The acceleration due to gravity is inversely proportional to the square of the distance from the centre of Earth. The acceleration due to gravity for a satellite orbiting 7000 km above the centre of Earth is 8.2 m/s^2.

Question

a) write a formula for this relationship.

b) at what height will the acceleration due to gravity be 6 m/s^2?

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I do not know how to approach this question because.. well all I know is that this function needs to be a rational function because this is the topic we are on. Please help and describe why you are doing the steps. Thanks in advance!!

Answer 1

g(d)=K/d^2
where
d= distance in km,
g= acceleration in m/s^2

Use the following relationship to find K
g(7000)=8.2 m/s^2
then use the calculated value of K to find
g(x)=6 m/s^2

Answer 2

addendum:
then use the calculated value of K to find x, where x is the distance from the centre of the earth to be found.
g(x)=6 m/s^2