Question

a geostationary satellite moves in an orbit of radius 6300km calculate the speed with which it moves in the orbit.

Answer 1

We have to find the speed of a geostationary satellite moves in an orbit of radius 6300 km.

solution : let the mass of geostationary satellite is m.

at equilibrium,

the centripetal force acting on the geostationary satellite equals to the gravitational force acting between the satellite and the earth.

i.e., centripetal force = gravitational force

⇒ $\bf{\frac{mv^2}{r}=\frac{GmM_{\text{earth}}}{r^2}}$

⇒ $\bf{v=\sqrt{\frac{GM_{\text{earth}}}{r}}}$

here radius of orbit, r = 6300 km = 6.3 × 10⁶ m

mass of earth, $M_{\text{earth}}$ = 6 × 10²⁴ kg

value of G = 6.67 × 10⁻¹¹ Nm²/kg²

now, speed of the geostationary satellite, v = $\sqrt{\frac{6.67\times10^{-11}\times6\times10^{24}}{(6.3\times10^6)}}$

= 7.97 km/s ≈ 8 km/s

therefore the speed of the geostationary satellite is  8 km/s.