Question

A satellite with a mass of 2273 kg is at an altitude of 42873 km above the surface of Saturn what is the strength of the gravitational force on the satellite

Answer 1

Answer on Question #64001, Physics / Mechanics | Relativity

Question:

A satellite with a mass of 2273 kg is at an altitude of 42873 km above the surface of Saturn. What is the strength of the gravitational force on the satellite?

Solution:

Gravitational force between two bodies may be calculated according to this formula:

$$F _ {g r} = G \frac {m _ {1} m _ {2}}{R ^ {2}},$$

where $G$ — gravitational constant $(6.674 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2})$,

$m_{1}$ and $m_{2}$ — masses of the bodies,

$R$ — distance between its centres.

In our case we must take into account Saturn’s radius (58232 km) and mass (5.683·10²⁶ kg).

So $R = 42873 + 58232 \, \text{km} = 101105 \, \text{km} \cong 1.011 \cdot 10^{8} \, \text{m}$

And thus $F_{gr} = 6.674 \times 10^{-11} \frac{2273 \cdot 5.683 \cdot 10^{26}}{(1.011 \cdot 10^{8})^{2}} = 8434 \, \text{N}$

Answer:

8434 N

https://www.AssignmentExpert.com