Newton's Law of Gravitation: Balancing Centrifugal Force & Internal Pressure

[Osvaldo]

How is the centrifugal force in an orbiting planet or star, balanced if according to Einstein there is not such gravity force and is only space time curvature. Also, how come in order to determine internal pressure of a planet or star, the force acting near the center is calculated using the Newton formula F = G mM/Rsquared.
Then was Newton wrong? If so why this formula still aplly?

 

[FactChecker]

Both questions are doubts about the amount of curvature giving the same effect as gravity -- not about whether there can be curvature that changes the definition of a "straight path". The fact is that the amount of curvature, both near and at a distance of R, and the resulting effect do match the effect of gravity. If they did not match, then there really would be a problem.

PS. Probably a better term than "straight path" would have been "unaccelerated path in space-time". The completely correct term is "geodesic path".

 

[PeroK]

How is the centrifugal force in an orbiting planet or star, balanced if according to Einstein there is not such gravity force and is only space time curvature?

In Newton's gravity, there is no centrifugal force. Instead, gravity provides a centripetal force that keeps an object in orbit. There is only one (inertial) force in this case.

In General Relativity, there are no forces on an orbiting body. Instead, its path through spacetime is a natural one (technically called a geodesic).

To calculate the path of an object in curved spacetime, you can use the Lagrangian principle. For the spacetime round a spherically symmetric star like the Sun, this gives a very close approximation to Newton's law of gravity.

 

[Dale]

How is the centrifugal force in an orbiting planet or star, balanced if according to Einstein there is not such gravity force and is only space time curvature.

There is no such thing as the centrifugal force either. (In exactly the same sense)

 

[Ibix]

In inertial frames in Newtonian physics, things move on straight lines if no unbalanced forces act on them. So there must be an unbalanced force if an object is not moving in a straight line - and that force is gravity.

General relativity basically modifies Newton's first law. Things experiencing no force don't move in straight lines. They follow paths called "geodesics". Far from any source of gravity, these are (arbitrarily close to) straight lines. Close to sources of gravity they (or their spatial projections) are curves. So no centripetal force is necessary because the orbital path is inertial.

 

[A.T.]

How is the centrifugal force in an orbiting planet or star, balanced if according to Einstein there is not such gravity force and is only space time curvature.

In Newtonian mechanics the inertial centrifugal force is used in rotating frames of reference. In General Relativity you instead use a different space-time metric for the rotating frame, and there is neither a force of gravity, nor a centrifugal force.