Strange speck of light in the picture sequence of the approach to 2014 Mu69 (Ultima Thule) In the picture sequence which was taken by New Horizons during the approach to Ultima Thule on the 3rd of Dec there can be seen a speck of light in the lower left corner, not as bright as 2014 MU69 but clearly visible.

Source: Here (German) or here (English), NASA / Johns Hopkins Applied Physics Laboratory / Southwest Research Laboratory / Henry Throop

Is there any theory what may have caused this signal? A particle from the probe itself, coincidentally passing in front of the lens? A variable star? A small object in the right distance and angle to be glimpsed upon by New Horizons? I think the latter would be an astronomically improbable event...

Here are some single frames of that image sequence, the speck is clearly visible on the 3rd of December.

It's probably a cosmic ray strike, a common artifact on New Horizons images.  The image, however, is of very poor quality which makes it difficult to analyse the exact nature of the spot.  I'll go into this more  at the end of the answer.
Possibilities:

Cosmic ray hit
A common occurance (see below); the most likely cause without evidence to the contrary.

Background star (e.g. a nova)
Novæ (and variable stars) brighten and dim over several days.  Were this a nova it would have shown in images from previous and later days.

Kuiper belt object
To not show in images from adjacent days it would need large relative motion and thus a sizable trail would be expected (none is evident).

Aliens
Possible?  Yes.  Likely?  Far, far, from it.  Not worth serious consideration.

Here's the New Horizons team's standard disclaimer:

This image contains one or more objects whose brightness exceeds the detector's saturation level. This sometimes produces a "tail" of bright and/or dark pixels to the right of the object. You may also notice a faint vertical white stripe passing through the saturated object; this is an artifact called "frame transfer smear" and is associated with the incomplete removal of signal produced when the image is transferred from the optically active region of the detector to the storage region of the detector. If the target is badly saturated, you may also notice a faint, X-shaped feature nearly centered on the object; these are optical diffraction spikes.
This image contains one or more streaks associated with cosmic rays passing through the detector. Nearly every LORRI image has at least one cosmic ray strike, but most are "single pixel" events (i.e., they only appear to be in single pixel and can easily be mistaken for stars). But sometimes a cosmic ray is energetic enough that it leaves a "trail" as it passes through the LORRI detector.

Example of cosmic ray hit and saturation trails:

Source: here (via "Learn more..." link), NASA/JHUAPL/SwRI
Note that despite being a PNG, JPEG compression artifacts can be seen in this image
The frame in question:

Source: Frame K-29 of this image taken from here, NASA/JHUAPL/SwRI/Henry Throop
Enlargement below is from frame K-29 of this image
The image in question is almost certainly a stacked composite of ~10 source images and appears to have been 2×2 binned (compare here).  To make faint objects more visible, the image was also likely contrast-enhanced.  The image also shows clear signs of lossy compression and quantization (from 12 bits per pixel to ~5), see enlargement below.  While these are (mostly) acceptable choices for the image's intended use it tends to obscure detail from the original images.
Crop showing artifacts:

Looking at the spot in question (enlargement below) a couple of things are noticable:
It is compact and relatively dim.  Its overall size in pixels is about half that of the stars and of MU69.  In addition, the drop-off in brightness moving away from its center is much more rapid than for the other objects.  This is consistent with a bright but compact object appearing in only one image in the K-29 stack.
This object also exhibits a less-blurry structure with two distinctly brighter spots or lines.  This is consistent with spray from a cosmic ray hit.
Crop showing mystery spot:

All in all, I think a cosmic ray hit is the most likely explanation.  Given the very poor quality of the image in question though it's difficult to give a definitive answer.  To make a proper determination one would need access to the yet-to-be-released raw imagery.

I've seen a paper with a more thorough discussion of New Horizons image artifiacts but don't seem to have saved a copy.  I'll add references from it when I track it down.

Looking closely, the spot has roughly same slightly noncircular, diffuse, extended shape and size as 2014 MU69 (optical or kinematic artifact) which would not happen from a cosmic ray or hot pixel.

This could be a real object, and simply much closer to New Horizons than MU69 is. That could certainly account for the object being visible on one day only. If its 10x closer than MU69 it can be 100x smaller than MU69 and still have a similar apparent magnitude, and the number of asteroids increases rapidly with decreasing size.

Left is object in question, right is MU69.

above: purely unscientific processing in order to perform "blobology": OP's image, blown up and then cropped twice (to get rid of the red arrow) then just plotted in python https://pastebin.com/8KWBHqnf


How can the universe be infinite? I've heard from renowned astrophysicists that we don't yet know whether or not the Universe is infinite. How is that possible regarding the big bang theory is accepted (as they all do)? Are they referring to the existence of other Universes when they say it could be infinite, or what?

What I mean is, even if it is capable of expanding, if everything originated at the big bang how can that space turn to be infinite in a finite time - the age of the universe.

In the standard ΛCDM model of the Big Bang, the universe is infinite and has always been such. The Big Bang singularity happened everywhere, in the sense that far back enough in time, the density diverges to infinity at every place.

But this is just a particular model--it assumes that the universe if spatially flat and is globally homogeneous and isotropic. There are extended models in which it is not exactly flat, and so could be finite even if it is still homogeneous and isotropic (if the curvature is even slightly positive). And of course we don't actually know whether it is homogeneous and isotropic at scales much larger than we actually see. Some inflationary models imply that it isn't.

To clarify: the ΛCDM model uses the assumes a spatially flat FLRW solution of general relativity, in which space is the Euclidean $3$-space The Euclidean $3$-space is the only flat homogeneous and isotropic $3$-manifold, so there no way to make it finite without violating at least one of those modeling assumption (e.g., a flat torus could have the same form for the metric, but would not be globally isotropic).

It would be cool if Hubble saw a signpost marked: "please do not go beyond this point, this is the edge of the universe." perhaps even a wall or a balustrade.

How can the universe be infinite? infinite size, infinite age, infinitely small quantum constructs? The main problem we have with infinity is that it defies human understanding.

Spherical and circular equations pervade the universe: Stars, CMB, planet and moon orbits, atoms, photons, Pi, they all can use sine-cosine equations. Rotations are infinite. Pi and sine-cosine are infinite.

If the cosmos is made up of infinite maths functions, why would it not be infinite?

How many angles does space have? infinity. how long does a galaxy turn around? eternity. The circles of angular momentum go on ad-eternum. rotations are infinite.

Why would there be a spacial limit to infinitely large or infinitely small space? Because it defies human understanding? that's not a good enough reason.

Everything in the known universe depends on mathematical principles which are infinite, numbers are infinite, angles are infinite, generally sine-cosine, linear, circular and spherical objects have infinite turns.

The mandelbrot set is infinite. It's a much simpler equation than the objects of the universe, and it is infinite. So, i'd encourage you to study the mandelbrot and ask yourself: how can it be infinite? Then you will have some advantage to apply that study to objects of the universe.

There is a curious thing that bridges the infinitely large and small objects in the universe: Black hole singularities are nearly entirely composed of sine-cosine maths descriptions, but they withhold millions of suns of atoms in the space the size a money coin or a CD or a nano-meter, all inside a sine-cosine disk, which is a circular phenomenon weighing billions of stars. If suns can fit into basketballs, and perhaps atoms, how can we judge what is big or small at all? If very big things are reborn to very small, and grow to very big again, it's kind of like the circle of life, and it means that you are the center of the universe, which is a good feeling. Atoms and Stars don't matter compared to you.


Why does it make sense to say the universe has no centre? If we suppose we and everything in the universe is perfectly flat.  That is, we have width and depth, but no height.  And we are situated on the surface of a balloon blowing up with air and expanding "outwards".  Us flat people can move around on the surface of our balloon but not through it, in much the same way we navigate around the earth, in a plane say. No matter where something is situated on the surface of the balloon, one point is no more central than any other point.  In other words, the surface of a balloon (the "universe") has no centre.  Is this why we say it makes no sense to say the universe has a centre, or edge for that matter, or is this analogy stupid?

The answer to this question lies in cosmology.

It's because of relativity in positions.  Every galaxy appears to be moving away from us and the universe we see is only the observable universe.  Further points are more in the distant past, when you observe the deep field you observe the past.  This may seem irrelevant to your question, but the idea of a "center" to a universe where any position in the universe, be it from our galaxy or from a galaxy in the Sloan Great Wall is the true center is not consistent with observation.  That's because galaxies/clusters of galaxies are moving away from each other, relative to each other.

Every galaxy is slowly being pulled apart from other galaxies, save for those in gravitationally bounded clusters.  (The whole architecture of the universe, with massive voids of absolute nothing and bunched up clusters of galaxies reflects this quite a bit)  If the universe had a central point, this would be easily observed because there would be variation in the color shift of galaxies that could be analyzed to deduce a central point where the galaxies are moving away from.

That is not what is observed.  Instead, pretty much most galaxies (save for exceptions like Andromeda or the Triangulum, who prove the rule since those galaxies are gravitationally connected to our galaxy via the local group) are moving away from us.  The Great attractor being not a path to the center of the universe, but the center of the recently discovered Laniakea super cluster.  So if there's attraction between galaxies, it's because of gravitational interactions.  The universe is also without any real edge unless you count the edge of the observable universe.  The observable universe being more a historical record than what the contemporary universe around us looks like and is a byproduct of light speed being so limited.  The speed of light in a vacuum is also the speed of information.  The whole universe is far more massive by comparison.

So to speak about a center of the universe would require the following:

A region of space that galaxy is moving away from or towards. (Which does not exist, instead relative trajectories and gravitational clustering is all regional at most.)
Edges that are defined enough to pinpoint a center (If such edges exist, they are impossible to observe due to the limited speed information travels in the universe)
Absolute positioning to pinpoint where this center would be. (All positions are relative, the galaxy, the sun and our planet all are moving at extremely fast velocities we don't notice thanks to relativity.)

Why does it make sense to say the universe has no centre?

We can't be sure it does.

  If we suppose we and everything in the universe is perfectly flat. That is, we have width and depth, but no height. And we are situated on the surface of a balloon blowing up with air and expanding "outwards". Us flat people can move around on the surface of our balloon but not through it, in much the same way we navigate around the earth, in a plane say. No matter where something is situated on the surface of the balloon, one point is no more central than any other point. In other words, the surface of a balloon (the "universe") has no centre.

This analogy is often used to justify that the claim that the universe has no centre. But there's no evidence of any higher dimensions. We simply don't know that there's any kind of "asteroids" curvature such that if you keep going one way you come back the other.

  Is this why we say it makes no sense to say the universe has a centre, or edge for that matter, or is this analogy stupid?

I wouldn't say it's stupid. But I would say it's presenting hypothesis as some kind of fact. For all we know our universe does have a centre and an edge.


Axial wobble or binary star system Is our solar system affected by a body unobserved as of yet that causes our solar system to curve through space in an orbit? Is this idea outlandish or us there any evidence to support it? Consider this information:

  "In 2007 Voyager 2 unexpectedly reached the edge of the heliosphere at a distance approximately 1.5 billion km less than the distance traveled by Voyager 1, indicating the SS is bullet shaped in the direction of the interstellar magnetic field."

Another bit of information is that a binary system with a moving SS was suggested as far back in modern times as 1894 -- with predictions 40x more accurate than an earth wobble to calculate precession of equinoxes (over 100 years).

Also unknown to me was precession was observed millennia ago, for which we have some records, but today's accepted notion was formed in the 1850's -- before it was accepted that the solar system even moved. Our current theory of precession takes no account for SS movement. Zero.

Lasly local bodies do not precess at all, only distant stars and -- from what I understand -- all of them.

Is a binary star system just bunk? Can it be tested for?
Is the axial wobble theory tried tested and come up true every time or Does this theory have predictability issues that have to be tweeked constantly?
Why is it that the moons orbit around the earth, as well as the earths orbit around the sun, are increasing and the precessional cycle is speeding up? Shouldn't that have the opposite effect?

There is absolutely no possibility that our Sun is part of a "binary star system". Even the least luminous star (with a mass of about 8% that of the Sun) would have an apparent brightness and proper motion that would easily have led to its discovery. See for example Is Sun a part of a binary system? and  Is it possible that the Sun has a binary partner (the Nemesis Theory) that has eluded detection?

Axial wobble may exist, or does exist in small permutations I would imagine. I am referring to precession -which causes us to see constellations ‘move’ in a circular pattern over a 26,000 year cycle. My understanding is the that the axial wobble has been attributed to this effect. There is no known confirmation of this wobble other than seeing the constellations change location in the sky over a period of time. Scientists who purported this theory have the earth axis of rotation a steady ‘wobble’ and this has accounted for the observed effect. Oddly local bodies in the solar system are not affected by the wobble in any observable form. the wobble only affects  viewable bodies outside of the solar system. Furthermore the precessionary cycle is ‘speeding up’ which the wobble does not predict. The observable evidence that would confirm a binary system or other non accounted for local gravity affecting body must be attained by seeking this information and not sitting on the precessionary wobble theory.


What exactly is a "moon"? Recently some new moons of Jupiter were discovered. However the moons are pretty damn small indeed - only a few kilometers wide. That makes me wonder if they should even be called moons in the first place. The Wikipedia article on natural satellites says there's no clear lower limit (or upper limit for that matter). But if we accept that, then Jupiter already has countless numbers of moons in its ring system, and even the Earth has multiple moons since the International Space Station is a "moon".

What exactly is a moon? Is it really a vague notion of "something that goes around a planet"? If so, why hasn't the IAU clarified what exactly a moon is? They've already done so for planets; it seems natural to do so for moons as well.

Unlike "planet" the IAU hasn't attempted to precisely define "moon". General usage requires that a "moon" is a natural satellite of a planet (or dwarf planet, asteroid, or perhaps even of another moon?) and it is big enough for us to have seen it as an independent body.

This contrasts with the "moonlets" that have been detected in Saturn's rings by their graviational effects on the even smaller ring particles. We know that a body exists there, but it is too small to be directly imaged.

As such the question "How many moons does Jupiter have" is probably unanswerable, since it depends on the sensitivity of your telescope and how close you are to the planet.

The smallest moons are about 10km across, but moonlets in the rings exist that are only a few hundred metres across. So in current usage, 10k might be roughly where people stop saying "moon" and start saying "moonlet".

Language exists to serve us, the definition of planet was only made to solve a particular naming problem.  No such problem has arisen for moons. So there is no authoritative answer.

"Moon" is a very broad term used for any natural satellite of a planet or asteroid. They can be as small and irregular as Deimos and Phobos (satellites of Mars) or the components of planetary rings or as big and planet-like as our Moon or the Galilean moons or Saturn's moon Titan.

That is not alright because it is like if we called every celestial body which orbits directly the Sun a planet including the tiniest asteroids. You're right that one must establish a definition of moon. Only ellipsoidal satellites should be called moons. According to this definition, Earth of course has one moon, Jupiter has four moons, Saturn seven, Uranus five, Neptune one, Pluto one and Eris possibly one (we don't know whether Dysnomia is spherical). Irregular satellites are asteroids that orbit a planet rather than a star. Asteroid satellites. Let's say a red dwarf orbits a blue main-sequence star, this doesn't make the red dwarf a moon or planet, it is still a star in a double star system.

Dr Alan Stern is even proposing to call the spherical moons planets / satellite planets. However that goes too far in my opinion, it would make our Moon a planet. It is too late to consider Earth-Moon a double planet system.


Unidentified color changing object in sky Yesterday, I was just star gazing and I noticed some star-like object moving with a high speed somewhere near the Orion's Belt and exhibiting all the seven colors i.e VIBGYOR and after a few moments, it disappeared. Any plausible explanations for this observation?

Probably a satellite flare

It sounds like a satellite flare.

Coming, showing up clearly for a few moments, moving, then going away, are characteristic of a satellite flare, like Iridium flashes.

Check Heavens Above or any other similar site to see if any predicted flares match with your location and time.

The changing colours can be explained with "Twinkling".


How many stars can be seen naked eye from outside the atmosphere? How dense is the "sky" from there? When I was 20, I went to Naxos (Greece) with friends. I was driving my car during the night on the mount Zeus (1003 meters - 3,291 ft) listening Pink Floyd.

Up there we stopped the car to take a walk, looked above and ... wooooooowwwwww!

The sky was dense! Full of stars. We didn't know it could have been like that.

My question is:

How dense is the deep sky from outside the atmosphere?

For example, on the ISS during the night (the Earth that cover the Sun) looking at the deep sky, how many stars can you see? I saw a lot of pictures of the stars taken by the Hubble telescope), but I don't think it can be compared, right?

Depending on your eyesight, the faintest stars you can see in a perfect environment have an apparent magnitude (brightness) of 6-6.5 (though some people have managed to see magnitude-7). According to this site, that translates into about 10,000 stars.

As for how it would look, I have seen the sky from the stratosphere (about 3 miles up, in a plane, where there is a lot less atmosphere to worry about, and no light pollution), and it is a surreal sight - with the sky absolutely littered with stars. However, it doesn't  quite look like a Hubble image, though - there's very little colour in these fainter stars, and Hubble tends to focus on narrower fields of view, at higher zoom.

You asked:
For example, on the ISS during the night (the Earth that cover the Sun) looking at the deep sky, how many stars can you see?

The answer is 0 (at ISS-night) and 1 (at ISS-day) which is called the Sun. Well, that is what NASA, the visitors to the ISS, the Apollo astronauts, the videos of the ISS space walks and other pictures produced by NASA say. There are no pictures still or video taken from the ISS that show more than 1 star, that well known nearest one.

Interestingly there was one Russian astronaut (Not on ISS but early Russian space craft) who saw something different when he was up in space. He saw the sky full of stars and the light from them.(I'll try to find you a link later).

There is clearly one obvious conclusion. You know what it is and it has nothing to do with optical effects, the physics of light or the way your eyeball works.


Why do aliens have to be carbon based lifeforms? So correct me if I'm wrong, but when searching for extra terrestrial life, scientists usually search for signs they would expect for life on earth to thrive in. We look for conditions on planets that meet certain criteria e.g close enough to a sun for water, environments for carbon based life forms to exist. I was wondering; why cant an alien be a sulphur based life form that for the sake of argument drinks lead and breathes in chlorine like we do oxygen.

I want to start with a disclaimer that I'm not a chemist and hopefully I don't screw any of the chemistry up. If I do, please let me know.

I think Bill Oertell hit the nail on the head. Just because you can imagine a species which can drink lead doesn't mean it's actually physically possible. Only specific atoms can form the basis of the (extremely) complex organic molecules needed to form life and Carbon happens to be the atom which can do that. The primary reason for this is that Carbon has four valence electrons and its outer shell can hold eight, allowing it to form strong and varied bonds that most other atoms just can't form. As such, Carbon is the most logical element to form the backbone of organic molecules.

Other ___-based Lifeforms

Moving down the periodic table, you can see that Silicon has the same properties (4 valence elections, 8 possible) and you might be inclined to think that you could form some sort of silicon based life. This topic has been widely considered, but you run into a number of problems that make Silicon-based life unfeasible. The primary reason is that Silicon is just much bigger and more massive than Carbon (having a nucleus with 28 nucleons compared to Carbon's 12). This makes it harder for Silicon to form the necessary bonds that Carbon can readily form and you're out of luck right form the get-go. Similar issues occur with other "Carbon group" elements, except they're even further exacerbated by even higher masses.

There are many other "organic" configurations chemists have considered such as boron-based life or sulfur-based life but they all have some sort of problem that makes it hard for it to exist. Some are more possible than others, but Carbon-based life, as we know it, just seems to be the best solution. If you gave someone all the elements in the periodic table and said, make organic life, they'd probably come back with Carbon-based life because its the easiest. You don't have to overcome as many obstacles.

Observations

Aside from the impracticality of non-Carbon based life, you have to consider that everything we've seen in the universe, as far as organic chemistry goes, points to the fact that the Universe is filled with Carbon-based chemistry. Astronomers have been able to look out at comets, interstellar dust clouds, and all sorts of places and time after time, they see complex, Carbon-based, organic molecules. For example:

We've found Polycyclic Aromatic Hydrocarbons (PAHs) all over the solar system and galaxy,
Astronomers have also found things like i-propyl cyanide in meteorites and in interstellar dust $-$ an organic molecule which is a necessary ingredient in amino acids,
Organic molecules have been found (and believed to have formed) on Ceres.

The point I'm driving at here is that the universe seems ready-made to start forming Carbon-based life everywhere. Everywhere we look, we see organic molecules which have Carbon as the backbone of their structure. Nowhere do we see complex silicon based molecules (or something even crazier). This is highly suggestive that Carbon is the way to go if you want to quickly and easily form life.

There are probably a 100 other reasons to favor Carbon over something else, but that delves into more complicated chemistry than I've touched on here and I'm not as knowledgeable about that. I would think this question would get a more in-depth chemistry answer on the chemistry stack exchange.

An oxygen-based life form may also be possible, given that oxygen readily bonds with other molecules. In addition, how do scientists actually know that the laws of physics, chemistry, and life apply everywhere? Why not just Earth or our solar  system? Why not just the Milky Way? There could be different laws and possibilities in different galaxies, which humans will most likely never discover. Who are we to decide what id true and what is not when it will never actually be known? For all I care, life on Earth could be the most simple and unimpressive in the entire universe. We could have the intelligence and lifespan of a maggot in comparison to some form of existence. Life is, after all, just a machine. What should we care anyway? We have to; that's the only known reason as to why life exists. To fill the void. To be there. What's beyond existence? Maybe that's where a black hole leads. In all honesty, this world is far beyond any conceivable understanding, far beyond the reach of any of us. At the end of the day, we are all bodies in the inconceivably large world of being. A fleck of dust in two-dimensional space. In reality, we are only worth something to ourselves.


Do planetary magnetic fields slow the movement of conductive extraplanetary moving objects via induction? A fixed magnetic field will induce an electrical current in a conductive object moving through the field.  The strength of the eddy currents will depend on the shape and composition of the conductor and also how fast it is moving.  The electrical current produces ohmic heating in the conductor, and some of the kinetic energy of the moving conductor will be turned to heat. This is how induction brakes work.

I wonder if this principle applies to fast moving conductors like asteroids or satellites that encounter planetary magnetic fields.  Are planetary magnetic fields strong enough to act as induction brakes on moving conductors?  A satellite experiencing induction braking would fall to a lower and lower orbit and eventually out of orbit.  Passing asteroids might have their course deviated more than would be expected just from gravity.

My search turned up only this abstract, which attempted to explain why meteorites are hot via this principle.

http://adsabs.harvard.edu/full/1946PA.....54..482R

A fixed magnetic field will induce an electrical current in a conductive object moving through the field.

No. It will induce an EMF in one direction as described in HyperPhysics. It will not induce a current since there is no return path.

This is different from induction braking, where you have a magnet with a non-uniform field moving near a conductor. It is the changing magnetic field at points within the conductor that induces the EMF and causes currents.

Alternatively, we can consider how electromagnetic fields transforn according to Relativity. If an object is moving at constant velocity through a uniform B field then, in its rest frame, it will experience a combination of uniform E and B fields which would not produce a current.  (Any current would have to be due to the spacial rate of change of the field, which would be tiny on the scale of the Earth's field.)


How does moonrise/moonset azimuth vary with time? In my tenacious attempts to observe moonrise (surprisingly difficult in a poor weather heavily urbanized hilly area with frequent bad smog, with busy work schedule and a bicycle) I was frequently trying to find good observation spots that would provide view to open distant horizon at specific azimuth.

While generally similar moon phases correlated with similar moonrise times I found the azimuth to vary in a way I have a difficult time to put my finger on. Sure there's a roughly monthly cycle of "wobble" between deviating about +/- 30 degrees north or south from "pure east" but while the mechanics of correlation between hour when the Moon is visible from behind the horizon and the degree it's lit by the sun are quite clear to me, the way its - or is it Earth's? - orbital plane is "off" relative to the ecliptic plane and Earth rotation plane eludes me. Could someone provide a sort of guide - preferably something that acts more as help in understanding the mechanics, as opposed to providing raw mathematical solutions, what does this deviation depend on, and how it changes with time?

The monthly variations are caused by the change in declination of the Moon as it travels (roughly) along the ecliptic.  This is caused by the tilt of the Earth's rotation axis, which results in an angle of about 23° between the equator (declination = 0°) and the ecliptic.  Around the constellations of Taurus and Gemini the ecliptic lies at much higher declination than near Saggitarius or Ophiuchus.  The same effect causes the change in rise and set times of the Sun during a year.

When you're in the northern hemisphere, a higher declination means that the transit altitude of the Moon or Sun is higher.  In fact, their whole daily (apparent - caused by the Earth's rotation) paths lie closer to the North star.  Because of that, the points where a daily path intersects with your local horizon lie further north, which you see as a change in rise/set azimuth of the Moon.

All this is true even without the 5° inclination of the Moon's orbit w.r.t. the ecliptic.  That inclination only mitigates the effect; the Moons declination does not exactly vary between -23 and +23° every month, but these extreme values themselves can lie between +/-18° or +/-28°, depending on whether the inclination effect increases (23+5°) or decreases (23-5°) the effect of the motion along the ecliptic.

Lastly, the rise/set azimuths do not correlate to lunar phase, as do the rise/set times.  Both phases and rise/set times are defined based on the Sun's position; we roughly define "noon" as the moment when the Sun is transiting in the south, and call the Moon "New" when it's in the same direction as the Sun, so there's no wonder that the New Moon transits around noon.  This is not true for the effects described above, and hence the corresponding periods are different.  The mean lunar period between twice the same equinox point (e.g. Aries) is called the Tropical month and lasts ~27.3d (this is roughly the same as the siderial month, but influenced by precession).  The effect of the inclination of the Moon's orbit has a mean period of one Draconic month, with a period of ~27.2d.  Instead, the Synodic month, the mean period between two cases of New Moon, lasts 29.5d, about 2.2d longer.  Hence, the declination and rise/set azimuths of the Moon do not correlate with the phases.

What we consistantly overlook and are fooled by, is our earths power and own quirky magnetic self. Earth also has a pull. Therfor, your carefully calculated 29+ day moon cyle which varies-is incorrrct. By about 4 more fluctuating days. We dont see it from earth and it appears normal because the moln takes its usual time to appear, that is why we "think" we understand it.   :)


what planet is the most radioactive? So as I understand it the source of most geothermal energy on Earth is due to radioactive decay. Jupiter is the most massive planet but if the bulk of it's mass comes from gaseous elements instead of heavier ones like uranium or whatever than it being the most massive might not necessarily mean it has the most radioactive material.

There's a few parts to this question, I'll give it a shot.  Also, since you're asking about the geothermal energy of the earth, I'm going to ignore radiation from space and radioactive van allen belts (Jupiter has a very radioactive van Allen belt).   Also, as voyager discovered when it left the solar system, there's more radiation in the form of cosmic rays out there, that the sun effectively shields most of the planets from.

But, because you mention the Earth's geothermal heat from radiation, so I'll focus on that.

Here's a very well answered similar question about radioactive elements inside the earth.  what percentage of the Earth's core is Uranium

  So as I understand it the source of most geothermal energy on Earth is
  due to radioactive decay.

A healthy share of Earth's core heat is from the planets formation.  This is a pretty good article on that subject - http://physicsworld.com/cws/article/news/2011/jul/19/radioactive-decay-accounts-for-half-of-earths-heat, it says that of the current heat, about 50% is from the energy left from the formation of the planet and about 50% is from radiation - so the radiation is very important, but it's probably not the cause of "most" of the heat in the earth.

As far as I know, no similar studies have been done on any of the other planets.

  Jupiter is the most massive planet but if the bulk of it's mass comes
  from gaseous elements instead of heavier ones like uranium or whatever
  than it being the most massive might not necessarily mean it has the
  most radioactive material.

That I pretty much agree with.  The two primary differences between the 4 gas giant planets (or, two gas giant, two ice giants if you like) and the 4 inner rocky planets is that the gas giants formed outside the frost line and key difference #2, the 4 outer planets are much larger, so they were more able to hold onto more hydrogen and helium, which are the 2 most abundant elements in the solar system.

Obviously, the 4 outer planets have a lower percentage of heavy elements overall.    As to their percentage of Uranium - well, your guess is as good as mine, but, probably a lower percentage of radioactive elements than the inner planets seems reasonable to assume.

Also, any radioactive elements in the 4 outer planets would likely be well below their thick gaseous surfaces, so it would be difficult to detect, outside of Neutrino detection I suppose, and more trouble than it's worth to try to collect.

The 4 inner planets (and lets throw the moon in there as well, and asteroids if you like) are more interesting I'm assuming David Hammen's answer is correct in the linked question above, and that most of the Uranium on earth is in the crust or mantle, the highest percentage in the crust, and so that's probably true for any other rocky planet that formed and was, at one time, molten enough to circulate, so all the inner planets probably have similarly small amounts of uranium and other radioactive elements as Earth.

Mercury may have had much of it's crust and some of it's mantle blown off in a giant collision, and if that's the case, Mercury might have lost a portion of it's radioactive elements.  Brief summary of that here, point #6:  http://messenger.jhuapl.edu/faq/faq_science.html

unrelated footnote, but if Mercury's crust was blown off, it might be a good planet to mine for rare earth elements, or maybe asteroids will be easier, who knows, but I've always been curious of the mining possibilities on Mercury.  Abundant solar energy too, but it's a hard planet to fly to because of the sun's gravity, so, maybe asteroids are the way to go for space mining.

The moon was also formed by a giant impact, so, the moon was formed by material from Earth's but it has a much higher percentage of mantle than the Earth, so it could have a higher percentage of Uranium and other radioactive elements than the earth.  How well the Moon's material was circulated in it's cooling process is another question.   Being smaller it probably cooled more quickly.

Venus and Mars, I see no reason why they shouldn't have similar percentages of radioactive elements than Earth.

 Source:  https://en.wikipedia.org/wiki/Internal_structure_of_the_Moon

One way to look at this question is to investigate how quickly the other inner planets cooled.  Far from exact, but that probably tells us something, since heat generated by radioactive decay inside the planet would probably lead to volcanism at some point.  Even the Moon appears to have had volcanic eruptions as recently as 33 million years ago, so some ongoing internal heating seems likely.

Volcanoes on the moon

Size is also a key factor in what keeps the inside of a planet hot, and in some cases, tidal heating (Io, Enceladus), but that's not really relevant to this question.

Neither Mars nor Venus are volcanically active like the earth, but Olympus Mons may have erupted as recently as 25 million years ago, and there is evidence of large lava flows on Venus.   As to how big a role radioactivity plays in heating up the cores of those 2 planets, I don't know precisely how much.

Overall, I think this is a good question on planet cores and radioactivity, as the inside of the planet is just as interesting as the surface, well, to me, at least.   I know this doesn't answer your question specifically as to which is the most radioactive, cause I don't know, but I like the question.

Jupiter is the most radioactive planet. It has the greatest Electromagnetic field of all planets in Solar system according to Juno space mission ( https://en.wikipedia.org/wiki/Juno_(spacecraft) ). When we know the size of Jupiter it is obviously logical that it must contain farther most mass of radioactive elements like uranium.


What if there was an asteroid belt with the mass of a planet? In the past, the asteroid belt was thought to be the remains of a shattered planet. Of course, that was all pseudoscience, the mass of the asteroid belt being 4% of the moon. I've been wondering, what would happen if this did occur. What would an asteroid belt with around 50% of the Earth's mass be like? How often would asteroids hit earth? Would it influence Mars?

The mass of a planet? There probably was, billions of years ago, and perhaps still is, but the debris of this planet-in-the-making has been shattered and dispersed by impacts. We know from fragments which have struck the Earth that the planet which was forming there had grown large enough to have a molten interior where the heavy metals, mostly iron and nickel, had sunk to the centre and differentiated from the rocky mantle. A massive impact must have shattered this forming planet about 4 or 5 billion years ago, and the debris has become so dispersed that it is difficult to assess how much there originally was. Some was kicked out of the asteroid belt completely, the rest is still there but much of it so finely shattered and dispersed that we can't see it (the asteroid belt covers an enormous area, much larger than the orbit of the Earth-moon system).

The resulting absence of a body with substantial gravitational field to attract comets & other objects has enabled them to pass on by, perhaps to impact the Earth and inner planets. Bodes Law says here should be a planet there, but whether it would have been a Mars-sized planet or not, nobody knows. The differentiation of nickel-iron from the rocky material becomes hard to explain without a fairly substantial planetesimal there to separate them, and in our solar system at least, Bodes Law seems fairly reliable.


What is the theoretical ages for Pop I stars How old could population I stars theoretically be? What's the earliest they could have formed?

Since Pop III stars are the oldest stars, then they could have theoretically began to form in the Cosmic Dark Age (CDA), see section 5, since the oldest galaxy we've observed so far (in infrared) is about half way through the CDA (~$480$ million years). As the article states,

  Stars and galaxies are formed when dense regions of gas form due to the action of gravity, and this takes a long time within a near-uniform density of gas and on the scale required, so it is estimated that stars did not exist for perhaps hundreds of millions of years after recombination.

So not only must the temperature of the universe be sufficiently cool, gravity must have acted for a long enough amount of time for baryonic structure to begin to form.


Do astronomers have an established, systematic way for saying what does or doesn't orbit what? (e.g. "Mars orbits Earth") A recent comment

  An object far enough away can certainly orbit the Moon and the Earth (and the Sun) -- Mars, for instance does this. An object in the Earth-Moon L2 is also orbiting both the Earth and the Moon.

A recent comment about that comment:

  according to your way of thinking all solar system bodies orbit Mercury, except the Sun, which is just silly. Or does the Sun in fact orbit Mercury as well? I think your use of the word orbit is not workable, nor shared by almost anyone else.

So I'd like to ask if astronomers have an established, systematic way for saying what does or doesn't orbit what within the solar system, and if so, a link to point to in the future would be greatly appreciated!

It is possible that there is nothing "official", there is just the technical use of language. For example Phil Plait notes that He incorrectly used the word "orbit" for the motion of the Hayabusa probe, which does not orbit the asteroid Ryugu. But hovers over the surface.

So what does Phil mean when he talks about orbiting?  I summarize the meaning thus: Object A is in orbit around object B if A moves around B (ie the True Anomaly of A increases from 0 to 360 degrees in fairly regular fashion) principally as a result of the gravitational field of B.

So although Mars does move around the Earth, its motion is not principally due to the gravitation field of the Earth, so it is not in orbit.  However the moon's motion is principally due to the gravitational field of the Earth. It is in orbit around the Earth.

The moon is also in orbit around the sun: It moves around the sun and the reason for this motion is principally the graviational field of the sun.

A body at the Earth Sun L2 point is not in orbit around the Earth (it is fixed relative to the Earth) It is in orbit around the sun. A body in the Earth Moon L2 point (which is probably very unstable) is orbiting the Earth and orbiting the sun. Its motion relative to the Earth is primarily due to the Earth (and secondarily due to the moon). Its motion relative to the sun is due to the gravity of the sun.

Cruithne is in a 1:1 resonance with the Earth, but its postion is not primarily due to the gravity of the Earth. It is in orbit around the sun, not the Earth.

Hayabusa is not in orbit around an asteroid, it is maintaining position by thrusters. Similarly, A Jumbo jet is flying not orbiting, it's motion is not mainly due to gravity.

This idea can be sharpened by the notion of a Hill sphere.
Inside the Hill sphere, a body will orbit. Outside it, the body will not orbit.

What if I told you that technically speaking, the Moon does not orbit the Earth, and the Earth doesn't orbit the Sun, and that the Sun orbits something that is nothing? Welcome to the world of barycenters, which seem to be skipped over in elementary school science, though for good reason. It would be a mouthful for the students to learn.

In the Earth-Moon system, the Earth does not orbit the Moon, and the Moon does not orbit the Earth. Rather, they orbit a common center of mass, referred to as the Earth-Moon Barycenter, or just barycenter if the situation is unambiguous (as you will see later, you can have multiple barycenters).

The Moon tugs on the Earth with the same force that the Earth tugs on the Moon. Therefore, the orbit looks more like this:

The Moon has roughly 1.2% the mass of the Earth. Therefore, the Moon should orbit roughly 83x further away (it's just $\frac{100}{1.2}$) from the barycenter than the Earth does. The Moon's semi major axis is 385000 km. Therefore, the Earth's semi major axis around the Earth-Moon barycenter (not the Sun) is roughly 4500 km. And that is the case, as shown below. The diamond symbol is what Space Engine uses for barycenter symbols.

If we zoom in we see the Earth's orbit around the barycenter:

Because the Moon has such a low mass compared to the Earth, the barycenter is actually located inside the Earth. As the Moon slowly travels away from the Earth in the next few hundred million years, the barycenter will slowly leave the Earth's surface.

Can the barycenter be located outside of the planet? It sure can. The Pluto-Charon system looks a bit like this:

In Space Engine it looks like this (brightness increased to you can actually see it):

What about the Sun-Earth system? Well the problem is that the Sun is also affected by all the other planets in the solar system. The sum of all these interactions is where the Solar Systemic Barycenter is located. It doesn't travel in a nice circle though, but it is mostly affected by Jupiter since Jupiter is the most massive planet in the Solar System. It looks like this:

How about binary stars? Well it's pretty much the same thing. Here's $\alpha$ Centauri.

Ok, last thing, how about systems with 3 or more stars? Well here's the thing. barycenters can orbit other barycenters. The Castor system is a sextuple (6) system. Here's what it looks like:

Those three points of light are actually two stars orbiting very closely together, so that they look like one star. So to answer you question, no they don't orbit anything really, but they instead orbit a common barycenter, and we determine what orbits what by seeing if it goes around that barycenter.


Account for radiation energy in the statement "total energy of universe is zero" I've read in Hawking's book The Theory of Everything that total energy of the Universe is zero. He explained this by saying that if there are two bodies separated by a distance and having some mass, they possess potential energy and the same amount of negative energy  with the gravitational field. Thus he concluded that total energy of the Universe  is zero. But here I've a question: how do we account for energy which is in the form of radiation?

The total energy of the universe consists of the mass energy of all the matter (both normal and dark), the mass-energy of the radiation and of the dark energy plus the gravitational potential energy of the universe (which is negative).  The hypotheses is that this sums to zero.  As far as I know, there is no experimental evidence for this.

But there is good evidence for the size of the various mass-energy terms.  The best current estimates are that the mass-energy of the universe is:

73% -- Dark energy
23% -- Dark matter
3.6% -- Interstellar gas
0.4% -- Stars (includes black holes)
v. small -- Relativistic neutrinos
v. small -- Radiation (CMB and stellar radiation combined)

This balance changes.  As the universe expands, the density of matter (dark and normal) varies as the inverse 3rd power of the size of the universe. (Matter stays the same and the volume expands as the cube of the radius.)

But the density of dark energy stays constant, since it is a property of empty space.

The density of radiation is proportional to the inverse 4th power of the radius, because not only does the increased volume dilute the radiation like it dilutes the matter, but also the radiation gets red-shifted, contributing an extra power of the radius.

(Incidentally, that means that the fraction of the total mass-energy of the universe in radiation decreases with time, and is estimated presently to be 1000:1 matter:radiation.)

So radiation seems simply to be too small to matter.

It must be the same situation as if you had bits of mass flying off the surface of the two masses in the simple model. It would not take much kinetic energy, at the huge $mc^2$ scale, to get those bits to fly off to infinity in a Newtonian potential energy, but you'd have a huge $mc^2$ lost from your system. So you must also have a similar loss in the general relativistic gravitational potential energy, if the energy was zero originally.

So the lost radiation must also represent a significant loss of potential energy, not just the tiny gravitational redshift. I don't know how Hawking is counting potential energy to get the energy to be zero, but it can't be the simple Newtonian potential. Remember that the zero in a potential energy scale is not usually of physical consequence, because it's only changes in potential that matter, but to get the total energy to be zero, he must have some way to get a relevant scale.  Much more formal mathematical arguments are available, such as http://www.prespacetime.com/index.php/pst/article/view/81, but even these are debated by experts, who each attribute different degrees of significance to the ability to make the total energy zero.  It is not at all clear that total energy is a relevant physical quantity in general relativity, but for those who wish to make it so, as Hawking does, it may indeed be possible.

Also note that the tiny energy in the radiation today is not really relevant to this question, because the question is about originating a universe.  When the universe originated, radiation was extremely important, so the question does need to be addressed for anyone who wishes the energy to be zero.  The real issue appears to be, whether or not that is an important goal in the first place.


How can astronomers determine the difference between "hydrostatic equilibrium" and "just happens to be spherical"? This is relevant for the definition of a dwarf planet.

I presume the answer will be, well, if we can tell the mass of the body and guess the material.   I don't find this very satisfactory because (1) may be impossible and (2) will have large error.

I think you're asking, "If we know an object's shape, can we determine if it is in in hydrostatic equilibrium?" If so, one might wonder if astronomers classify basketballs or ball bearings as being in hydrostatic equilibrium, since they're so spherical.

Below about 100 km in radius, the answer is in general no. Given some population of randomly lumpy objects (like asteroids), some of them will be close to the shape of a sphere purely on accident. The composition matters too -- an object of this size made of hydrogen gas would assume a spherical shape from hydrostatic equilibrium, but an object made of rock might not (like Mathilde below). We could make better predictions given detailed knowledge of the materials and environment of the object, but this is not always possible, as you mentioned. For small objects, intermolecular and atomic forces dominate gravity.

Once you get to a certain size of object, it becomes much easier to make a prediction about hydrostatic equilibrium. This is still very much context-dependent, and you still get complications from material composition, temperature, etc. However, atomic binding forces have some fixed strength, but gravity scales like mass. Given ordinary astrophysical materials, we can be very sure that a body like Jupiter is under hydrostatic equilibrium.

You can make some order of magnitude estimates by assuming that the atomic interaction energy must be at least as large as the thermal energy (Hughes and Cole 1995). If you check out equation 5 of that paper, you'll see an explicit expression for a radius that divides spherical objects and nonspherical ones. At some mass, the binding atomic energy becomes dwarfed by the gravitational potential, and you always get a spherical object.

tl;dr -- small objects no, big objects yes, medium objects may require detailed modeling.

For a celestial body to be a sphere in hydrostatic equilibrium, it needs to be a fluid. Hydrostatic equilibrium does not make sense for solid bodies.

So Earth and Mars are not in hydrostatic equilibrium. It is spherical for the good reason of being a massive body where its own gravity is enough to avoid big irregularities, but it is not supported by (fluid) pressure, but by (solid) incompressibility and material resistance.

On the other hand, Jupiter and the Sun are in hydrostatic equilibrium since the force that avoids them collapsing is actually (fluid) pressure.


DIY tracking motor - gear mating I have a Skywatcher 130/900 and I found that if I do an accurate polar alignment I'll need only one motor to track a celestial body, so I decided to build my motor. Right now I'm facing a problem with the mating of the spur gear that drive the worm gear

Using a caliper I found that the gear has the outer diameter of 50mm, and a tooth is 1mm in height, so the reference diameter is 49mm; the gear has 140 teeth, and so the module (reference_diameter / n_of_teeth) is 0.35.
After this I used Solidworks to model a spur gear that could match it, and printed this

When I tried to check the mating, I found this

The teeth seems right, but they're too short and can't mate.
I used a caliper and counted the teeth to obtain the gear specs, and I think is kinda stupid as approach, but I could not think of something better to mate my gear. Is there a better approach to this?
Then, the idea was to try and remove the gear (removing the screw) and replace it with a 3d printed gear, but it does not seems to work (and I think it could break the telescope mount). Did someone try to do it?
Searching online I found that (obviously) there are some tracking motors and another question came to my mind: how can they mate the gear? Is there some kind of standard? Does it mean that every telescope's mount has some kind of standard gear? If yes, where can I found them?
EDIT: That's the situation: on the right there is the spur gear that I'm trying to mate (or eventually remove, if possible) and in the center there is the worm gear that move the telescope on the RA

EDIT2: Here's the project of an involute gear with Solidworks. (I followed this tutorial) but as you can see, the teeth overlap.

As a reminder, I have the following parameters

Pitch diameter (PD): 49mm (caliper measurement)
Number of teeth (Z): 140
Module (PD/Z): 0.35

Am I doing something wrong (or am I missing something)?

Gear teeth usually have a special shape which is either an epicycloid or involute curve. Making worm gears is even more complicated because the teeth have a helical curve in addition to having an involute profile.

Making good-quality gears requires specialized tools, knowledge and equipment.

Ok, there is a lot of calc's and table references to go through.
Punching in the Numbers from above into s Sheet I had done during my Advance diploma days.
Gear Pitch circle diameter = 49.3 ( note this is the OD - Addendum)
Number teeth = 140
Module  m = 0.352 (same as Addendum) = 49.3/140
Whole depth =   0.759264 (Addendum + Dedendum)
Clearance = 0.055264
Dedendum =  0.407264
Outside Øg =    50.0
Root Øg =   48.49
All this information makes up the involute tooth profile for your gear.
the rootØ is the absolute bottom of the gear tooth.
I hope some of this makes sense, there are some online references, i got mine from my work books going back a few years. Note: i used metric calcs.


What color is earthshine? What color is earthshine (e.g the average color of earth that shines on the moon)?  I am making a solar system exploration game, and would like to know this for the lighting of my moon level at night, with a "full earth".

Edit: With your answers, this is what I get:

Edit:
Here is a video including the moon level, bathed in earthshine as the specified color in the answer at "night time" (clip is 12 seconds into the video):
https://www.youtube.com/watch?v=HKGCtkps8gk&list=PL9Bk1v7iJfdCpRaQ6vTGYOM-lXAO7RAQ1&index=1

If interested in my game I am making, here is a link to it:
https://jonathanlcopeland.wixsite.com/planetary

In my answer to Color of planets I estimated the colour of the Earth as #2f6a69 (based on averaging the colour in various images of Earth, and adjusting for albedo), but noted that it is the hardest of the planets to give a single colour to.

If you were on the near side of the moon with no sun the cones in your eyes would not be fully active: you would be have Mesopic vision. Also your eyes would adapt to the blue light conditions. As a result you probably wouldn't notice blueness of the light much.

The reason the earth is blue is Rayleigh scattering -- same reason the sky is blue.  Think of it as a big, faintly glowing blue light bulb.


Are digital adaptive optics possible? Adaptive optics generally apply slight changes to mirrors to account for atmospheric turbulence. These generally require either a mirror to be broken up into smaller mirrors, each with their own actuator, or for a single large mirror to be slightly deformed by many different actuators.

Is it possible to do much of this digitally?

Couldn't software slightly attenuate or amplify each pixel at each time-slice collected from a passive mirror? These changes would depend on the distortions measured by a guide star or laser (this digital system would still require a guiding light)? I suspect this would probably be less accurate than true adaptive optics, but it would also be far less expensive (as you wouldn't need so many actuators).

Has this approach been studied and dropped? Is it ridiculous and not even theoretically possible? I'm curious if anything has researched this idea.

The problem with your approach is that the deformable mirror changes the phase of the light across the mirror, where the light is not focussed.  The light at the sensor array is focussed, and what you get is the intensity which is, roughly, the Fourier Transform of the phase front at the mirror.   By the time you have intensity, the phase information has been lost.

edit for clarity:

The sensor array measures the intensity, at which point the phase info is irretrievable.  If you remove the sensor array and re-measure past the focal plane, yes, you can get phase info -- see "Plenoptic cameras."

Now, there are other techniques -- you might be interested in searching for papers on "Lucky Imaging" , which basically takes as many images as possible and throws away the distorted ones.

With enough computational power every pixel of a camera sensor could be processed individually. Outputs amplified or reduced to compensate for variations of light levels across the sensor. Stacking algorithms can discard those pixels that do not receive a constant input.

Photo shopping to the max. Make the Astro Photographers life easier. The problem for everyone else would be in deciding where science becomes art.


Does Absolute Velocity Exist? It seems everyone is on the same page about there being no "absolute velocity" due to the fact that everything is relativistic. However, this leaves me confused. This seems to be disconnected with the concept that the speed of light is in fact an unchanging constant. But to state that all speed is relative to an object is to essentially say, "speed does not exist, but is only relative to an observer". But yet, the speed of light is a calculable constant that never changes. How then, can we say, there is no such thing as absolute speed?

If I throw a flashlight in space that is turned on 50mph, does the speed of the emitted light from the flashlight increase by 50 miles per hour in the direction I threw it? Of course not. We know this. But if this is truly the case, how then can there not be an absolute velocity which could be calculated by determining the speed of light in relevance to the object we're measuring (since the speed of light is constant)?

Please help because this is bothering me.

Chris, you are actually on the verge of understanding how special relativity works. You're very close. You only need to take one extra step.

  to state that all speed is relative to an object is to essentially say, "speed does not exist, but is only relative to an observer"

This is correct. Absolute space, as in newtonian physics, does not exist. Same for absolute time. Both are just relations between objects, and between events.

As long as you hang on to the notions of absolute space and absolute time, relativity cannot be understood. If you let go of them, relativity actually seems natural.

Einstein simply noticed this:

A) All previous experiments (like Michelson-Morley) have shown that whenever you measure the speed of light, you always get the same result, no matter what.

B) Maxwell's equations for electromagnetic fields (such as light) include the speed of light, and the value of that speed is frame-independent. Which means, they always show the speed of light to be the same, no matter how the observer is moving.

Both A and B tell the same thing: speed of light is always the same. But how can that be, when different observers are moving through absolute space at different speeds?

The answer is - absolute space is not a thing. Space is just a background for a special type of relation between objects, called "distance". Time is just a background for a special type of relation between events, called "duration". But neither space nor time are things, separate from objects and events. Only when you put together a whole lot of "distance" type of relations, space seems to appear.

The really important thing is speed of light. It's a fundamental constant of nature, like the Planck energy, etc. This universe is built in such a way that speed of light and other constants like it remain the same no matter what.

But space and time are derivative notions. They are not primordial realities like the speed of light. So they depend on the observer. For me, the bundle of distance relations we call "space" looks a certain way. For you, the same bundle looks a bit differently. This is okay, because space is not absolute; it's derived from a lot of other things.

When you throw the flashlight, the speed of light from it is the same for everyone. But how can that be, since different observers are moving in different ways? Simple: they all see the bundles of distance relations differently; those differences are such that speed of light always remains the same.

And that's special relativity in a nutshell.

Does Absolute Velocity Exist?

Yes it does.

  It seems everyone is on the same page about there being no "absolute velocity" due to the fact that everything is relativistic.

I'm a "relativist", but I'm not on that page. Because of the CMBR. Google on CMBR reference frame and check out the CMBR dipole anisotropy. It isn't an absolute frame in the strict sense of the word. But you can use it to gauge your speed through the universe. And the universe is as absolute as it gets.

  However, this leaves me confused. This seems to be disconnected with the concept that the speed of light is in fact an unchanging constant.

I'm afraid it isn't. Check out Is The Speed of Light Everywhere the Same? on the PhysicsFAQ website:

"Does the speed of light change in air or water? Yes. Light is slowed down in transparent media such as air, water and glass."

"These gyroscopes send light around a closed loop, and if the loop rotates, an observer riding on the loop will measure light to travel more slowly when it traverses the loop in one direction than when it traverses the loop in the opposite direction."

"In this passage, Einstein is not talking about a freely falling frame, but rather about a frame at rest relative to a source of gravity.  In such a frame, the not-quite-well-defined "speed" of light can differ from c, basically because of the effect of gravity (spacetime curvature) on clocks and rulers."

The answer is no. The speed of light is not everywhere the same. But you measure the local speed of light to be the same because you define our seconds and your metres using light. So when you use them to measure the speed of that light, you always get the same answer. See
Comments on "Note on varying speed of light theories" by Joao Magueijo and John Moffat.

  But to state that all speed is relative to an object is to essentially say, "speed does not exist, but is only relative to an observer".

Speed exists. It might be relative to something else, even if that something is the universe. But even though it's only relative, that's no reason to say it doesn't exist. A bullet is just a harmless lump of lead that you can weigh in your hand. But a speeding bullet will kill you dead. Think about how that sits with "speed does not exist, but is only relative to an observer".

  But yet, the speed of light is a calculable constant that never changes. How then, can we say, there is no such thing as absolute speed?

We can't. We can say there's no such thing as an absolute reference frame, such that you won't find your experimental results in your sealed box are affected by the speed of that box. But like I said, the universe is as absolute as it gets, and you can measure your speed relative to the universe.

  If I throw a flashlight in space that is turned on 50mph, does the speed of the emitted light from the flashlight increase by 50 miles per hour in the direction I threw it? Of course not. We know this.

Correct. Because light has an E=hf wave nature. The speed of a wave depends on the medium it's passing through, not on the speed of the emitter.

  But if this is truly the case, how then can there not be an absolute velocity which could be calculated by determining the speed of light in relevance to the object we're measuring (since the speed of light is constant)? Please help because this is bothering me.

It's simpler than you think. Look at the definition of the second and the definition of the metre:

The SI definition of second is the duration of 9 192 631 770 periods of the radiation...

The metre is the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second.

You measure the local speed of light to be constant because of the way you define your seconds and your metres, and because of the wave nature of matter. Check out things like pair production and electron diffraction. Ask yourself this: if you and your rods and clocks were made out of sound waves, such that you defined your metres and second using the motion of sound waves, how would you ever measure the local speed of sound to be anything other than 340 m/s?

Edit 14/09/2017:

To check out what I said above, see this in the Einstein digital papers dating from 1920:

"As a simple geometric consideration shows, the curvature of light rays occurs only in spaces where the speed of light is spatially variable. From this it follows that the entire conceptual system of the theory of special relativity can claim rigorous validity only for those space-time domains where gravitational fields (under appropriately chosen coordinate systems) are absent."

The speed of light in vacuo varies. Also see this PSE answer which quotes professor Douglas Scott:

"However, the crucial assumption of Einstein's theory is not that there are no special frames, but that there are no special frames where the laws of physics are different. There clearly is a frame where the CMB is at rest, and so this is, in some sense, the rest frame of the Universe. But for doing any physics experiment, any other frame is as good as this one. So the only difference is that in the CMB rest frame you measure no velocity with respect to the CMB photons, but that does not imply any fundamental difference in the laws of physics."

Special relativity pre-dated the CMBR. Also see this in the Einstein digital papers, again from 1920:

"Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether".

See Wikipedia and above for the definition of the second and the definition of the metre. They are both defined using light.


If 50 tons or more of debris falls to earth everyday, is Earth getting heavier? In turn, would that increase our gravitational pull?

The Earth loses mass because hydrogen and helium (plus other elements in trace amounts compared to hydrogen and helium) escapes the Earth's atmosphere. The Earth gains mass because incoming asteroids (most of them very small) impact the Earth's atmosphere; a few make it all the way to the surface of the Earth. Whether those incoming asteroids burn up in the atmosphere or make it all the way to the surface is irrelevant; the Earth gains mass.

Whether the net result is a mass gain or mass loss is a bit up in the air; the uncertainties on both are rather large, and they overlap. The Earth might be gaining or losing a tiny bit of mass every year. That said, most research leans toward atmospheric losses being greater than mass gain from impacting asteroids, comets, and dust.

Whichever is the case, it's a bit irrelevant. Even the most extreme upper estimates on mass loss or mass accumulation are incredibly tiny compared to the mass of the Earth itself.

Most of it burns up in the atmosphere and never actually makes it the surface. So no, as far as I know or have ever heard/read the Earth is not getting more massive. Any increase in mass due to space debris (or other things like more humans being born) is negligible compared to the mass of the Earth anyways so it has a null effect in terms of the gravitational attraction.


Would all neutron stars inevitably collapse into black holes due to quantum tunneling? The materials inside a neutron star are densely packed (extremely close to each other) and as time goes by say about an eon later, most of the neutrons would eventually tunnel into each other and voila! the neutron star becomes black hole? sound suspicious to me but can it happen?

The materials inside a neutron star are densely packed (extremely close to each other) and as time goes by say about an eon later, most of the neutrons would eventually tunnel into each other

Based on what ?

The material's collapse was halted from an astonishingly high speed collapse by the neutron degeneracy pressure that exists precisely because the universe doesn't want to let two neutrons fuse.  The enormous forces involved in the collapse and the enormous forces keeping the mass compact are not high enough to overcome this.  That's why it exists in the first place.

Over time "tunnelling" works in many, many ways. If two neutrons were to fuse in this manner the list of possible by products is enormous, and a black hole is most unlikely, IMO.  We've a lot of experience of whacking particles into other particles in extreme conditions ( think CERN ) and we haven't seen any sign of a black hole yet ( and believe me, they're looking for them ).  So I think the odds of a fuse into a black hole are extremely low.  Over time it's more likely the neutron star would "evaporate" into other particles.  But over those time scales you're looking at the cold death of the universe and protons decaying and so on.

And if, for argument sake, a mini black hole formed from two neutron's "fusing" it's life expectancy would be minuscule as tunnelling effects ( predicted by Hawking ) suggest it would "evaporate" in the blink of an eye.  So isolated fusing events, even f they happened, would be unlikely to produce a black hole that grew, but instead one that just blew up as fast as it was created.

  and voila! the neutron star becomes black hole? sound suspicious to me but can it happen?

No evidence I am aware of suggests neutrons will fuse in the manner you're describing.

"Neutron Star" is probably something of a misnomer.  Apart from neutrons, current models ( "educated guesses" ) suggest that the core of such a body might be a lump of something called quark-gluon plasma, which is essentially mush made from neutrons.  This is what you get when you fuse neutrons together -  a form of mush made up of the stuff that neutrons and protons are made from - quarks.

So theory and evidence suggests that you don't get a black hole from just waiting for a neutron star to change into one.

Would all neutron stars inevitably collapse into black holes due to quantum tunnelling?

Not to my knowledge. Where did you hear that? I don't think it's true, because if it was you could make the same claim about any massive body.

  The materials inside a neutron star are densely packed (extremely close to each other) and as time goes by say about an eon later, most of the neutrons would eventually tunnel into each other and voila! the neutron star becomes black hole? sound suspicious to me but can it happen?

I can't say no it can't happen with confidence. But nor can I say with confidence that you won't receive a visit tomorrow from a fairy riding on the back of a unicorn. The thing to focus on here is the "quantum tunnelling". Do you know of any actual experiments where two particles do some "quantum tunnelling" and morph into something else. Because I don't.


Maximum distance light can travel? If we assume that there is nothing except the sun in the universe then how far the light can travel ??

Using your scenario, and lets ignore dark energy expansion and red-shifting at greater distances,.  There would be no distance where the sun will disappear.  That might seem counter intuitive but it's true.

On Earth, we receive about 10^17 photons per square CM.  (source).  Using the inverse square rule, to receive 10 photons per second on a pair of human eyes, that distance would be 100 million AU - give or take, or about 1,580 light years.    We probably can't see just 10 photons, but in pitch black, with eyes adjusted to the dark, maybe we could.   That's about the distance where the sun would give of steady but very very dim light.

Further than that, what happens has more to do with the quantum nature of light than the brightness and distance.   As you double the distance you see 1/4th the frequency of photons.   At 5,000 light years you see 1 photon per second, basically a very dim blinking light, but just as bright as it is at 1,580 light years, just appearing less often.     Double the distance again and it flashes once every 4 seconds.    There's no distance where you stop seeing the sun, you just see it less and less often, but it never appears dimmer than 1 photon.

Well, one reckons that light from the sun will travel to the end of our universe, if in fact it has an end.  One way to calculate the actual distance to the end of our universe is as follows:
(1)  assume that our universe is a very large "black hole" ----- understanding that a "black hole" is simply a volume of space from which light cannot escape.  (2)  use Schwartzschild's famous formula for the radius of a "black hole":

R  =  2GM/c.c  where "M" is mass of universe.  If one use numeric value M = 1.58E58 grams (following Sternglass), then one calculates that sun-light will reach the end of our universe after travelling approximately 2.35E30 cm.


How does gravity have an effect from the inside the event horizon of a black hole with the rest of the universe? According to general relativity, as I understand it, the space around a black hole's event horizon is distorted by gravity, such that the distance to a point approaching the event horizon from an observational point further out from the EH approaches infinity.

So if the distance to any mass inside the EH appears to be infinite, how does this mass assert gravitational effects outside the EH?

Perhaps a different question, what is the difference between the gravitational effects of a mass inside the EH of a black hole and a similar mass that is outside the cosmic event horizon of an observational point?

(edit as follows)
My original intent for this question is rethink how we think about black holes.  The distance to a point on the event horizon of Sag A is as far to the point on an observer's cosmic event horizon.  You can travel no farther than such a point on the CEH than you could to a point on Sag A's event horizon, at least using our 4D coordinate system.  BTW, I think all talk about a black hole having a singularity at its center is bunk, first of all, we can never get there to confirm or deny. Secondly, the density of Sag A if it were uniform, would mathematically would be around the density of liquid water as it exists on earth, but we would never be able to know, just as we would we would ever be able to know the density of the universe outside of our cosmic event horizons.  Any answers to those two questions would be meaningless anyway, as long as there is no away around the speed of causality rule enforced by our universe.

Now I believe I have read that Hawking Radiation has been shown to exist.  However, does that mean the part of whatever is outside our cosmic event horizon is evaporating as well?

As is the case even in Newtonian gravity, the gravitational attraction from a spherical body exterted on a far-away object is identical the that exterted by a point mass located at the the center of the body. This is the so-called shell theorem.

To an outside observer, due to the infinite time dilation at the event horizon of a black hole (BH), all mass that has ever fallen into the BH has actually never reached the event horizon, but is instead placed in a shell around the BH, still falling ever-so-slowly toward the BH.

Thus, what we feel is in fact the gravitation not from a point mass, but from a shell of matter, but there is no way for us to tell the difference.

Now you may ask, "What if we drop a massive object, e.g. a planet, into a symmetric black hole? Since it never reaches the BH, won't the effective gravitational potential be asymmetric?" What happens is that the way that space is "warped" around the black, the gravitational field is bent along with it in such a way that sufficiently far from the BH+planet, the gravitational field looks symmetric. Sort of like the following drawing shows close to (left) and far from (right) the BH.

Inside the event horizon, or what is thought of as the mass of the black hole is the section in which you can tell the "strength" of the pull from the singularity. The larger the event horizon (which is initially based on the star it originated from, r= 2GM/c^2, this gives the event horizon radius where G is the gravity constant and c is the speed of light) the stronger the singularity is, and the more dense the black hole is. By adding mass, or having the particle anti-particle pairs forming and then adding mass to the singularity, then the density decreases which decreases its strength therefore it decreases the radius of the event horizon. Where the event horizon is what we "see" or detect through equipment it just takes up more space, and by taking up more space, it has the greater pull on things around it. So basically by the size of the black holes event horizon, it will have a greater pull on things outside in space.


How do we know the universe's expansion is speeding up? Please forgive my ignorance, I am not an astronomer, just an interested layman.

The further away a galaxy is from us, the faster it is moving away from us.  But the galaxies we see exist in the distant past because it takes a long time for their light to reach us. The closer galaxies are, the more recent their light is, and the slower they move away from us. Doesn’t this seem to indicate that the expansion of the universe is slowing down, because the more recent light from galaxies, appears to be moving away slower? Does this make sense?

Quote from Wikipedia:

  Hubble observed that the distances to faraway galaxies were strongly correlated with their redshifts. This was interpreted to mean that all distant galaxies and clusters are receding away from our vantage point with an apparent velocity proportional to their distance: that is, the farther they are, the faster they move away from us, regardless of direction.

As a fellow layman, I'll give this my best shot.

  The further away a galaxy is from us, the faster it is moving away
  from us. But the galaxies we see exist in the distant past because it
  takes a long time for their light to reach us. The closer galaxies
  are, the more recent their light is, and the slower they move away
  from us.

All true.   Think of a single point explosion, at any given time, the object twice as far should be moving twice as fast, cause they both started in the same place at the same time, so twice as fast moves twice s far.   There are, complications - with the explosion there's air resistance, with the universe well, I'll get to that.

  Doesn’t this seem to indicate that the expansion of the universe is
  slowing down, because the more recent light from galaxies, appears to
  be moving away slower? Does this make sense?

OK, it sounds like you have an incorrect assumption there.   Expansion means the far away is moving away faster and the closer is moving away slower, that's true with accelerating or decelerating expansion.

What they look for when studying expansion is measuring the precise speed and comparing that to distance.   In steady expansion, you expect to see the galaxy 8 billion light years away to be apparently moving away twice as fast as the galaxy 4 billion light years away.  (I say apparently cause we can only observe the relative velocity from 8 billion years in the past).

So, whether the galaxy 8 billion light years is traveling slightly more or slightly less than twice as fast away from us as the galaxy 4 billion light years away - that's what tells us about acceleration vs deceleration.

Imagine a car driving 60 MPH, and the driver puts the ever so slightest pressure on one of the pedals, but you don't know which one, and similarly the car driving 30 MPH does the same, but we can only see how fast the 60 MPH car was driving 6 minutes ago and we see how fast the car driving 30 was driving 3 minutes ago - that gives the 30 MPH car more time to apply the acceleration or deceleration.    It's that time differential that gives us the information.

So, like the cars above, the galaxy 4 billion light years away has been in the accelerating expansion of space longer than the one 8 billion years ago and that's what tells us that the acceleration of expansion is happening, the nearer galaxies are moving a bit faster away from us than they would in a steady expansion or a gravitationally slowed expansion.  (edited to make a bit more clear)

  The newer light is moving slower. The older light moving faster. So
  from this it seems that the universe was expanding faster in the past?

light doesn't move slower or faster.  it red-shifts when objects are moving away from each other.  The faster they move away the greater the red-shift.  That's one way relative velocity can be measured.

Brilliant question and great guess. The farther we see in space, the farther we see back in time; and the farther we see back in time, the faster was acceleration. And vice versa.
In fact, our local universe--Laniakea--is contracting. Laniakea is 500 million light years across. It suggests that the expansion stopped 500 million years ago and contraction began.
Galaxies farther than 500 light years away we still see redshifted because more than 500 million years ago they still were running away. Today they are blueshifted but humans will see this blueshift only in very distant future.


How are gravitational lensing and dark matter related? In a lecture which I attended at my institution on gravitational lensing, the lecturer linked gravitational lensing and dark matter research. Can anyone explain what is the relation of both?

Gravitational lensing of background galaxies and quasars is used to probe the amount of gravitating matter in foreground objects such as clusters of galaxies.

Here is an example, taken with the Hubble Space Telescope.

The foreground object is a cluster of galaxies and the lensed background objects, some of which are marked, are galaxies and quasars that are much further away.

The shapes of these lensed objects can be used to deduce the gravitational potential in the foreground cluster. This potential is due both to the galaxies that can be seen, hot intra-cluster gas (that can be seen in X-rays), but chiefly is due to dark matter that pervades the cluster. Thus a combination of optical, X-ray and lensing observations can map the distribution of dark matter and hot gas in the cluster.

An example is shown below for Abell 1689, where the diffuse, blobby emission is a false-colour representation of the density distribution of dark matter inferred to be in this cluster from the many lensed images of background galaxies that can be seen.

http://hubblesite.org/news_release/news/2010-37

A particularly important example that is a landmark in dark matter research is the Bullet Cluster. This is actually two clusters that appear to have collided and passed through each other about 150 million years ago. The distribution of galaxies in the clusters can be seen in optical images; the hot gas can be traced by X-ray observations and the dark matter is traced by looking at the lensed images of distant background galaxies.

The key image is shown below - it illustrates the distribution of optical galaxies, the X-ray-emitting hot gas (pink/red) and the inferred distribution of dark matter (blue).

As the clusters move through each other, the hot gas interacts and piles up into bow-shocks that are displaced from the distribution of optical galaxies. On the other hand, the dark matter, which is thought to consist of non-baryonic, non-interacting particles remains centred on the visible galaxies and each dark matter "cloud" has apparently passed through the other with no interaction occuring.

The displacement between the hot gas and the majority of the gravitating matter, that is dark, is very strong evidence for a non-baryonic particle description of dark matter, rather than some of the alternatives to dark matter like Modified Newtonian Dynamics.

Gravitational lenses magnifies the appearance of themselves so in the case of a galaxy it looks bigger than it is. Thus the outer stars in a galaxy seems to move faster than they do.
For example the Sun deflects light passing from minus infinity to us 1.75 seconds of arc. Say that half of that value is the amount it deflects its own light at its edge, then the Sun looks 200 km wider.


Influences from outside the observable universe explaining dark energy and expansion? Could some influence from outside the observable universe be causing the expansion?

EDIT - The original question was edited to enable it to be reopened, but my answer below responded to the way the question was initially framed. I've left my answer intact as it may be useful in addressing confusion about the difference between "the universe" and "the observable universe".

  Could some pressure from outside of our universe

According to Wikipedia, the Universe is "all of space and time and their contents". So it makes no sense to talk of something "outside" all of space and time.

You might, of course, be referring just to the observable universe, "a spherical region of the Universe comprising all matter that can be observed from Earth at the present time."

However, if the conditions beyond the observable universe are what is causing expansion, then the Universe is neither homogenous nor isotropic. While we have no way of disproving this idea, all the evidence points to a homogenous and isotropic Universe and the vast majority of physicists subscribe to this model.

  causing the expansion

The metric expansion of the Universe is a generic property of the Universe under the FLRW metric, an exact solution of Einstein's field equations of general relativity. There is no need to propose an external cause for the expansion.

I think the original question is valid and I have been pondering that question myself for years

First I am having difficulty understanding the logic in stating there is nothing outside the observable universe. The term 'observable universe' by definition limits knowledge to whatever is observable and does not exclude any thing outside of it that is not observable.  This has been mentioned in earlier posts.

However there could be observable effects within our universe that may give a clue to the existence of an outside influence upon the known universe.

One of these is the fact that distant galaxies are accelerating, apparently, away from us.  One phenomenon that has this ability to cause acceleration is gravity. One hypothesis could be that the distant galaxies are caught in a gravitational field outside our known universe. This would place our known universe within, for want of a better word, a 'bubble' within this gravitational influence causing it to expand in all directions.

Of course this would change the idea of a big bang theory, not in its effect but its origins.  One has difficulty in imagining the whole of our universe being crammed into a single point as unstable as that may be.  However one could imagine it coming into existence by, for want of a better word, 'squirted' into a void within an outside existence of a meta-universe.  This also does away with the need for dark energy as we once thought we needed the ether to carry radio waves.

Karl Popper says that any hypothesis/theory/etc must be falsifiable.  The above  is certainly one of those things. It only needs to be proven non-falsifiable, possibly, with physics not yet known.


Is there a possibility that a white dwarf can turn into a neutron star or a black hole? I know that a white dwarf is mainly balanced by electron degeneracy pressure and that if it gains more than 1.4 solar masses from any source (such as a companion star or a collision), it explodes as a type I supernova. But is there any possibility that a white dwarf can turn into a neutron star (or possibly a black hole)?

The answer is: to a neutron star - possibly; to a black hole, no.

The process whereby a neutron star is formed is known as an accretion induced collapse and is being seriously debated, especially in the case of white dwarfs that are born at the upper end of the "natural mass range" for white dwarfs and then accrete more mass as part of a binary system. An excellent read are the introductory sections of Taurus et al. (2013), who go through the motivation, process and (limited) observational evidence. See also Schwab et al. (2015); Ruiter et al. (2018).

Explosion vs Collapse

A white dwarf can respond to the accretion of material by exploding or collapsing. It depends on the competition between energy released in fusion reactions and the energy being locked away by endothermic electron capture (also known as neutronisation) reactions.

If thermonuclear reactions are initiated then the likely outcome is a runaway nuclear reaction - the pressure inside the star does not rise rapidly enough to prevent the entire star undergoing fusion. The energy released exceeds the gravitational binding energy and the likely outcome is a type Ia supernova.

On the other hand, the white dwarf is supported by electron degeneracy. If neutronisation begins to occur in the core, then protons (in nuclei) capture electrons to form neutrons. This destabilises the star causing it to collapse. The collapse would proceed (quickly) in a similar way to a core collapse supernova. The nuclei would dissociate, neutronisation would run to near-completion and the collapse would be halted by the formation of a neutron star.

There is little possibility that a black hole could be formed by such a collapse. The collapsing object would be of order 1.4 solar masses and comfortably smaller than the maximum mass of observed neutron stars (at least 2 solar masses). Therefore the collapse will be halted at the neutron star phase.

White dwarfs of moderate mass

Most white dwarfs of moderate mass have a C/O composition. They will need to accrete a lot of mass to get to a density (at about $4\times 10^{13}$ kg/m$^3$, reached at $1.38M_{\odot}$ in a non-rotating WD) where neutronisation becomes energetically feasible. Before this happens, it is probable that fusion reactions are ignited (due to high density, rather than temperature). The threshold density for ignition is *lower * for nuclei with lower atomic number (He < C < O) because of lower Coulomb repulsion, and the ignition threshold densities for He and C are also lower than the neutronisation threshold for C.

This means that in a C/O WD that has accreted a lot of matter, ignition could take place in C at the core, or it could be triggered in He (at even lower densities) at the base of a deep accreted shell of material. The outcome would likely be runaway thermonuclear fusion and the complete destruction of the star.

More massive white dwarfs

O/Ne/Mg WDs are made as the final stages of more massive stars ($8-10M_{\odot}$) and are probably born as remnants with much higher mass $>1.2M_{\odot}$ than typical C/O WDs. More massive WDs are smaller, with higher density. The neutronisation thresholds for O, Ne and Mg are only $1.9\times10^{13}$, $6\times 10^{12}$ and $3\times 10^{12}$ kg/m$^3$ respectively (all lower than for C, especially for Ne and Mg). This means that a O/Ne/Mg WD may have to accrete very little mass to reach this central density, begin neutronisation, which leads to collapse. In addition if such densities are insufficient to trigger C burning in a C/O WD, then they certainly won't be high enough to trigger burning in O/Ne/Mg because of stronger coulomb repulsion. Further, if little mass is accreted, then there won't be a deep envelope of accreted material in which to ignite burning off-centre.

For all these reasons, O/Ne/Mg WDs may be more likely (Liu et al. 2018; but see also Wang 2018) to collapse than explode (the collapse would cause a type of core-collapse supernova though).

Does accretion induced collapse occur?

At present there is only indirect evidence. When we look at recently formed neutron stars - identified as fast-spinning pulsars - we see they generally have very high velocities. These velocities are thought to result from an asymmetric "kick" delivered by a type II core-collapse supernova. This in turn suggests it might be quite difficult to retain a neutron star in a binary system, but many neutron stars are observed to be in binary systems, and many of these, particularly the millisecond pulsars, are thought to have undergone significant mass transfer in the past.

Further evidence comes from the retention of a significant population of neutron stars inside globular clusters. Again, the kicks might have been expected to expel most of these. In addition, there are a number of examples which appear to be "young", in that the ratio of their spin periods to rate of spin decay indicates they were formed recently. Since there are no high mass stars in globular clusters, and so no possible progenitors for these objects via the core-collapse of massive stars, then accretion induced collapse of a high mass white dwarf is a possibility.

If it gains enough mass, like if enough matter falls down onto the white dwarf, causing the mass limit to be exceed, then sure