Question

A satellite of mass 5000 kg orbits the Earth (mass = 6.0 x 1024 kg) and has a period of 6000 s. In the above problem the altitude of the satellite above the Earth's surface is

Answer 1

Answer:

altitude of satellite from earth surface is 7140 km

Explanation:

given data:

mass of satellite = 5000kg

altitude of satellite from earth surface can be calculated by using given relation

$p^2 = \frac{(4* \pi^2)(a^3)}{(G*M)}$

where,

p -  satellite's period in seconds,

a - satellite's altitude in meters,

G - gravitational constant (6.67 x 10^-11 m³/kgs²) and

M -  mass of Earth 5.98 x 10^24 kg

solving for altitude we have

$a^3 =\fracp{(G*M*p^2)}{(4*\pi^2)}$

$a^3 = 3.637 * 10^{20}$

a = 7,138,000 meters = 7,140 km

altitude of satellite from earth surface is 7140 km