Space-time molded by the mass

[quiet]

I want to talk about a detail of General Relativity that has always puzzled me, with the hope of acquiring concepts that allow me to understand that detail naturally.

Suppose a road operator declared the following. I have not caused the fall of the old woman. I have only dug the well where she introduced the foot.

General Relativity proposes a logic similar to the operator's argument, since it implies the following idea. No massive object causes gravitational force on another. It only contributes to shape the spacetime and at the same time, in the place where it is, it obeys the local form of the molded spacetime.

Example. In the vicinity of the sun, the form of spacetime depends a lot on the solar mass and little on the masses of the planets, on the stars that are not the sun, etc. The orbit that a probe travels around the sun depends a lot on the sun.

Far away from the Sun are the most massive planets in the solar system. Those planets orbit around the sun. Does that mean that also at distant points, where there are several planets with huge masses, the greatest contribution to the local form of spacetime corresponds to the Sun?

[Strange]

The effect of gravity falls off as the inverse square of distance. So, close to those planets, their effect on spacetime curvature dominates (hence their moons orbit them) but, further from the planets, the sun’s mass dominates. Hence they all orbit the sun (with slight deviations caused by the presence of the other planets). 

[quiet]

45 minutes ago, Strange said:

The effect of gravity falls off as the inverse square of distance.

Hello, Strange. General Relativity baffles me, not Newton's formula.

[Strange]

5 minutes ago, quiet said:

Hello, Strange. General Relativity baffles me, not Newton's formula.

They are equivalent (in low energy contexts like this). 

[quiet]

9 minutes ago, Strange said:

They are equivalent (in low energy contexts like this). 

My bewilderment is not alleviated by showing that RG and Newton's formula give very similar results quantitatively. It is not a quantitative bewilderment. It is conceptual, referring to the role of spacetime and the relation of its local form to the distribution of mass ... of the whole universe?

[beecee]

1 hour ago, quiet said:

Example. In the vicinity of the sun, the form of spacetime depends a lot on the solar mass and little on the masses of the planets,

Quote

on the stars that are not the sun, etc. The orbit that a probe travels around the sun depends a lot on the sun.

 

Quote

Far away from the Sun are the most massive planets in the solar system. Those planets orbit around the sun.

Does that mean that also at distant points, where there are several planets with huge masses, the greatest contribution to the local form of spacetime corresponds to the Sun?

Ok, I'm going to assume you are talking about "hot Jupiters"  and extra solar planets with regards to the parts I have highlighted from your post.

I believe that most astronomers/cosmologists accept planetary migration as a means of explaining the Jupiter size planets that orbit other stars. This would logically happen due to interactions with smaller debris from the planetary disk, extra densities in the inter stellar gas which would/could act to change orbital parameters to varying extents. This is also hypothesised to have occurred within our own solar system with Jupiter much closer in with the early stages of the solar system, and having migrated outwards.

I'm not sure what this has to do with GR as it is explained by Newtonian concepts, but I'am sure that GR does not vary from the conclusions.

The spacetime warpage mad by the Sun, keeps all the planets in orbit, while the planets themselves create smaller warpages which keep the moons in orbit about themselves, and any over-lapping of warpages, can also have overall effects on other bodies within the system.

Not sure if any of that has covered your query but anyway........

[Strange]

4 minutes ago, quiet said:

My bewilderment is not alleviated by showing that RG and Newton's formula give very similar results quantitatively. It is not a quantitative bewilderment. It is conceptual, referring to the role of spacetime and the relation of its local form to the distribution of mass ... of the whole universe?

I'm not quite sure what your confusion is. The curvature caused by the presence of mass extends to infinity and so always has some (rapidly diminishing) effect. It will readily be overwhelmed by the local curvature caused by other masses. (And, at a sufficient distance, all those masses can be treated as one - for example at a distance the curvature caused by the entire solar system can be approximated by a single object with the mass of the sun plus all the planets.)

[studiot]

Popular explanatory diagrams often show huge amounts of curvature, whereas in reality even Jupiter sized planets cause very mild levels of curvature.

The original experimental proof of the curvature at the surface of the Sun sought a deflection of 1.6 seconds of arc for grazing light.

The masses required to create Swartzchild conditions are many times larger.

Perhaps Marcus could comment on this or Mordred (if he comes back). This is really their baby.

[quiet]

30 minutes ago, beecee said:

Not sure if any of that has covered your query but anyway........

 

27 minutes ago, Strange said:

I'm not quite sure what your confusion is.

beecee, Strange, very interesting all those data. I take them, regardless of how much relationship they have with my conceptual confusion. Thank you very much.