The gravitational force between a planet and its moon is 6 &#x00D7;<!-- × --> 10

anniferathonniz8km

anniferathonniz8km

Answered question

2022-05-08

The gravitational force between a planet and its moon is 6 × 10 16 N. For another moon orbiting the same planet with twice the orbital radius and 3 times the mass, what is the gravitational force?

Answer & Explanation

Skyler Barber

Skyler Barber

Beginner2022-05-09Added 17 answers

Step 1
The given data are:
F = 6 × 10 16 N R = 2 R M = 3 M
Here, F denotes the gravitational force, R' denotes the radius of the second moon, R denotes the radius of the first moon, M' denotes the mass of the second moon, M denotes the mass of the first moon.
Step 2
The gravitational force between the planet and the first moon can be given as,
F = G M m R 2
The gravitational force between the planet and the second moon can be given as,
F = G M m ( R ) 2 = G ( 3 M ) m ( 2 R ) 2 = 3 4 ( G M m R 2 ) = 3 4 F = 3 4 ( 6 × 10 16 N ) = 4.5 × 10 16 N

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