Gravity along a shifted sun-earth line?

[nomadreid]

The fact that gravity takes 8 minutes (or a bit more) to get to the Earth would seem to imply that the perpendicular to the Earth's orbit should be aligned along a line between the Earth and where the sun was eight minutes ago. This would not be a problem if the orbit were perfectly circular and the sun didn't move, but neither of these conditions is true. So why does not the orbit become unstable?

 

[ashwaninair]

Hi Nomadried,

A small correction, its light that we assume to reach Earth in 8 minutes. If we are to assume that gravity takes 8 minutes its only because that's how strong our measuring equipments are. We don't know the speed at which gravity acts.

Again, when you say "if the orbit is circular and if the sun dint move", it depend on your reference. I.e. if you are on the sun, then it don't move. So, when you consider Sun and Earth as a system, then Sun don't move. Also, elliptical orbits are as stable as circular as both will exchange energy with the system.

To your specific question. The orbit is not stable. We (earth) are moving away from Sun, but very slowly as universe expand. Also, we are not just acted upon by Sun's gravity, but many (many many many) other bodies in the universe. Each body act upon every other body, its just the magnitude of that force that differs. For e.g. when in earth, we feel the Earth's gravity more than any other planet's gravity.

Hope this is of some help.

 

[nomadreid]

Ah, OK, I should have been a bit more precise, saying that gravity is assumed to travel at the maximum speed of information, but that is a red herring, because all I need in my question is that the movement of gravity is instantaneous. Also, I should have asked whether the time lapse I mentioned introduces any more instability into the Earth's orbit than the ones already classically attributed to things like the sun's loss of mass, the other gravitational influences in the solar system, and so forth. I also realize that an elliptical system can be stable, but the point is that the point is that in an ellipse, although one treats the center of the ellipse in a lot of calculations as the effective center, the gravity itself is a relation to the relevant focus, and not the center. I also understand that for most things the movement of the sun with respect to the galaxy is negligible because the solar system forms a tightly-knit system in its gravitational relations, but my question precisely questions how close knit that really is. Given all these caveats, my question could be restated as follows:
Do precise calculations concerning the gravitational relations of the Earth to the sun proceed with the assumption that the Earth's centripetal vector is pointing to where the sun was at t = (the present time minus the time the gravitational information took to reach the earth), or is there some "correctional measure" that is included in the gravitational information that allows one to calculate the vector as pointing to where the sun is at the time the information is received?

 

[ashwaninair]

Hi Nomadreid,

I should admit here that I don't know the answer to your specific question, but just a thought.

We are talking about a distance which is 8 x 60 X c meters = 8 x 60 x 3 X 10^8 meters.

How much difference will it make in terms of vector angle towards the direction of sun. Also, it would specifically depend on what is your reference to measure sun's motion. As mentioned earlier, if the system you consider is only Earth and Sun, the vector (direction) would change because of Earth's motion around sun and not because Sun is itself in motion WRT some other celestial body.

So, I would assume that, it is safe to assume the direction towards sun (which is constant WRT earth). But remember this may not be perpendicularly inward but at an angle considering the position of Earth in its elliptical path at that point of time.

 

[D H]

A small correction, its light that we assume to reach Earth in 8 minutes. If we are to assume that gravity takes 8 minutes its only because that's how strong our measuring equipments are. We don't know the speed at which gravity acts.

General relativity says that gravitation propagates at the speed of light. Some experiments have confirmed this hypothesis, but whether those experiments were measuring the speed at which gravity versus light propagates is in question.

19^th physicists showed that orbits would be unstable if Newton's law of gravity was to be modified to incorporate a delay term. However, that delay is not the only difference between Newtonian gravity and general relativity There are other predictions from general relativity that come very close to canceling out this time delay for smallish masses and velocities. The end result is that gravitation does not appear to have a lag.

The effects do not quite cancel for Mercury. 19^th physicists had also discovered that Newtonian gravity could not fully explain the precession of Mercury's orbit. General relativity did explain that mismatch between theory and observation.

 

[nomadreid]

First, to D H: thank you, your post was very interesting. Please correct me if I am wrong, but are you saying that the bending of spacetime (or the effect of the stress tensors, or however you wish to phrase it) around the sun causes gravity to act as a "curve ball" so that the gravity absorbed (for lack of a better word) by the Earth at time t from the sun acts as if it were coming in a straight line from the sun's position at t rather than at t-minus-eight-minutes? But that the curve doesn't quite do the same for Mercury, so that tracing the light back at time t in a straight line would miss the sun? In any case, would these effects have anything to do with the rate of the sun's rotation, so that if the sun were rotating, say, in the opposite direction to the earth, the Earth would also precess? ( I take "learn from your mistakes" quite seriously, so I put my neck out in order to have it cut off, so hack away!)

to ashwaninair's remarks: thanks for your thoughts. 500 seconds of time difference for gravity's trip would correspond to about 21 seconds of arc, or about 1500 kilometers. It is not a foregone conclusion that these numbers are insignificant. And yes, you are correct, I should not have used the word perpendicular, as the elliptical shape would alter this a bit. I do not understand your comment that the direction earth-sun is constant.