Question

A satellite orbits Earth at an altitude of 350 km. What is its orbital period? A) 1.1 min B) It can not be determined without the satellite's mass. C) 65 min D) 91 min E) 1440 min

Answer 1

Answer:

The orbital period is 91 min.

(d) is correct option.

Explanation:

Given that,

Altitude = 350 km

We know that,

Radius of earth $r=6.380\times10^{6}\ m$

$R=6.380\times10^{6}+350\times10^{3}$

$R = 6.73\times10^{6}\ m$

Mass of earth $m =5.980\times10^{24}\ kg$

We need to calculate the orbital period

Using formula of orbital  period

$T^2=(\dfrac{4\pi^2}{GM})R^3$

Where,

G = gravitational constant

M = mass of earth

Put the value into the formula

$T^2=\dfrac{4\times3.14^2}{6.67\times10^{-11}\times5.980\times10^{24}}\times(6.73\times10^{6})^3$

$T=\sqrt{30139598.473}\ s$

$T=91\ min$

Hence, The orbital period is 91 min.