Question

derive a formula that relates g with G​

Answer 1

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G is the gravitational constant. It is defined as the force exerted when two objects of mass 1 kg are within a range of 1 m. Its value is 6.67×10−11Nm2kg−2

, as defined in Newton’s law of universal gravitation:

F=GMmr2 , where M is the mass of the planet , m is the mass of the object and r is the radius of the planet for this purpose.

Since M , G and r are constant, we can define a new constant called g - the acceleration due to gravity:

g=GMr2

If you substitute the values for earth, you will find the value of g to be 9.81ms−2 . Be aware that this value is only accurate near the surface since we take the value of r to be the radius (distance from the core to the edge), and the value of g changes depending on where you are.

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Answer 2

Explanation:

G is the gravitational constant. It is defined as the force exerted when two objects of mass 1 kg are within a range of 1 m. Its value is 6.67×10−11Nm2kg−2

, as defined in Newton’s law of universal gravitation:

F=GMmr2 , where M is the mass of the planet , m is the mass of the object and r is the radius of the planet for this purpose.

Since M , G and r are constant, we can define a new constant called g - the acceleration due to gravity:

g=GMr2

If you substitute the values for earth, you will find the value of g to be 9.81ms−2 . Be aware that this value is only accurate near the surface since we take the value of r to be the radius (distance from the core to the edge), and the value of g changes depending on where you are.