Question

A satellite is in orbit 3.117106 m from the center of Earth. The mass of Earth is 5.9821024 kg. Calculate the orbital

Answer 1

Answer:

T = 1733.16 s = 28.88 min

Explanation:

The orbital velocity of a satellite about Earth is given as follows:

$v = \sqrt{\frac{GM}{R}}$

where,

v = orbital speed = ?

G = Gravitational Constant = 6.67 x 10⁻¹¹ Nm²/kg²

M = Mass of Earth = 5.982 x 10²⁴ kg

R = Orbit Radius = 3.117 x 10⁶ m

Therefore,

$v = \sqrt{\frac{(6.67\ x\ 10^{-11}\ Nm^{2}/kg^{2})(5.982\ x\ 10^{24}\ kg)}{(3.117\ x\ 10^{6}\ m)}}\\\\v = 11.3\ x\ 10^{3}\ m/s$

but the velocity is given as:

$v = \frac{distance}{time}$

for distance = circumference = 2πR

time = time period = T = ?

Therefore,

$11.3\ x\ 10^{3}\ m/s = \frac{2\pi(3.117\ x\ 10^{6}\ m)}{T}\\\\T = \frac{2\pi(3.117\ x\ 10^{6}\ m)}{11.3\ x\ 10^{3}\ m/s}$

T = 1733.16 s = 28.88 min