- #36
Andre
- 4,311
- 74
Exactly, this would give a complicated movement indeed. However if in the gedanken experiment you would allow for a Earth with uniform mass, the force on the body would be proportional to the distance to the centre. Sounds familiar? It is exactly the same as a mass and spring system. It would oscilate with a sine type movement. If there is no drag, you would oscilate in the hole from the entry on the one end to the exit on the other end indefinitely and it would take exactly the same oscillation time as a hypothetical satelite that would orbit Earth at ground level.That is because all the matter at a sphere above you at equal distance to the center of gravity, will have a neutralized gravity pull. It is as if you were atracted only by the sphere defined by the center of gravity and radius = distance towards the center.
In theory (if Earth would have a constant density everywhere) gravity force would drop linearly, but as the matter deeper down has more pressure on it from above, it is denser and heavier deeper down, so in the beginning the gravity would fall less slow as linearly, and later on faster as you would near the center