Question

A satellite is to revolve around the earth in a circle of radius 8000 km with what speed should this satellite be projected into the orbit? What will be the time period? (Take g = 9.8 m/$s^2$ and radius of the earth = 6400 km)

Answer 1

The speed of the satellite = v
By using Newton's second law,
$\frac{GMm}{r^2}=\frac{m{v}^2}{r}$
$\frac{v^2}{r}$ is the acceleration of the satellite.
Where, 'r' is the radius of the orbit.
$v^2=\frac{GM}{r}$
But $GM=g{R}^2$
$v^2=\frac{G{R}^2}{r}=\frac{9.8\times (6400{)}^2\times {10}^3}{8000\times {10}^3}$
$v=224km/s$