Universal Gravitation Formula

Gravity is the attractive force that exists between any two objects in the universe. Such an attractive force between two objects depends on the masses of the objects involved as well as on the distance between the objects. Newton’s Law of Universal Gravitation is very important in this regard. It quantifies this attractive force by an important equation. This article will explain this Universal Gravitation Formula with examples.

What is Acceleration due to Gravity?

Acceleration due to gravity is the acceleration due to the gravitational force. It has a magnitude as well as direction. We represent acceleration due to gravity as g. Its standard value on the surface of the earth is 9.8 ms². Its computation formula is based on Newton’s Law of Universal Gravitation.

What is the Universal Gravitational?

In close distance to the surface of Earth, the acceleration due to gravity is approximately constant. But, at large distances from the Earth, or around other planets or moons, it is varying. The law of universal gravitation states that any two objects in the universe attract each other with a weaker kind of force. This force is directly proportional to the product of their masses, whereas inversely proportional to the square of the distance between them.

Source: en.wikipedia.org

The Formula for Universal Gravitation:

Each object in this universe attracts the other objects. The gravitational force formula which is also known as Newton’s Law of Gravitation usually defines the magnitude of the force between the two objects.

According to it,

\(F = G \times \frac{M_{1}M_{2}}{r^{2}}\)

In the above equation, \(M_{1} and M_{2}\) represent the masses of the objects involved. Here there is no difference in how big or small are the objects. Here r represents the distance between the objects.

G is the universal gravitation constant having fixed value as \(6.673 \times 10^{-11} Nm^{2}kg^{-2}\). Gravity is commonly misunderstood as a force that simply holds us on the Earth or it keeps planets in orbit. However, there are gravitational forces between all objects but normally we cannot feel it because Earth is having a very large mass and hence its gravitational force overshadows all of these other ones.

Also, the unit of the gravitational force is Newton (N). It is the general Physics law which is derived from the observations done by Isaac Newton. This law states that every point mass attracts another single point mass by the force pointing along the line intersecting both the endpoints.

Solved Examples for Universal Gravitation Formula

Q.1: Find out the gravitational force, if two masses are 30 kg and 50 kg placed at a distance of 4 m.

Solution: Given parameters are,

• \(G = 6.673 \times 10^{-11} Nm^{2}kg^{-2}\)
• \(M_{1} = 30 kg,\)
• \(M_{2} = 50 kg,\)
• r = 4 m

Universal Gravitation formula is:

\(F = G \times \frac{M_{1}M_{2}}{r^{2}}\\\)

\(F = 6.673 \times 10^{-11}  \times \frac{30 \times 50 }{4^{2}}\\\)

\(= 6.25 \times 10^{-9} N.\)

Thus gravitational force will be \(6.25 \times 10^{-9} N.\)

Q.2: Calculate the gravitational force if the mass of two objects is 80 kg and 200 kg and they are placed at a distance of 6m.

Solution: Given parameters are,

• \(G = 6.673 \times 10^{-11} Nm^{2}kg^{-2}\)
• \(M_{1} = 80 kg,\)
• \(M_{2} = 200 kg,\)
• r = 6 m

Universal Gravitation formula is: \(F = G \times \frac{M_{1}M_{2}}{r^{2}}\\\)

\(F = 6.673 \times 10^{-11}  \times \frac{80 \times 200}{6^{2}}\\\)

\(=2.965 \times 10^{-8} N\)

Thus gravitational force will be \(92.965 \times 10^{-8} N.\)