Question

Almost every beginning physics course will teach you that the force on an object due to gravity is F = mg, where g is just the acceleration due to gravity at the surface of the Earth. In other words, this equation is just a specific example of Newton’s second law. The mass of the Earth is M⊕ and the radius of the Earth is R⊕. Write down an expression for g in terms of M⊕ and R⊕.

Answer 1

Answer: g = GM0/R0

Explanation:

Second law of Newton (gravitational law) postulates that

The gravitational force on a body on the earth is

i) directly proportional to the mass of earth M0

ii) directly proportional to the mass of the object m

iii) inversely proportional to the raduis R0 of earth.

The gravitational constant G is the proportional constant linking all of these parameters

F = GM0m/R0

But F = mg

Where F is the weight (i.e gravitational force on the object)

m is the mass of the object and

g is the acceleration due to gravity

Hence mg = GM0m/R0

m is cancelled as it exists on

both sides

GM0/R0 = g

Therefore

g = GM0/R0