Earth spins about its axis with uniform angular speed ω=7.27×10−5rad s−1. Consider a rocket launched radially outward.
(a) Derive an expression for the minimum launch speed required at the equator so that the rocket escapes Earth’s gravitational influence, taking the rotational motion of Earth into account.
(b) Using RE=6.4×106m, ME=6.0×1024kg and the value of ω given above, calculate this launch speed in km s−1.
(c) Determine how much this speed differs from the escape speed that would be required if the rocket were launched from the geographic pole (where the surface tangential speed due to rotation is zero). Express the difference in km s−1.
(d) State one practical advantage of launching space missions from sites near the equator in light of your calculation.