if the distance between a spaceship and the center of the earth is increased from one earth radius to four earth radii, the gravitational force acting on the spaceship becomes approximately?

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Jimm1961 Jimm1961

15-12-2022
Physics

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if the distance between a spaceship and the center of the earth is increased from one earth radius to four earth radii, the gravitational force acting on the spaceship becomes approximately?

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sarbajitpanda sarbajitpanda · Answer 1 · 2022-12-22T02:51:00-05:00

The gravitational force acting on the spaceship becomes approximately 1/16 of the initial gravitational force between the earth and the spaceship.

What is gravitational force?

Each object having mass attracts other objects having mass towards itself with a certain force known as Gravitational Force. Therefore, this force can be described as a study of the attraction between two masses.

The magnitude of Gravitational force has an inverse relationship with the square of the distance between the center of the respective masses and is directly proportional to the multiplication of the masses. Therefore, the gravitational force can be written as:

[tex]\displaystyle F= G\frac{M_1M_2}{r^2}[/tex]

If the distance between a spaceship and the center of the earth, R = 4r

[tex]\displaystyle F'= G\frac{M_1M_2}{R^2}[/tex]

[tex]\displaystyle F'= G\frac{M_1M_2}{(4r)^2}[/tex]

[tex]\displaystyle F'= G\frac{M_1M_2}{16r^2}[/tex]

[tex]\displaystyle F'= \frac{1}{16}F[/tex]

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