Question

Cumulative Problem 3 1 2 What speed is needed to launch a rocket due east near the equator into a low Earth orbit? Assume the rocket skims along the surface of Earth, so r RE. Repeat the calculation for a rocket fired due west 1) What speed is needed to launch a rocket due east near the equator into a low Earth orbit? (Express your answer to three significant figures.) km/s Submit 2) Repeat the calculation for a rocket fired due west. (Express your answer to three significant figures.) km/s Submit

Answer 1

Time period of rotation of earth of its own axis is $T=24\,hrs$

Speed of any point on earth's equator is $v=\frac{2\pi R_E}{T}=\frac{2\pi (6371*10^3)}{24*3600}=463.31\,m/s$ and is directed towards east.

The speed required for the rocket to move in low earth orbit is $v_o=\sqrt{\frac{GM_E}{R_E}}=\sqrt{\frac{6.67*10^{-11}*5.972*10^{24}}{6371*10^3}}=7907.13\,m/s$

The speed needed to launch a rocket due east is $v_{east}=v_0-v=7907.13-463.31=7444\,m/s=7.44\,km/s$

2)

The speed needed to launch a rocket due west is $v_{west}=v_0+v=7907.13+463.31=8370.4\,m/s=8.37\,km/s$