Question

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

Answer 1

Answer:

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

$T^2 = (\dfrac{4\pi^2}{GM_e})r^3$

$r = (\dfrac{T^2GM_e}{4\pi^2})^{1/3}$

$r = (\dfrac{8640^2\times 6.67 \times 10^{-11}\times 5.98\times 10^{24}}{4\pi^2})^{1/3}$

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