Question

An object when orbiting the Earth at a height of three Earth radii from the center of the Earth has a weight of 1.00 N. What is the object’s mass? (g at the surface of the Earth is 9.8 m/s^2)

Answer 1

Answer:0.918 kg

Explanation:

Given

Object is at a distance of r=3 R from earth surface

where R=radius of Earth

acceleration due to Gravity is given by

$g=\frac{Gm_e}{R^2}$

at earth surface $g=9.8 m/s^2$

g at $r=3 R$

$g'=\frac{Gm_e}{(3R)^2}$

$g'=\frac{Gm_e}{9R^2}$

$g'=\frac{g}{9}$

Weight at r=3R is 1 N

thus Weight at Earth surface will be 9 times at r=3R

weight at  Earth surface =9 N

$mass=\frac{9}{9.8}=0.918 kg$