Question

At weight should a satellite is required to orbit the Earth in a period of 24 hours?

(Orbital period of the moon :27.3 days,

Radius of orbit of the Moon:3.83 × 10^8m)

Answer 1

The centripetal acceleration must be equal to the force of gravity:

$$m\frac{v^2}{R+h}=G\frac{mM}{(R+h)^2},\\\space\\ v^2=G\frac{M}{(R+h)},\\\space\\ \bigg(\frac{2\pi (R+h)}{T}\bigg)^2=\frac{GM}{(R+h)},\\\space\\ h=\sqrt[3]{\frac{GMT^2}{4\pi^2}}-R=35863\text{ km}.$$