I have to find the time it takes for a particle to travel through a hole drilled

Question

I have to find the time it takes for a particle to travel through a hole drilled through the earth, with using the values G, Re, Me. Where M and R are the radius and mass of the earth. I have already stated that due to the conservative nature of gravity, the time it takes to go the whole way is twice the time it takes to go halfway. To go halfway, have the following

I've combined the whole thing, and its a big huge thing, and i was wondering if there was anyway for me to reduce x into anything. Or is there a different way that im supposed to do this

Explanation / Answer

density of Earth = Me/(4Re3/3)at r from the center of Earth, the gravitational force
F = -Gm(*4r3/3)/r2 = -GmMer/Re3 = m d2r/dt2

d2r/dt2 + (GMe/Re3)r = 0

solution is r = Recos(t), where = (GMe/Re3)

the period T = 2/

the required time is T/2 = [Re3/(GMe)] = 2535 s 42 min

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects