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# Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.

The gravitational force between the earth and an object is called the weight of the object. It is also equal to the product of acceleration due to the gravity and mass of the object.

The magnitude of the gravitational force between the earth and an object on the surface of the earth.

Gravitational Force = F = GMm/ d2

Where G is the universal gravitational constant

M is the mass of the earth

m is the mass of the object on the surface of the earth

d is the distance between the two bodies.

### Newton’s Law of Gravitation

According to Newton’s law of gravitation, “Every particle in the universe attracts every other particle with a force whose magnitude is,

• Directly proportional to the product of their masses i.e. F ∝ (M1M2) . . . . (1)
• Inversely proportional to the square of the distance between their centre i.e. (F ∝ 1/r2) . . . . (2)

On combining equations (1) and (2) we get,

F ∝ M1M2/r2

F = G × [M1M2]/r2 . . . . (7)

Or, f(r) = GM1M2/r2 [f(r)is a variable, Non-contact, and conservative force]

As f(r) varies inversely as a square of ‘r’ it is also known as inverse square law force. The proportionality constant (G) in the above equation is known as the gravitational constant.