Question

With a mass of 560 kg, Anik A was placed in a geostationary orbit 35,800 km above the Earth's equator. What is Anik A's weight while in orbit?

Answer 1

Answer on Question #43410, Physics, Mechanics | Kinematics | Dynamics

With a mass of $560\mathrm{kg}$ , Anik A was placed in a geostationary orbit $35,800\mathrm{km}$ above the Earth's equator. What is Anik A's weight while in orbit?

Solution.

The relation for weight of object:

$$W = m g$$

Where $g$ is gravitational acceleration. In the orbit force of gravitation is:

$$F _ {g r a v} = \frac {G M m}{(R + h) ^ {2}} = m g = W$$

Where $M$ is mass of Earth, $m$ is mass of Anik A, $R$ is radius of Earth.

So:

$$W = \frac {G M m}{(R + h) ^ {2}}$$

Numerically:

$$W = \frac {6 . 6 7 \cdot 1 0 ^ {- 1 1} \frac {m ^ {3}}{k g \cdot s ^ {2}} \cdot 5 . 9 7 \cdot 1 0 ^ {2 4} k g \cdot 5 6 0 k g}{\left(6 3 7 1 0 0 0 m + 3 5 8 0 0 0 0 0 m\right) ^ {2}} \approx 1 2 6 N$$

Answer: $126N$

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