Answer to Question #286725 in Classical Mechanics for elle

Question

what is the orbital radius of a 300 kg satellite that completes one circular orbit around the earth every 3.6hr?

Answer 1

Answer

Time period

T=3.6hr=12900 sec.

Mass M=300kg

Using kepler third law

$T^2=\frac{4\pi^2}{GM}r^3$

So radius of satellite

$r^3=\frac{T^2GM}{4\pi ^2}\\$

=$\frac{(12960)^2\times 6.67\times10^{-11}\times300}{4\times(3.14)^2}\\=\frac{3.361}{39.44}\\=0.085$

So radius

r=0.44m