 #1
 69
 2
Homework Statement
I'm trying to show that any tunnel through the Earth (not necessarily through the center) will have a freefall time that is the same. I heard this was true somewhere.
Homework Equations
acceleration of freefall = GM / r^2 where r is changing
I believe this involves trig and calculus.
The Attempt at a Solution
I attempted a solution (attached please bear with me. I'm sorry if it's not very clear or if my process is weird).
I considered the acceleration of freefall for a particle at an arbitrary position in a tunnel x that makes an arbitrary angle theta with the radius of the Earth. I eventually solve for the acceleration as a (complicated) function of x and theta.
Not sure what to do after that... If it involves integration, I feel like it's hopelessly complicated.
Attachments

122.9 KB Views: 159