Question

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

• A. 7.08 km/s, 118 minutes
• B. 11.08 km/s, 18 minutes
• C. 8.08 km/s, 111 minutes
• D. 4.08 km/s, 11 minutes

Answer 1

The correct option is A

7.08 km/s, 118 minutes

Suppose, the speed of the satellite is v.The acceleration of the satellite is $\frac{v^2}{r}$, where r is the radius of the orbit.The force on the satellite is $\frac{GMm}{r^2}$ with usual symbols.Using Newton's second law,

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

or, $v^2=\frac{GM}{r}=\frac{g{R}^2}{r}=\frac{\left(9.8m/s^2\right)(6400km{)}^2}{\left(8000km\right)}$

giving v = 7.08 km/s.

The time period is $\frac{2\pi r}{v}=\frac{2\pi \left(8000km\right)}{\left(7.08km/s\right)}\approx 118$minutes.