The change in the value of g at a height at a depth d below the surface of earth. When both d and h are much smaller than the radius of earth, then which one of the following is correct?

When analyzing the change in gravitational acceleration g at a height h above or a depth d below the Earth’s surface, the variations depend on their relationship to the Earth’s radius R. For both h and d much smaller than R, the following approximations hold:

1. At a height h above the surface, g decreases proportionally to 1 – 2h/R, due to the inverse square law of gravitation.
2. At a depth d below the surface, g decreases proportionally to 1 – d/R, because the effective mass contributing to gravity reduces linearly with depth.

If d = 2h, the proportional reduction in g at height h and depth d would be equivalent, demonstrating a symmetry in the changes under these conditions.