescope to be able to see a distant object bigger in an image. When the object is bigger in the image, the light will spread out following the real shape of the object, and instead of seeing a white blur spot you will see detailed colour. Think of a car approaching you from a far.

To be precise, what you need is a telescope with good "angular resolution," which is equivalent to the "aperture" size in this context.

So, if you know the physical size of an object and its distant, you can work on some math to estimate the minimum aperture that your object will be spatially resolved.

Check https://en.wikipedia.org/wiki/Angular_resolution.


How to compute the perihelion precession of Earth's orbit? I want to simulate the perihelion precession of Earth. I tried searching  other posts in stack exchange as well relating this question but may be it's my fault that I couldn't understand their answers. I read the history about mathematicians and physicists trying to find a good theory accounting the precession. I read that there are many planetary equation by Newton,Laplace,Hill,Poincare etc. But I am not sure which one gives the more accurate result. I am not even sure if I going on a right track searching the correct theory.
I'd really appreciate if anyone could help me with the theory which gives fast and more accurate result?

For simulation only, you should be able to show it by simple code as following:
$$
\vec{a}_t = - \frac{GM}{r_t^2} \hat{r} \\
\vec{v}_{t+1} = \vec{v}_t + \vec{a}_t \Delta t \\
\vec{r}_{t+1} = \vec{r}_t + \vec{v}_t \Delta t
$$
where $t$ is time step, $\vec{a}$ is acceleration, $\vec{v}$ is velocity, $\vec{r}$ is position, $\hat{r}$ is a unit vector in radial direction from the origin (set the Sun at the origin), $G$ is gravitational constant, $M$ is Sun mass in this case, and $\Delta t$ is size of time step. You will have to play around with the initial values and step size to get certain orbit representing the case. To make it more real, you derive the initial values from the real parameters, if known.


Why is the color of the moon so similar to the clouds? Why the moon looks like the cloud-structure on the blue sky among the clouds?

The Moon is a dark gray in color -- it reflects light poorly but uniformly. (Its color is about the same  as fresh asphalt!  It's albedo is about 12%)  Clouds are (usually) light gray with an albedo ranging from 10% to 90%.

Both the Moon and the clouds shine by reflected sunlight, so they're both the same color. (Clouds usually have a greater surface brightness owing to their lower albedo.)

Sry Guys ;) english is not my main language so maybe i mesed in question :) still  i think i found the answer , it serms  everything on a blue sky would look cloudish ? My main concern was why moon looks more cloudish than clouds moonish ;) but now i think its just the contecst ;)
Thx


What causes the antipodal bulge? The Wikipedia article on tides shows a diagram with a tidal bulge both towards the Moon and on the antipodal point (the Sun isn't included in the diagram). Surely that's wrong - what would cause the antipodal bulge?

Image courtesy of Wikipedia user Jhbdel under the Creative Commons Attribution-Share Alike 3.0 Unported license.

That is because the moon attracts both the water and the earth. The gravity of the moon reduces with distance (by the inverse square law). So, the moon's gravity is

Greatest at the point nearest to the moon (called sub-moon point)
Is lesser on the earth's center, and'
Is the least in the opposite side of the earth.

Assume that earth is falling to wards the moon. Now, as the force on the point near the moon is the maximum and it has 'fallen' the maximum distance, while the earth 'falls' a lesser distance and the farthest of all, the antipodal point 'falls the least'.

"Tidal-forces". Licensed under CC BY-SA 3.0 via Wikimedia Commons.

The above figure shows the forces acting on earth due to moon, The top figure shows the actual gravitational forces acting, while the bottom one shows the forces after subtracting the force on the earth itself. That should explain the antipodal bulge. See the wikipedia ariticle in Tidal forces

The bulges are caused by the fact that the earth's center is free falling  and the rest of the planet is not properly.  The vector force aplied by the Moon in a certain point minus the vector force aplied by the Moon on the Earth's center is not equal to zero. This difference causes the bulges. The Earth and Moon are orbiting the center of mass of the system. Consider someone in a box free falling. The person will not feel force acting. The diference between what the Moon's force on an Earth's point is and what the Moon's force on this same point should be is the cause of the bulges. When I said should be I meant that this point falls with the Earth but only the Earth's center of mass is free falling "correctly" with F =Mm/r^2


Expansion of the Universe Please forgive my ignorance. I dare say that these questions arise from me trying to understand the nature of the Universe using Newtonian physics. There are a few things that really bother me when topics such as red shift and expansion are discussed.

1) We can view a Galaxy that is 30bn light years away because the light we are seeing it as it was 13bn years ago, and at that time it was only 13bn light years away. So, it has travelled 17bn years further in the last 13bn years? Faster than the speed of light?

2) 13bn years ago, it was 13bn light years away. That is around the time of the big bang. How did it manage to get that far away so soon after the Universe began.

3) How is the known Universe even as big as 40bn light years, after only 13bn years in existence.

The current explanation is that "space" is continuously created in the intergalactic void, "pushing" the galaxies apart. From what i understood ( i am also ignorant ), the current rate at which "space" is created is expressed by the Hubble's constant 67.15 ± 1.2 km/s/Mpc ): for every million parsecs of distance from the observer, the rate of expansion increases by about 67 kilometers per second, which means that the distance between 2 points that are 1 megaparsec apart grows with 67km every second; between 2 points that are 2 megaparsecs apart with 134km/s, and so on so the relative speed between 2 points that are 5000 Mpc apart would be 335000 km/s which is more than the speed of light. In fact, two objects at this distance would not move, but 335000km worth of "extra space" would be "created" between them every second.

However in the last week there was an article depicting the shape of the universe, and it is hard for me to understand how it got to look like this : http://ifreepress.com/wp-content/uploads/2014/09/laniakea.png

http://en.wikipedia.org/wiki/Laniakea_Supercluster


Which star has the highest mass loss rate? We have known lists of stars with high luminosity, temperature, mass, size, and much more. However, I have not seen a list that compares each star's mass loss rates. So, which star (or stars) have the highest mass loss rates, and is it going to be more likely to be an LBV, RSG, or a WR star?

Some very hot and massive stars have strong stellar winds, known spectroscopically as "P Cygni profiles" after the type star. P Cygni 'erupted' in the 17th century to magnitude 3 and is now visible as a mag.5-6 star near the central star of the 'Northern Cross' that is Cygnus. An ordinary pair of binoculars will show it easily. So P Cygni stars have probably the highest mass-loss rate as I believe you are thinking of.

It is my impression that some sort of supernova is likely to be losing mass at the fastest rate for a short period of time.
@fasterthanlight responded to my comment and sugggested that supernovae be ignored.
And there are a few rules applying to stars which are not having supernova events at the moment.
Stars tend to go through several phases or stages  of development, and they tend to lose mass at different rates during different stages of development.  If two stars start out with identical mass and composition but at greatly different times, and go through identical paths of development, their phases of development will be different at any one time, and so one may be losing mass faster at one time, and the other may be losing mass faster at another time.
As a star increases in mass, and thus the density, pressure,  and temperature of its core, it requires more light pressure, produced by fusion, and thus more conversion of mass into energy and thus more mass loss, to prevent collapsing into a singularity.
So more massive stars fuse and convert into energy more mass per second compared to less massive stars.  Of course more massive stars have more nuclear fuel to fuse than less massive stars.  The math of the situation is that more massive stars burn off their fuel at a higher rate, relative to their total mass, than less massive stars as well as at a higher absolute rate.
So the more massive a star is, the more matter it will convert into energy each second both in absolute terms and as a proportion of its total mass.
Stars also lose mass by stellar wind, where charged subatomic particles in the atmospheres of stars flow outward from the star at great speeds. This varies a lot over the lifetime of a specific star, and varies a lot between various types of stars.
The Sun ejects more matter than normal during solar flares.  Many small class M stars have much larger flares in absolute terms, and even more in relative terms, than the Sun and are called flare stars.  So a flare star might eject less matter per second than the Sun most of the time, but eject more matter than the Sun during large flares.
Overall, as a rough guess, a super massive star at the upper mass limit for a star, and almost blowing itself apart, should lose more mass by conversion to energy per second while on the main sequence stage of its development than any other star on the main sequence.  And if its mass loss at various stages of stellar development is proportional, then when it is at the star where typical star loses mass most rapidly it might be losing mass more rapidity than any other type of star.
Such super massive stars have many times the minimum mass necessary to become supernova, and so they should all eventually lose mas rapidly as supernovae.
However, it is certainly possible that astrophysical calculations will show that some other type of star at another stage of development might lose mass more rapidly.
For example, binary stars vary greatly in the distances between the two stars.  Many orbit so closely that they almost touch.
If the two stars in a close binary have different masses, one will progress from stage to stage of development more rapidly and thus will swell up into a red giant star before the other one does.  And as the red giant expands wider and wider, its surface may expand beyond the point where the gravity of the other star is stronger than its own gravity.  Thus a lot of the material of the more massive star may leave it, and much of that matter may flow to the less massive star.
A star can lose mass very rapidly in such a situation.
So an astrophysicist should be able to select the type of star which loses mass at the fastest rate, and perhaps select the known example of such a star which is losing mass faster than any other star known at the present, although in many cases the data might be too uncertain.


Ramifications of black hole stellar system Recently, I got around to seeing the movie Interstellar. In it, the characters of the movie visit a stellar system that appears to be built around a black hole instead of a star. On top of this, their mission is to find a habitable planet in this system. Question: I was wondering how stable the system, as a whole, would be in terms of operation and would any of the planets be habitable at all due to the obvious differences between a star and a black hole.
In the movie the black hole is supposed to be a 'supermassive rotating black hole'. As for being a binary star system, it's never stated as such nor depicted as such. It's depicted visually as the black hole alone being the center. However one of the characters does mention a "Neutron Star" as part of the system so it could possibly be a binary star system. The ambient lighting for the planets is generated by the accretion disk of the black hole. The size and rotation speed of the event horizon are not defined in the movie. At least not that I can remember.
As for the planets, their proximity varies, with the first planet depicted as being so close to the event horizon that it is effected by time dilation. The distances of the other two are not specified directly, but traveling to the second planet out seemingly takes days, while traveling to the third planet out is stated to take months, if I remember correctly. As for their surface gravity, the first planet is depicted as having higher surface gravity than Earth but not so much higher that movement is impossible, just strained. The second planet is depicted as being '80% Earth's gravity', if memory serves me correctly.
To better help define certain variables relevant to the question I found an info-graphic related to the movie that illustrates the size of the black hole and it's rotational speed: http://tinyurl.com/pqph8wl

For those who haven't seen it:

Some human explorers land on a planet orbiting a black hole. The black hole is surrounded by a large accretion disk. The planet orbits at a distance such that going any closer to the black hole will mean that your odds of getting out are slim; it's also composed of water. Finally, time dilation from the black hole means that even though the characters spend about two hours on the planet, a decade or so passes for their colleague on board.

The basic answer is that a planet can orbit a black hole. There are stable circum-black-hole orbits, just as there are stable orbits around just about any celestial body. There's a problem: A black hole typically forms as a result of a supernova. This will eject most nearby planets out of the stellar system. Alternatively, it's unlikely that a planet could be captured by a black hole and be in a stable orbit, so the whole premise - while possible - is highly unlikely. Then again, it's improbable that a planet will be made out of water, a wormhole will open up near Jupiter, or Matthew McConaughey will star in a decent sci-fi movie, so why should anything else in the story be normal?

However, you can't just put a planet anywhere near a black hole, give it a strong enough push, and hope it orbits. The innermost orbit is at the boundary of the photon sphere. On this sphere, only photons can orbit. Inside it, nothing can orbit. However, the only stable orbit is twice as far away, at $2r_p$.
The radius of the sphere is
$$r_p=\frac{3GM}{c^2}$$
We'll assume that the object is not rotating (I don't remember exactly if it is or isn't rotating, but it's simpler in this demo to say it isn't.). The formula for gravitational time dilation is
$$t_0=t_f \sqrt{1-\frac{3r_0}{2r_f}}$$
where
$$r_0=\frac{2GM}{c^2}$$
Assuming that $t_0$ (the time for the observer inside the field) is two hours (7200 seconds) and $t_f$ is ten years (315360000 seconds),
$$\frac{t_0}{t_f}=\frac{1}{43800}=1-\frac{(3)2GM}{(2)r_fc^2}$$
Simplifying, and saying that $\frac{2GM}{c^2}=\frac{2}{3}r_p$,
$$\frac{r_p}{r_f}=\frac{43799}{43800}$$
$$r_f \approx 1.0000228315715 r_p$$
which is outside the photon sphere, but just barely. However, it's well inside $2r_p$, and so most likely instable. The planet is, in short, not going to survive for long. And so giant waves - mini-spoiler - are the least of Matthew McConaughey's problems.

Post-question-edit modifications:
It couldn't have been a supermassive black hole; these form at the center of galaxies. It could have been a stellar-mass black hole, though an intermediate-mass black hole is also likely - if not likelier, if the massiveness is emphasized.
The existence of the neutron star is interesting. If the black hole were intermediate-mass, I would expect that it would have gobbled up the neutron star by now - and the planets, too. So I'd bet the black hole is a slightly-more-massive-than-average stellar-mass black hole. I highly doubt that multiple planets could orbit a black hole - for the reason I gave above; the supernova would have destroyed them or flung them out of the system.
Would any of the planets be habitable? I doubt it. The accretion disk could heat up enough to provide some light, but there probably wouldn't be a lot. I'll write up the calculations either later today or possibly tomorrow, as I'm a bit LaTeXed-out after writing a math-heavy answer on Worldbuilding to find the luminosity, but I suspect it'll be negligible - as will Hawking radiation, in case any smart-aleck was planning on bringing that up.

If you are orbiting a 1-sun-mass black hole at 1 AU, gravity-wise it would be just like it is for us orbiting the sun.  Gravity is gravity and mass is mass.  The planets would have to have been captured after formation of the black hole or moved in from distant orbits.  However, the accretion disk would be likely to be emitting lots of X-rays and not anywhere near enough visible light, so life on that planet would be pretty grim.


Explosions of black holes I was bopping around YouTube and observed this enjoyably produced video. In it, when describing the behavior of a black hole with the mass of a US nickel, the narrator says, "Its 5 grams of mass will be converted to 450 terajoules of energy, which will lead to an explosion roughly three times bigger than the bombs dropped on Hiroshima and Nagasaki combined."

Of all the fun things illustrated there, that was the one whose pretense I didn't understand. Do black holes explode after they've radiated away all of their mass? Or would the "explosion" just come from the rapid pace at which the black hole would consume nearby matter?

The Googling I've done thus far has provided no firm answer. The closest I've come is from the Wikipedia page on Hawking Radiation, which states, "For a black hole of one solar mass, we get an evaporation time of 2.098 × 10^67 years—much longer than the current age of the universe at 13.799 ± 0.021 x 10^9 years. But for a black hole of 10^11 kg, the evaporation time is 2.667 billion years. This is why some astronomers are searching for signs of exploding primordial black holes."

Some other websites refer to the last "explosion" of the Milky Way's supermassive black hole being some 2 million years ago, but is that the same mechanic mentioned on the Wikipedia page? Or the YouTube video, for that matter?

Thanks in advance. =)

What this video is talking about is Hawking Radiation, as you've linked. Hawking Radiation is a proposed hypothetical (by no means verified or proven) way for a black hole to radiate its energy into space. The basic idea is that a black hole is nothing but mass/energy compressed to an infinitesimal point, which is radiating its energy into space over time. For large black holes (such as solar mass or bigger), this radiation process is tiny and the time taken to leak all the black hole's energy into space (and thus for the black hole to "evaporate") is exceedingly long. For tiny black holes however, the time to radiate all the black hole's energy is exceedingly short.

You can calculate how long it will take for a black hole of mass $m$ to evaporate (and release all its mass/energy) with the equation

$$t_{\text{ev}} = \frac{5120\pi G^2 m^3}{\hbar c^4} = (8.41\times 10^{-17}\:\mathrm{s}\:\mathrm{kg}^{-3})\:m^3$$

For $m = 5\:\mathrm{g}=0.005\:\mathrm{kg}$, you get $t_{\text{ev}} \simeq 4\times10^{-19}\:\mathrm{s}$. Now that means in this tiny amount of time, the black hole will radiate all of its mass/energy away and completely evaporate. But the output of all the energy in 5 g of mass is a huge output. Putting out 450 Terajoules of energy in $10^{-19}\:\mathrm{s}$ is basically just an explosion. You can determine the total energy output from the famous equation

$$E=mc^2$$

Just plug in $m = 0.005\:\mathrm{kg}$ and $c = 3\times 10^8\:\mathrm{m/s}$ and you'll get $E=4.5\times 10^{14}\:\mathrm{J} = 450\:\mathrm{Terajoules}$.

So in short, hypothetical calculations (not even theory at this point) suggest that a tiny black hole with the mass of a nickel would immediately explode out in a huge amount of energy. Whether such a black hole can form, or if such an evaporation would/could occur is still highly debated and ultimately unknown at this point.

No black hole can explode, no matter the size.  It can radiate energy outside its event horizon, but a proper "explosion" of energy from the black hole itself would have to exceed the speed of light, which is not currently possible.

Also, if an object has the mass of a nickel, it is not a black hole.  More specifically, its event horizon is small enough to fit inside its own surface area which is true for all massive objects that are not black holes.  In fact, the event horizon of something with the mass of a nickel is literally immeasurably small (although NOT non-existent).  Nickels (and other objects of similar mass) do not have enough gravity to form a black hole.  I suspect perhaps you are confusing "mass" with "size"...?

However, if a process existed that could turn the mass of a nickel into the energy it embodies (per E=mc^2), then yes, it would be a tremendous amount of energy.  The only such process known to exist would be to have an object with half the mass of a nickel interact (touch) an antimatter-object with half the mass of a nickel.  The combined mass of the 2 objects would total the mass of the nickel, and would release the appropriate amount of pure energy with no mass leftover.


Is there any difference between parallel universes and multiverse? Nowadays we come across with these two terms - parallel universes and multiverse. I wonder if this is the same thing or its two entirely different principles because the names are a bit confusing to me. Can anybody please shed some light on this?

I'd like to see the notion "parallel universe" restricted to universes similar to each other in some sense. This applies best to the many-worlds interpretation of quantum theory. Two universes in this sense can be almost identical, just different in a couple of quantum states.

Two such parallel universes could be interpreted (in the simplest case) as two elements of a Hilbert space. A Hilbert space defines a metric as a measure of distance between two elements (here applied to universes).
This may be seen in some analogy to points (universes as analog) in an Euclidean plane (many-worlds multiverse as analog). Here the notion "parallel" can make some sense. At least, it's possible to compare the items in some way (by the distance between two points/universes).

Talking of universes as parallel in the very general case of items in a multiverse, when there is no similarity at all between these items, would be a bit too lax in my eyes.

In my own mind the multiverse could consist of either multiple universes occupying the same "space" (as in different dimensions) and/or different areas of space where what we consider to be our own universe is only one "bubble", outside of which are an infinite number of other bubbles, possibly created by their own Big Bangs.

The first variant above is what I would refer to as parallel universes, i.e. not the "bubbles". Or to put it another way, The different universe instances in the multiverse could be parallel.

Note that my understanding of current hypothesis and theories in this area is very limited. These are just my own thoughts.


Is ours the first universe? I see here that after a very long time into the future, "Estimated time for random quantum fluctuations to generate a new Big Bang".

This begs the question, do we speculate that our big bang was the first?  Or are we one of many in a never ending chain?  Or do I miss the point entirely (being ignorant in the subject)?

It is very hard to tell whether we are in a unique Universe. The difficulty is the closer we attempt to probe in the fractions of a nano second after the Big Bang our current forumlations of Gravity and the three our fundamental forces do not work. So it is very hard to tell whether our Universe is unique.

However, with all that said, my own personal belief is that our Universe is not unique. The estimated time for random quantum fluctuations to generate a new Big Bang as quoted in the page that you have referred to is an UNIMAGINELY large time scale.

My question I will pose back to you is, how could we ever tell we are a unique Universe, or part of a collection of Universes?

With regards to first Universe I must say that it is first in many ways from within the Universe and within our own perspectives. I will try to stay close to the idea of first because you are unique. In the whole Universe there cannot be an exact, (exact containing the same molecules atoms and energy), copy of you out in this Universe so you, the rest of us and the planet are unique. Extrapolating from this, an argument could be made for the Universe being uniquely the first based on many assumptions but the crucial fact is, with the arrow of time the way it is, we are able to formulate such questions within our minds. Having an answer to such a question may not be as important as the question itself. Going forward the true realization maybe understanding how far our minds may reach. Since this question speaks of first it really is a temporal one and the passage of time can be understood as the progression of events in only one way. The singularity at the beginning would be where there is only that event {with no events?). Be that as it may we are living in side the result of that singularity at this event and as far as we can understand it is singular.


Does a parabolic trajectory really exist in nature? It seems it is very difficult to have e=1 perfectly in nature. The final state (being captured or running away) of a celestial body with a parabolic trajectory,
is determined by minor perturbation?

No, but nor do elliptical or hyperbolic trajectories.  These are features of a model we have for gravity, not part of nature.
The modelling process involves constructing a mathematical framework that describes a natural system and allows for predictions. It is often said that "no models are correct, but some models are useful".  For gravity, one common model is the Newtonian model.  In the Newtonian model, you can set up two particles in such a way that one follows a parabolic curve (in some inertial frame) Parabolic trajectories exist in the Newtonian model.
In nature, there are more than two particles in the universe and so there are no parabolic, elliptical nor hyperbolic trajectories.  Moreover, the Newtonian model is known to only approximate gravity (even General Relativity is probably an approximation, gravity is probably some kind of quantum interaction. But the details are not yet known)
Nevertheless.  The Newtonian model is a very useful model for solar system dynamics.  Long-period comets, falling from the distant Oort cloud, will have orbits that are very long and are well approximated by parabolas. (but only approximated, as comets, in particular, have significant non-gravitational accelerations due to reaction forces from outgassing, in addition to gravitational perturbations of the planets, and effects from the non-spherical shape of the sun)

Sure. Go to the moon, and throw a rock.
When you're on a planet with no atmosphere, like the Moon, gravity can be considered as a field oriented in a constant direction, straight down, and its force is a effectively constant value in a constant direction. When this occurs, and there is no atmosphere to cause wind resistance, then the trajectory of an object thrown into space and experiencing no other forces will be parabolic in shape as it goes up and then comes back down, as long as its initial speed doesn't exceed the escape velocity of the planet, and it doesn't travel enough distance (vertically or horizontally) for the force of gravity to notably change.


How did the authors of Surya Siddhanta find the diameters of other planets in the solar system? The Surya Siddhanta, "a Sanskrit treatise in Indian astronomy from the late 4th-century or early 5th-century CE" is truly a great work.

But how was it possible for the writers to find the exact values of the diameters of different planets and the distance between the sun and the earth?

Also, are there any mistakes in this book?

If there's any problem in my question please inform me.

The authors assume a geocentric universe (first thing that is wrong). They then assume that the planet Mars has the same apparent diameter as a globe 30 yojana in diameter (about 150 miles) in the same orbit as the moon, from a perspective at the centre of the Earth. This is just stated, and appears to be supposition. It is an incorrect figure. It is conceivable that some kind of system for sighting through a pinhole could be used for this estimate. This method tends to over estimate the apparent size of planets.
They next claim that the other planets have apparent sizes that would be the same as globes with diameter 37.5 (Saturn), 45 (Mercury) 52.5 (Jupiter) and 60 yojana (Venus). These form an arithmetic sequence with a common difference of 7.5, but apart from that, these values seem to be arbitrary (and are wrong). They might have been based on some kind of pinhole observations, but rounded to a simple sequence for the sake of the poetry or for easier memorisation.
There is uncertainty about the ancient value of the yojana. A different conversion to miles will give different values throughout.
Using this assumption and the distance already calculated to the moon they calculate the apparent angular diameter of each planet. The actual values they get are wrong, In fact, the angular diameter varies as the planet's distance varies.

Planet
calculated value
modern observed value

Mars
2 arcmin
(actually 0.06 - 0.39)

Saturn
2.5 arcmin
(0.25 - 0.34)

Mercury
3 arcmin
(0.08 - 0.17)

Jupiter
3.5 arcmin
(0.51 - 0.83)

Venus
4 arcmin
(0.16 - 1.05)

As you see the calculated values are much too large (ie wrong). They are comparable with values supposed to have been found by Hipparchus, but without a known observational basis. Tycho Brahe also gave similar values, found by sighting through a pinhole. This simple method doesn't give a good estimate of the angular size. The simple pattern in the calculated values is due to the original assumption that the globes were in an arithmetic sequence.
There is then a calculation of the geocentric orbital radii of the planets. They assume that Venus, Mercury and the Sun all orbit at a distance of 3.4 million miles.  This is a significant underestimate, especially for the sun (this is wrong). The distances to Mars, Jupiter and Saturn were also underestimated.
One can then combine the apparent angular diameter (which is too large) with the calculated distance (which was too small) to obtain an estimate of the planetary diameter. When this is done, it gives exceedingly good estimates of the diameter of Mercury and Saturn (within 1%). A good estimate for the diameter of Mars (about 10% out), and a poor estimate for Venus and Jupiter (about 50% of the accepted modern values).
It is clear that there is much that is wrong. A combination of overestimates of some values and underestimates of others cancels out to give some impressive looking figures for two out of five planets. But do note that the estimates for Jupiter and Venus were a long way out, and all the numbers which the calculations were based on were wrong. In total there are 15 values calcuated here 5 apparent diameters, 5 geocentric distances and 5 actual diameters. Of these only 2 values are impressively accurate.
They did better than other pre-telescopic observers, but it isn't clear that they obtained values by anything other than luck.
Source

First of all I would like to clear some misconceptions about the date of compilation of Surya Siddhanta SS.
As per recent findings, SS was initially composed around 12595 BCE. Like many other Hindu books on Religion Astronomy etc., it was not composed in one go. Findings have also suggested that there are updates to longitudes of Asterim's 28 junction stars around 7500 BCE, update introducing a limited number of Rsines values and of value of pi = sqrt (10) around 2528 BCE, another update to latitude values of junction stars around 590 AD.
The diameters of various planets are stated to be calculable as per Sutra 13 and 14 of chapter 7 of SS. Actual values have not been calculated. These were calculated later by various scholars, Indian as well as Foreign and found very large in comparison with the modern values. Needless to say that that the observations were made with naked eyes, and therefore grossly incorrect values was found. Quoting from Rev. Burgess's translation of SS.
"This table shows how greatly exaggerated are wont to be any determinations of the magnitude of the planetary orbs made by the unassisted eye alone. This effect is due to the well-known phenomenon of the irradiation, which increases the apparent size of a brilliant body when seen at some distance."

Various distances are given in Yojana, a unit of distance used then. In Hindu traditions there are 2 different definitions of Yojana. Obviously they did not have any Standards Laboratory where a standard unit would be kept for reference. One of the definition gives reasonable correct distance of sun and moon from earth whereas the other unit does not. We do not know, for certain, which unit was used by the author(s) that the time of composition/update of SS.

There are no mistakes in the book, per se. In the book there are statements and formulae for calculating various required quantities, but no explanations.
If at all some are there, these could be due to various reasons, like
(a) Original manuscript was mutilated and restored later on the basis of practices being followed.
(b) Not being able to comprehend what the author stated at the time of composition. One example of this being the interpreted period of precessional motion of Earth's axis to be 7200 years. Although there exists internal evidence in SS to support a value of 24000 years.

It is worth mentioning here that astronomical observations made in SS, or Hindu Astronomy, are sidereal and not tropical. Therefore, observations are not only firm but are also independent of Geocentric or Heliocentric model of solar system.
Hope this answers.
Source
Source 2


Does the event horizon of a black hole increase or decrease by adding mass? So a black hole is a something that has enormous gravity, therefore mass accelerates faster towards it. But if the black hole double  it's mass, will it's event horizon increase in length , or will it decrease?

The radius of the event horizon ($r_\mathrm{s}$) is directly proportional to the mass of the black hole (M). More exactly:

$$r_\mathrm{s} = \frac{2 G M}{c^2}$$

The black holes whose merger was detected by LIGO would each have been about 90 km in radius, and after merger, a little less than 180km.

Read about the Schwarzchild radius

particle and anti-particle pair - basically it has a particle that is attracted to the black hole and one that is repelled by it. Since these particles contain mass, the particle that is repelled is left as radiation, and the one that is attracted is added mass, and by adding this mass it will decrease the total density, since it isn't just an addition problem, there is lost mass increase that makes the density and the mass of the black hole a inverse relationship. This states that the more mass the less dense which means that is will shrink and decrease in length.


Can an Earth-like planet survive if our Sun went Supernova? First, I would like to point out, yes, our sun does not have enough mass to be a candidate for Supernova, this is a scenario were our sun is though, and after the various life cycle stages of the sun and whether or not life managed to survive or not on the planet, The Sun goes of as a Supernova, it is 1 AU from an Earth-like planet, or equivalent to 1 AU from a massive star, would the planet still be standing or would it be obliterated from the face of the Galaxy?

Here are some of the links that I have been looking through but could not find an answer for:

https://www.physicsforums.com/threads/effective-destructive-range-of-supernovae.312925/
https://earthsky.org/astronomy-essentials/supernove-distance
https://www.popularmechanics.com/space/deep-space/a26483/supernovas-deadly-twice-as-far-away/

One way of estimating this is to look at how much energy could be received by the planet. At distance $d$ it takes up $r^2/4 d^2$ of the sky as seen by the supernova. So for a $10^{44}$ J blast that is about  $4.5444\times 10^{34}$ J.

The gravitational binding energy of Earth is about $2\times 10^{32}$ J. So we have about 227 times as much energy as is needed to separate all pieces of the planet to infinity. It is also a few thousand times the energy needed to heat up an Earth-mass of iron from 0K to vaporisation. So, yes, it looks like it could well obliterate the planet.

Whether it actually does so is a complex question of how protected the evaporating planet is by its plasma sheath during the explosion. Given that actual terrestrial exoplanets in close orbits at 2000K may lose an Earth mass per gigayear it looks plausible that at least slower scenarios can vaporise planets.

If the sun were a much larger and more massive star of the kind that supernovae are made of, the Earth at 1AU would be in pretty poor shape anyway, a scorched cinder. Life would never even get started, never mind survive. In the supernova explosion the surface of the Earth would be blasted away and whatever was left propelled at great speed out of the solar system, and pretty much obliterated from the galaxy. The actual fate of the Earth is more interesting, as it is really going to happen in about 5 billion years time. When the sun becomes a red giant, the Earth will be scorched to a cinder and all life on Earth will cease. After expelling some mass, the sun will finally become a white dwarf about the size of Earth.


How long was a lunar month in ancient times? As the Moon is getting farther and farther from Earth, it's natural that the time it takes to circle around our planet is going to increase, thus the month will be longer.
However, I read that the reason it's straying from us also is causing the Earth to revolve more slowly. As the day is getting longer, maybe a lunar month will remain more or less the same?
Fast rewind it back to billions of years ago, did that hold true too? How many 'days' did it take for the Moon to go around the Earth, say, 4bya? Are there any formulae to calculate this?
I'd appreciate more the answers that consider both the day length of specific ancient times and its conversion to modern day, for easy imagination. Any sources that list several values for different periods in the past would be great, too.

'Day' is the worst possible unit to measure the revolution of the Moon around Earth as it is the temporal unit which is directly influenced by the tidal friction and deceleration. We can reasonably assume that the length of the year is not impacted by lunar tides and subject to much less variation.
This is only a partial answer as I will have to leave the math to get an actual number for time reasons.
The only measurable quantity for the past is the length-of-day of Earth and the tidal rythm by means of their impact on biorythms and in turn its impact on sediment stratigraphy and growth markers e.g. in fossil shells and similar.
One summary with some values and further references on how the past rotation can be estimated is this paper by Deines & Williams. If you know the length-of-day at a time, you can calculate the yearly angular deceleration of Earth. That knowledge can be employed, using the conservation of angular momentum and calculate the orbit of the moon and thus length of month (thus one full orbit around Earth).


Moon's revolution around the Earth and it's rotation around it's axis? Does Moon rotate around itself while it makes one revolution around Earth or not?

Yes. Exactly once. This is how we get the light and dark side of the moon. The reason for it being exactly once is due to something called tidal forces. Wikipedia explains this quite well: https://en.wikipedia.org/wiki/Tidal_locking.


What is our universe expanding into? From inflation theory and other theories explaining the birth of the universe, the universe is expanding and recently it's been discovered that the expansion has been accelerating. My question is simple, what is happening on the boundary of our inflating universe and what is that 'space' that is experiencing that boundary?

It's a rather difficult concept to grab but, in short, the image of expansion you have in your mind is wrong. It's not your fault, it's everywhere out there, the inflatable balloon etc. And it's terrible :)

Another way to look at it is that the universe properties are changing. Whether it is infinite or finite, its size (as measured within itself) changes. Things are pulled appart. You could imagine that free vacuum keeps being generated between all objects but that would be a misrepresentation of the theory.

The most simple way I see it is actually what the equations say. It's lame but sometimes the math are the simplest way to understand a phenomenon. The equation say the metric is expanding. It means two point in the fabric of the universe are measured at increasing distances over time. As a result, unless objects are pulled to each other with sufficient force, they tend to drift appart. It's a property of the universe that has not been explained yet (at least not completely), and we still are on the fence as to what influences the expansion rate.

Ultimately, this concept is very easy to accept when you cease to represent the universe from outside of itself. The universe is everything that is so if any image in your mind represents the universe from outside, it won't give you a good picture. Balloons are especially bad :). If you need an image, draw a grid or take a notebook, draw some points here and there on it and imagine the grid keeps getting bigger and bigger. But don't look at the whole page, forget the page limits, focus on the grid. And keep in mind that the points do not expand, only the grid does...

Most of the Astronomers and the community of Astrophysics, will agree that the fate of planet earth is "The Big rip, most comparable to The Big Bang;but polar opposites.Where the universe is expanding to it's breaking point, total expansion of the know universe.


How do I prevent or reduce shake when observing with binoculars? I have some 16 x 50 binoculars that my parents bought me years ago. Recently I have tried to do some basic lunar and planetary observations with them but I am seriously struggling with shaking. This was most noticeable tonight while attempting to observe the ISS.

While I accept that keeping the image of a moving target stable is going to be next to impossible, I would like to know how I could reduce my shaking while observing the moon and other objects.

Is anyone able to provide some simple techniques to reduce shaking?

Don't hold the binoculars in your hands. Humans are made of meat. wobbly wobbly meat. There's apparently devices that let you mount binoculars on tripods - (this google search would be a start). Those and a tripod would probably be helpful in decreasing shake.

I suppose it would affect mobility a little but that's a tradeoff.

Helmet mounted binoculars is best, but if all you had was your binoculars kneeling is better then standing and prone position is best.


Shape of neutron stars I've heard that the more an object spins, the less of a true sphere it is.
Using this logic most of neutron stars would be far from spherical,in general what shape are most neutron stars?

I don't think you'll find a single agreed shape for a rotating neutron star, not least because we don't have an agreed single model for the equation of state of the material in a neutron star (which is more complex than the name suggests).

I found one openly available paper (I'm sure there are more) which will give you a rough flavor for the complexity of modeling the shape of neutron stars.  As you'll see the difficulty of no single model for an equation of state (EOS is the shorthand typically used) is just one issue.

I think "ellipsoid" should be considered as an approximation, although it's not something I'd consider written in stone.

Remember that to be useful a paper has to provide not just a model for what the shape might be, but also someone has to provide a way to measure this, which is challenging.  I think one of the hopes for the new era of gravitational wave astronomy is to be able (eventually) to make more useful and measurements that help us investigate the interior of neutron stars.

So this is an open question, I think.

@Rob-Jeffries asked a question in comment about typical numbers for the deformation, and I answered in comment but comments can be removed by the system, so I'm adding that information as an edit :

In the first section of the paper I linked to they do quote fractional deformations as being typically $10^{−5}$, perhaps $10^{−4}$ in special cases and in extreme cases up to $10^{−3}$. However another paper gives an analysis based on crustal rigidity and a very small deformation for a particular neutron star. The paper I initially liked to describes an upper limit based on gravitational wave considerations, I think, rather than a general analysis.

Logically speaking, they should be spherical as things with higher gravity tend to collapse into spheres.  Neutron stars are extremely dense, and have high gravity.  However, they are as far as we know rotating extremely fast as well (e.g. Pulsars).  It should be that the faster they rotate, the more disc-like they would become (like an ellipse or slight possibility of more of a disc in extreme cases).  So, depending on rotation speed, sphere for no to fairly high rotation speed, ellipse for high rotation speed, or possibly even a disc for extremely high rotation speed.  There is room for debate here, but this is how I logically see it.

Edit: By ellipse, I mean a 3 dimensional ellipse, like an egg, but "squished the other way".  Basically a sphere that has been stretched out on its equator.  The faster it spins, the more it should be deformed (stretched along the equator).  Dantopia's answer shows the shape I am describing.


If our galaxy is mostly empty space then why does it look so solid? This question has probably been asked quite a few times, but I'm having trouble finding anything due to the fact that this question is very specific in nature. So I'm asking again.
We know that outer space is mostly empty and stars are very far apart from each other. So much so that when two galaxies collide, the stars within them will just fly past each other instead of crashing. But when I look at pictures of the Milky Way, (some of them are real pictures of the center of the Milky Way taken from earth, while others are renderings) it looks so bright and so solid, like theres so much stuff in there. It becomes hard to believe how it can be that it's mostly empty.
Can anyone please explain what's going in there?
Thanks.

You are mostly empty space.  Every atom in your body is very tiny compared to the relatively vast spaces between it and its nearest neighbors.  And the same goes for every "solid" object you ever saw.
But when you look at yourself in a mirror, the number of atoms you see is so incredibly vast that you don't see the spaces between them but instead think that yhour body is a solid object.
And probably the wavelengths of visible light are too long to fit between atoms and so get bounced back from the surface of your body.
That is not the case with the galaxy, since the spaces between stars in the galaxy are wide enough for all wavelengths of light to pass through instead of being reflected.
But if you look at our galaxy from a distance of about one million light years, the average separation between stars of about 6 light years will be a very small angle.  I believe that at one million light years distance, one arc second will be about 4.848 light years wide.

The maximum angular resolution of the human eye is 28 arc seconds or 0.47 arc minutes,[19] this gives an angular resolution of 0.008 degrees, and at a distance of 1 km corresponds to 136 mm. This is equal to 0.94 arc minutes per line pair (one white and one black line), or 0.016 degrees. For a pixel pair (one white and one black pixel) this gives a pixel density of 128 pixels per degree (PPD).

https://en.wikipedia.org/wiki/Visual_acuity#Physiology[1]
So at a distance of one million light years the smallest detail a human could see would be 28 arc seconds, or 135.7 light years wide.  So such a smallest possible thing you could see would be a square about 136 by 136 light years wide, and possibly containing about 350 stars in a single layer and all the vast interstellar spaces between them.
Furthermore, galaxies are not a single layer deep.  Depending on the size of a galaxy, the distribution of stars within it, and the angle from which it is viewed, a viewer might see  tens, hundreds, or thousands of layers of stars one behind the other.  The stars are not arranged in any sort of regular lattice pattern, but orbit around the center of the galaxy in separate orbits and their relative positions slowly change, thus making their relative positions random.
Thus the empty spaces between stars in the outermost layer of a galaxy will show the light of stars farther behnd them.
So when you look at galaxy from a distance of one million light years, the smallest part of the galaxy you can see will have the light of hundreds or probably thousands of stars blended together with the black space between them to make a pale grayish light.
The farthest objects which humans can see with the unaided eye are the Andomeda Galaxy M31 about 2,540,000 light years from Earth, and the Triangulum Galaxy M33 about 3,200,000 light years from Earth.  Since they are several times a million light years away, the smallest part of them which can be seen with the unaided eye will combine the light of even more thousands of stars together.
Astronomers have photographed galaxies tens of millions, hundreds of millions, billions, and tens of billions of light years distant.  With astronomical telescopes they can detect some individual stars in galaxies tens of millions of light years away.
But any photograph which shows an entire galaxy will show the light of millions or billions of stars blurred together into a blob of light.

First, you are correct that galaxies are mostly empty space, at least in terms of stars.  The Milky Way may have as many as 400 billion stars while Andromeda has roughly two and a half times that number.  For the Milky Way that comes out to roughly one star every four light years, on average.
Viewed from a distance, however, those stars are extremely bright against a dark background.  Four hundred million of anything in a 6x10 glossy are going to look like a clump.
But galaxies are more than stars; there is also a tremendous amount of gas and dust, with a scattering of larger bits of rock. Some of the light from those stars interacts with that gas and dust, sometimes reflecting and other times absorbing and re-emitting.  This scatters the light in much the same way a lampshade scatters light from a bulb.  It appears as though the lampshade is a solid mass of something, but it is, in fact, an illusion, if you will, caused by the scattering or diffusing of a much smaller, central light.  You may have seen very large balloons lit from a relatively small light; the entirety of the balloon appears to glow.

This balloon is lit by one small LED.  Remember, though, that it is gas and dust rather than any sort of membrane which is diffusing light in galaxies, and that the dust and gas can be lit by any number of stars.  So, the combination of extreme distance, huge numbers of stars and the diffusion from dust and gas, in contrast to the darkness of space surrounding the galaxies, is essentially the effect we are observing and gives galaxies their "solid" appearance.