Recent content by ActaPhysica

G * 4/3 rho pi r = a = d^2r / dt^2 4/3*G*rho*pi dt^2 = 1/r d^2r 4/3*G*rho*pi *t dt = Ln (r) dr 4/3*G*rho*pi * t^2/2 = r*Ln(r) - r Is this detailed enough?

Well if you integrate 1/r that gives Ln(r) And if you integrate Ln(r) it gives rLn(r) - r The other side is pretty straightforward.

It's not my Hooke's Law it's Hooke's Law :) Can you point out my mistake?

The usual approach for solving for the time it takes to fall to the center of the earth neglects air resistance & uses Hooke's Law. But if you solve it "the hard way"... Gme*m/r^2 = ma me = 4/3 rho pi r^3 G * 4/3 rho pi r = a separate variables, integrate twice r*Ln(r) - r = 2/3 G rho pi t^2 The...