Question

A 2010 kg space station orbits Earth at an altitude of 5.35×105 m. Find the magnitude of the force with which the space station attracts Earth. The mass and mean radius of Earth are 5.98×1024 kg and 6.37×106 m, respectively.

Answer 1

Answer:

Force, F = 16814.95 N

Explanation:

It is given that,

Mass of space station, m = 2010 kg

Altitude, $d=5.35\times 10^5\ m$

Mass of earth, $m=5.98\times 10^{24} kg$

Mean radius of earth, $r=6.37\times 10^6\ m$

Magnitude of force is given by :

$F=G\dfrac{Mm}{R^2}$

R = r + d

$R=6.37\times 10^6\ m+5.35\times 10^5\ m=6905000\ m$

$F=6.67\times 10^{-11}\times \dfrac{2010\ kg\times 5.98\times 10^{24} kg}{(6905000\ m)^2}$

F = 16814.95 N

So, the force between the space station and the Earth is 16814.95 N. Hence, this is the required solution.