Question

How can you calculate how large the perihelion shift should be under Schwarzschild conditions in general relativity for minimally disturbed circular orbits in the strong field limit?

I think there is a functioning expression that works well in the weak fields of our solar system.

What would the perihelion shift be for a minimally disturbed circular orbit just above the minimum stable circular orbit at r=6GM/c^2 and, for instance, at r=9GM/c^2, r=12GM/c^2 and r=15GM/c^2 ?

Answer 1

The perihelion shift under Schwarzschild conditions in general relativity can be calculated using a formula that takes into account the mass of the central object and the distance from the center.

Step-by-step explanation:

The perihelion shift under Schwarzschild conditions in general relativity can be calculated using a formula that takes into account the mass of the central object and the distance from the center. In the strong field limit, the perihelion shift is given by:

Δθ = (6πGM)/(c²r)

where Δθ is the perihelion shift, G is the gravitational constant, M is the mass of the central object, c is the speed of light, and r is the distance from the center of mass. This formula works well in the weak gravitational fields of our solar system, including for the case of Mercury's perihelion shift.

To calculate the perihelion shift for a minimally disturbed circular orbit just above the minimum stable circular orbit at r=6GM/c², we can substitute the values into the formula:

Δθ = (6πG(1.99 × 10³⁰ kg))/(((3.00 × 10⁸ m/s)²)(6(6.67 × 10⁻¹¹ N·m²/kg²)))

Calculating this gives us the perihelion shift for the specified distances of r=9GM/c², r=12GM/c², and r=15GM/c².