Question

An artificial satellite circling the Earth completes each orbit in 144 minutes. (a) Find the altitude of the satellite.

Answer 1

Step-by-step explanation:

given,

time taken to complete the each orbit = 144 minutes

t = 144 x 60 = 8640 s

mass of the earth = 5.98 x 10²⁴ Kg

radius of earth,R = 6.38 x 10⁶ m

Using Kepler's 3rd law

`T^2 = ((4\pi^2)/(GM_e))r^3`

`r = ((T^2GM_e)/(4\pi^2))^(1/3)`

`r = ((8640^2* 6.67 * 10^(-11)* 5.98* 10^(24))/(4\pi^2))^(1/3)`

r = 9.1 x 10⁶ m

the altitude of the satellite

H = r - R

H = 9.1 x 10⁶ - 6.38 x 10⁶

H = 2.72 x 10⁶ m