Question

how to derive expression for gravitational constant

Answer 1

The acceleration due to gravity acting on any object can be given using the following equation:

When the object is on or near the surface of the body, the force of gravity acting on the object is almost constant and the following equation can be used.



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Answer 2

Hey Mate ....
FORMULA

The acceleration due to gravity acting on any object can be given using the following equation:



Here, G is the universal gravitational constant whose value is fixed and is equal to 6.673 × 10-11 N.m2/Kg2. M is the mass of the body whose gravitational pull is acting on the object under consideration, r is the radius of the planet and h is the height of the object from the surface of the body.

When the object is on or near the surface of the body, the force of gravity acting on the object is almost constant and the following equation can be used.



DERIVATION

From the Newton’s Second Law of Motion, we can write

F=ma

Here, F is the force acting on the object, m is its mass and ‘a’ is the acceleration.

Also, as per Newton’s Law of Gravity, we can write,



It is the gravitational force acting between two bodies lying in the gravitational field of each other. This force acts inwards and is attractive in nature. Each of the two bodies experience the same force directed towards the other.

Using the Newton’s second law of motion, in order to find the acceleration of the body under this condition,



Here, m is the mass of the object for which the acceleration due to gravity is to be calculated.





Also, when the object is on or near to the surface the value of g becomes constant and does not change considerably with the height. Hence, we can write,





Hope it helps You