From: phfrom@nyx.uni-konstanz.de (Hartmut Frommert)
Subject: Re: Two sticky questions on astrophysics
Organization: Dept. of Physics, University of Constance
Date: Tue, 17 Nov 1992 10:44:35 GMT

Although this belongs to sci.astro or sci.physics (but please don't 
crosspost):

ednclark@kraken.itc.gu.edu.au (Jeffrey Clark) writes:

>1. Nothing can travel faster then the speed of light. Therefore
>gravitational influence takes time to travel. 

Right. An approximate formula for the gravitational potential in the 
linearized, Newtonian (weak field) limit of Einstein theory is

  U(r,t) = - G * \int d^3 r' (1/|r-r'|) \rho(r', t - |r-r'|/c)

("retarded" potential)

>Therefore the influence of
>objects on the other side of the galaxy are being felt in our solar system
>as those far flung objects were some 80,000 years ago, yes? More to the
>point the massive centre of our galaxy (possibly contains a mega-black hole)
>will not influence us from it's current position for another 30,000 years.

But from the position where it was 30,000 years ago.

>Now this (according to my naive musings) should not present a problem if we
>are orbiting the centre of our galaxy in a near perfect circular orbit, but
>I would surmise that our solar system would have some eccentricity in it's
>orbit. According to me the solar system is falling toward a non-existant
>centre and has been doing this (as all galactic objects do) since the
>beginning of galactic history.  Should this not cause orbital deviations
>that are measurable? Can someone help me out here please am I missing some
>obvious relativistic point?

Of course there are influences on the Sun's orbit around the galaxy. At
least approximately (i.e. when General Relativity is strictly valid) the Sun
(and with it the Solar System) is moving along a timelike "geodesic", i.e.
the straightest possible line in curved spacetime, where the curvature of
spacetime is caused by the massive bodies in it. 

So for now, you can imagine spacetime as a "deformable" substrate, where all 
mass and energy cause thedeformation, i.e. curvature, at the place and time 
(i.e. "event") they are.
(BTW, this is exactly the physical contents of Einstein field equations.)
The deformations then propagate with the velocity of light, i.e. spacetime 
is no more a static background, but dynamically influenced by matter. On the
other hand, matter is "bound" to spacetime, and a particle, or the Sun and 
planets, trying to move as straight as possible, move along geodesics, i.e.
are effected by the curvature of spacetime, at the place they are.
(BTW, this is expressed in the equation of continuity for the energy momentum
tensor in GR).

>2. An object is detected 15 billion light years away, pushing the beginning
>of time to at least that many years ago. But surely it pushes that time to
>double 15 billion years (ie 30 billion years). 

As nobody has rods to measure the actual distance of the object, one has to 
derive the distance from other features. At that large distances you 
mention, there are (at least to my knowledge) no "standard candles" 
resolvable for telescopes. Instead of a real distance, only the redshift
of the object is measured. According to Hubble's law of expansion, you may
then calculate the corresponding distance, depending on the Hubble constant.
Therefore you can only conclude that the object is seen at a time when the
universe was, say, 10 % as large as now (it's rather complicated, indeed). 
This may be 15 billion light years in one and 8 billion in another model.
Thereby you can, of course, never conclude how old the universe is, from the
distance of objects: The 15 billion years come from the theory of stellar 
evolution (age of globular clusters in our Milky Way galaxy).

BTW: If we knew H_0  we could determine the approximate distance *today* 
  from Hubble's law.

>Nothing can travel faster
>than light. 

That is true only locally. But the object observed is (at least 
approximately) at rest locally, i.e. moving at most with some % of light 
velocity with respect to its own neighborhood. Only at the large distance 
it *seems* to move nearly with v=c, because the universe expands. Therefore
it is well possible that there are regions of the universe that seem to
escape faster than light from us.

>The object that generated that radiation did so 15 billion years
>ago from 15 billion light years away. But first we had to get 15 billion
>light years away from this object. Both the object and the particles that we
>consist of must have been together at the Big bang. In order for the light
>to have taken 15 billion years to reach us, the object must have been 15
>billion light years away from our current position 15 billion years ago. In
>other words the earth and the object relative to each other must have been
>travelling for some 15 billion years (at least) to get that far apart before
>the light was emmitted from far-flung object. Once again am I missing some
>obvious relativistic point or have I just doubled the age of the universe?

As above, all the events you describe are local, according to GR. The light
was emitted by the object approx. 15 billion years ago. Then it was moving
with v=c, getting redder and redder due to cosmic expansion, independent of 
the emitter as well as the observer. At last, after traveling a long time 
and distance, which is difficult to calculate exactly, it arrived at a 
telescope, and we can calculate the distance, etc. from the redshift. That 
we can observe the latter is only possible because the spectra of the 
chemical elements are the same at the place and time of emision in the 
distant object and in Earth based laboratories.

>[...] Depending on the answers I've got some other queries as well.

But please don't post them on sci.space.
 Hartmut Frommert                 <phfrom@nyx.uni-konstanz.de>
 Dept of Physics, Univ of Constance, P.O.Box 55 60, D-W-7750 Konstanz, Germany
                                           -- Eat whale killers, not whales --