Gravitational Force Formula

Gravitational Force

There are many forces in the world, plenty of pushes and pulls. One still pushes or pulls something, only the field. There are only four fundamental forces in physics from which all new phenomena are derived:  gravitational force, electromagnetic force, strong force and weak force.
Newton’s law of gravity states that the gravitational force among two bodies is proportionate to their masses and inversely related to the square of the distance among them. All bodies, counting you, are tugging on every other body in the whole universe! This phenomenon is termed as Newton’s Universal Law of Gravitation.

The universal law of gravitation states that:

Everybody in the universe pulls every other body with force that is directly proportional to their mass-produced and inversely proportional to the distance square between them.

The Gravitational force formula is given by

\(\begin{array}{l}F=\frac{Gm_{1}m_{2}}{r^{2}}\end{array} \)

G is universal gravitational constant,
m1 and m2 are mass of bodies
r is the radius between the two masses

Solved Examples

Example 1: Calculate the gravitational force if the mass of the sun is 1.99 × 1030 kg and earth is 5.97 × 1024 kg separated by the distance 1.5 × 1011 m?(Gravitational constant G = 6.673 × 10-11 Nm2/Kg2


The gravitational force is given by:

\(\begin{array}{l}F=\frac{Gm_{1}m_{2}}{r^{2}}\end{array} \)
\(\begin{array}{l}\frac{6.673 \times 10^{-11}Nm^{2}/Kg^{2} \times 1.99 \times 10^{30}kg \times 5.97 \times 10^{24}lkg}{(1.5 \times 10^{11}m)^{2}}\end{array} \)

F= (7.93×1044)/(2.25 × 1022)

F= 3.5 × 1022N

Example 2: What will be the force of gravity in between two balls of mass 2 kg and 3 kg separated by 2m distance?

The gravitational force is given by

\(\begin{array}{l}F=\frac{Gm_{1}m_{2}}{r^{2}}\end{array} \)
\(\begin{array}{l}\frac{6.673 \times 10^{-11}Nm^{2}/Kg^{2} \times 2kg \times 3kg}{2m^{2}}\end{array} \)

F = 1 × 10-10 N

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