Physics

Problem

Consider a satellite moving very close to the Earth’s surface in a circular path. a. (i) Starting from the general expression for orbital speed obtained from fundamental laws, show that for an orbit where the altitude

h

is negligible compared to the Earth’s radius

R_{\rm E}

, the speed can be written as

v=\sqrt{gR_{\rm E}}

, where

g

is the acceleration due to gravity at the surface. b. (ii) Using

g=9.8\,\text{m\,s}^{-2}

and

R_{\rm E}=6.37\times10^{6}\,\text{m}

, evaluate the speed numerically. c. (iii) Hence find the minimum horizontal speed that must be imparted to a projectile at the Earth’s surface so that it just enters such a circular orbit, assuming no air resistance.

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