Question

A satellite is orbiting Earth at a distance of 42.0 kilometers. The satellite has a mass of 900kilograms. What is the force between the planet and the satellite? Hint: Recall Earth's mass aradius from earlier problems.

Answer 1

8716.97 N

Step-by-step explanation:

The force between the planet and the satellite can be calculated using the following equation

`F=G(m_1m_2)/(d^2)`

Where G = 6.67 x 10^(-11) N m²/kg², m1 is the mass of the satellite, m2 is the mass of the Earth and d is the distance from the center of the Earth to the satellite

Since the radius of the Earth is 6,371 km, we get

d = 42 km + 6,371 km = 6413 km

Then, to convert to m, we need to multiply by 1000

d = 6413 km x 1000 m/km = 6.413 x 10^6 m

Finally, replacing m1 = 900 kg, m2 = 5.972 x 10^24 kg, and d = 6.413 x 10^6 m, we get:

`\begin{gathered} F=6.67*10^(-11)((900)(5.972*10^(24)))/((6.413*10^6)^2) \\ F=8716.97\text{ N} \end{gathered}`

Therefore, the force between the planet and the satellite is 8716.97 N