|
First off... think of forces.
The force pulling you down is gravity F(g) = Gm1m2/r
Drag force is proportional to the velocity^2 (double velocity, quadruple drag).
Now, you will accelerate as you move down, but the force will become increasingly smaller as you approach the center (the summation of all the forces from all the mass particles is decreasing).
What will happen is you will accelerate downwards until you reach terminal velocity within your fluid (air likely). This will slowly decrease as the force will decrease.
You will decelerate as terminal velocity drops (your drag force is greater than your gravity force).
Then once you reach the center, you will start to decelerate even further until you stop and switch direction.
With aerodynamic drag acting as a damper (this is a 2nd order diff eqn), you will likely only get a fraction of the distance past the center and slightly oscillate around that until you stop in the center. The damping is actually greater than you would think (on a large scale)
Without drag, you would actually just oscillate back and forth forever.
Make sense?
|