Question

Match the formulas for different quantities of satellites.
Assume terms have their standard meanings.

• A. $\sqrt{\frac{GM}{R+h}}$
• B. $2\pi \sqrt{\frac{{(R+h)}^3}{GM}}$
• C. $\frac{GM}{{(R+h)}^2}$

Answer 1

Using universal law of gravitation and newton's second law of motion,
$F=mg=\frac{G{M}_{e}m}{(R_e+h{)}^2}$
$g=\frac{G{M}_e}{(R_e+h{)}^2}$

Using formula for centripetal acceleration,
$g=\frac{v^2}{R_e+h}$
$v=\sqrt{\frac{G{M}_e}{R_e+h}}$

For uniform circular motion, time period is given by:
$T=\frac{2\pi (R_e+h)}{v}$
$T=2\pi \sqrt{\frac{(R_e+h{)}^3}{G{M}_e}}$