Video: The Gravitational Force between Two Bodies at Different Distances

If the gravitational force between two masses was 10 newtons at a certain distance, what would the gravitational force become if that distance was doubled?

02:11

Video Transcript

If the gravitational force between two masses was 10 newtons at a certain distance, what would the gravitational force become if that distance was doubled?

Newton’s law of universal gravitation states that for two masses 𝑚 one and 𝑚 two, the force of gravity 𝐹 between them will be given by the following relation: 𝐹 is equal to 𝐺 multiplied by 𝑚 one multiplied by 𝑚 two divided by 𝑠 squared, where 𝐺 is the gravitational constant, 𝑚 one and 𝑚 two are the two masses, and 𝑠 is the distance between them.

In this case, we have that 10 is equal to 𝐺 multiplied by 𝑚 one multiplied by 𝑚 two divided by 𝑠 squared. Our new force 𝐹 one when the distance has doubled is equal to 𝐺 multiplied by 𝑚 one multiplied by 𝑚 two divided by two 𝑠 squared. As two 𝑠 all squared is equal to four 𝑠 squared, we can say that 𝐹 one is equal to 𝐺 multiplied by 𝑚 one multiplied by 𝑚 two divided by four 𝑠 squared.

This can be rewritten as 𝐹 one is equal to a quarter of 𝐺 multiplied by 𝑚 one multiplied by 𝑚 two divided by 𝑠 squared. As the initial gravitational force was equal to 10 newtons, we can substitute 10 into this equation: 𝐺 multiplied by 𝑚 one multiplied by 𝑚 two divided by 𝑠 squared is equal to 10.

This means that 𝐹 one is equal to a quarter multiplied by 10. A quarter of 10 is five over two or five halves. This is equal to 2.5 newtons. Therefore, when the distance between the two masses is doubled, the gravitational force has quartered or we have divided it by four.

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