Re: Is gravity relative?
- From: Tom Roberts <tjroberts137@xxxxxxxxxxxxx>
- Date: Wed, 08 Apr 2009 13:35:23 -0500
brentlmt@xxxxxxx wrote:
I'm having a bit of a problem resolving what appears to be 2
contradictory
aspects of gravity/relativity.
1. If the sun were to disappear, the earth would continue to orbit
where
the sun was for about 8 minutes until both the sun's light and gravity
would vanish at the same moment.
It is not possible for the sun to just "disappear" -- all of its energy and momentum must go somewhere, they cannot just vanish.
Let me suppose that the sun suddenly splits into two equal parts flying apart with a speed ~0.9 c, neither of which hits the earth. Then yes, knowledge of this splitting would reach the earth simultaneously via light and gravity, ~8 minutes after the split.
2. If the sun was accelerated in some direction instead then the
earth
would be pulled towards where the sun was rather than where it
appeared
to be. This would occur either instantly or over time. If this
occurred
over time then at some point the sun's gravity would have to
propogate
FASTER then light.
Again, this cannot happen without obeying the conservation laws of both energy and momentum.
Let me suppose that the sun suddenly splits into two parts, 99% and 1% of its mass, moving at speeds comparable to c such that momentum and energy are conserved, neither of which hits the earth. The earth will be gravitationally pulled toward both parts, primarily toward the larger. But the acceleration of both parts of the sun would be so great that the earth would be left far behind. That is, gravity is not nearly strong enough to transfer such a huge acceleration to the earth.
If we want the earth to be dragged along with the larger part of the sun, it must move with speed less than the orbital speed of the earth (approximately). In this case the trajectory of the earth would be extremely complicated, and cannot be summarized as "pulled towards where the sun was rather than where it appeared to be". The whole process would take much longer, of course (on the order of years, not 8 minutes).
I guess my question should be how can
we see the sun in one location and "feel" it in another?
Because light and gravity are quite different things. At night we don't see the light from the sun, but we still feel its gravity (though you do need sensitive instruments to measure it anytime).
Consider an inertial frame instantaneously comoving with the earth. In this frame, light from the sun arrives at the earth from a slightly different direction than the direction to the sun's position at the time the light arrives. But the "gravitational force" from the sun felt on earth at that time points toward the sun's position in this frame at that time. Light and gravity just behave differently.
Do not be deceived by this difference in directions into
thinking that "gravity propagates faster than c". In our best
theory of gravity, GR, the "gravitational force" is not
a central force, and the motion of the sun in the above frame
accounts for the difference in direction between light and
"gravitational force". In GR nothing propagates faster than
c, and changes in gravitation propagate at c (which is
what this is).
This is indeed rather subtle. A good place to start learning about this and other interesting aspects of GR, see:
Geroch, _General_Relativity_from_A_to_B_.
Tom Roberts
.
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- Is gravity relative?
- From: brentlmt
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