Question

Question 1

(a)What is the angular frequency $\omega$ of a satellite that orbits the Earth just above the surface? Ignore air resistance . Radius of Earth is R_e and centripetal acceleration is a_c = (v²)/R. The acceleration at Earth's surface is a = g = (GM_e)/(R_e²) where M_e = mass of Earth. Keep your answer in terms of G, M_e, R_e.

(b) How long would it take you to fall through the center of the Earth and come out the other side? Assume no friction , no Earth rotation, and that the Earth is of uniform density. So M(r) = M_e(r/R_e)³ for r<R_e. Again keep you answer in terms of G, M_e, R_e.

(c) Now yo dig a tunnel that doesn't go through the tunnel. Again, ignore friction and assume the Earth is of unifrom density. Hint: note that sin$\phi$ = y/r

Answer 1

we can find the angular frequency of satellite by providing gravitational force as a centripetal force and time by equation of simple harmonic motion as solved below