The gravitational force is an attractive force that a mass exerts on another mass when the former is placed in the latter’s gravitational field.

Fig 1

In fig 1 above we have two masses m_{1} and m_{2} that are situated at a distance r apart. As you know these two masses will create gravitational fields around themselves such that mass M_{1} will exert a gravitational force F_{2} on mass M_{2} while the mass M_{2} will exert a gravitational force F_{1} on mass M_{1}. That is each mass will exert a gravitational force on the other mass.

And from the third law of motion we know that “For every action there is an equal and opposite reaction.

Hence the gravitational force F_{2} will be equal to the gravitational force F_{1} .

F_{1} = F_{2}

If the two forces are equal then they have the same magnitude and as a result

|F_{1} | = |F_{2} | = F

We can thus replace F_{1} and F_{2} by F as shown in fig 2 below.

Fig 2

**Law of gravitation**

In order to calculate the magnitude of the force that each mass will exert on the other the law of gravitation must be used.

It merely states that the gravitational force that the two objects will exert on each other is directly proportional to the product of the two masses and inversely proportional to the square of their distance of separation.

Simply written in an equation it will be as shown below:

Removing the proportionality sign you will obtain the equation below:

Where G is the universal gravitational constant

G = 6.67 x 10^{-11}N m^{2} kg^{-2}

Example 1

The moon and the earth are separated by a distance of 3.8x 108 m. The mass of the moon is 6.4 x 1022 kg while that of the earth is 6.0x1024 kg. Calculate the gravitational force between the moon.

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