Question

A satellite of mass $1000kg$ is supposed to orbit the earth at a height of $2000km$ above the earth's surface. Find its speed in the orbit.

Answer 1

From Newton's second law,

$\frac{GMm}{r^2}=\frac{m{v}^2}{r}$

$v=\sqrt{\frac{GM}{r}}=\sqrt{\frac{GM}{R+h}}=\sqrt{\frac{g{R}^2}{R+h}}=\sqrt{\frac{\left(9.8\right){\left(6400000\right)}^2}{6400000+2000000}}=\sqrt{\frac{9.8{\left(6400000\right)}^2}{8400000}}=6.9km/s$

Asnwer is $6.9km/s$