Question

How much is the gravitational force that keeps an artificial satellite of mass 3500 kg in orbit around the earth at an altitude of 4200 km

Answer 1

The gravitational force acting on the satellite is $1.42\times 10^4\ N$.

Explanation:

It is given that,

Mass of the satellite, m = 3500 kg

Altitude at which the satellite is orbiting is 4200 km or $42\times 10^5\ m$

Mass of the Earth, $M=6\times 10^{24}\ kg$

Radius of Earth is 6400 m.

Total distance is, $r=(6400+3500)\ km=9900\times 10^3\ m$

Gravitational force is given by :

$F=G\dfrac{mM}{r^2}$

$F=6.67\times 10^{-11}\times \dfrac{6\times 10^{24}\times 3500}{(9900\times 10^3)^2}$

$F=1.42\times 10^4\ N$

So, the gravitational force acting on the satellite is $1.42\times 10^4\ N$. Hence, this is the required solution.

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