Question

The geostationary orbit of the earth is at a distance of
about 36000 km from the earth's surface. Find the
weight of a 120-kg equipment placed in a geostationary
satellite. The radius of the earth is 6400 km.​

Answer 1

Given :-

The radius of the earth = 6400 km

Equipment weight = 120 kg

Geostationary orbit of the earth is at a distance of about 36000 km from the earth’s surface.

To Find :-

The  weight of a 120-kg equipment placed in a geostationary  satellite.

Solution :-

We know that,

• r = Radius
• g = Acceleration of gravity
• d = Distance

Given that,

The radius of the earth (r) = 6400 km

Equipment weight = 120 kg

Also given, geostationary orbit of the earth is at a distance of about 36000 km from the earth’s surface.

According to the question,

The value acceleration due to gravity above the surface of the Earth.

$\sf g'=G \times \dfrac{m}{(R+h)^{2}}$

Substituting their values,

$\sf g'=G \times \dfrac{m}{(36000+6400)^{2}}$

Acceleration due to gravity is 9.8 m/s²

$\sf g'=G \times \dfrac{m}{(6400)^{2}}$

$\sf 9.8=G \times \dfrac{m}{(6400)^{2}}$

Now, the ratio

$\sf \dfrac{g'}{g} =\dfrac{G \times \dfrac{m}{(36000+6400)^{2}} }{G \times \dfrac{m}{(6400)^{2}} }$

$\sf =0.0228$

$\implies \sf g'=0.0228 \times 2.8 =0.223$

Taking g = 9.8 m/s² at the surface of the earth

For a 120 kg equipment placed in a geostationary satellite, it will be mg' = 120 × 0.233

$\implies \sf 2.67 \approx 27 \ N$