Correlating/deriving space time bend with law of gravitation

[San K]

We know that

1. Mass causes bend in space-time and this is the how gravitation occurs.

2. The formula for gravitation (per the universal law of gravitation) is product of masses divided by the square of the distance between them and multiplied by the universal gravitation constant.

I wonder if the following been done:

Calculate the amount of "bend" in space time via use of 1 & 2 above.

for example take Earth and sun. both are causing "bends" (3D/4D) in space-time.

 

[elfmotat]

No, you can't. The inverse square law is an approximate special case solution of the Einstein field equations for weak potential and low velocity.

 

[bcrowell]

You're comparing apples and oranges. Force is an interaction between two objects. Curvature is an effect on spacetime that can come from a single object. If you go to a patch of empty interplanetary space, you'll have curvature due to the sun, but there is no force.

But I think the thrust of what you're asking is whether general relativity is consistent with Newton's law of gravity. The answer is yes, in the case of weak fields and velocities much less than c. That's required by the correspondence principle: http://en.wikipedia.org/wiki/Correspondence_principle