Gravity Formula

Gravity is without a doubt one of the most fundamental forces in nature. A physics student encounters gravity in various ways. Thus, it is important to understand its meaning and what formula is utilized for finding out gravity of anything. Similarly, you will find all you need to know in the details below including the gravity formula.

Definition

Gravity is referred to be the force that is responsible for the attraction between two bodies towards each other. For instance, it is the same force that causes the apples to fall from the tree on the ground. Similarly, it is what allows the planets to orbit the sun. Therefore, one can say that more massive an object is, the stronger it will be its gravitational pull.

In other words, it is the same thing causing an object to have weight. For instance, if you want to find out your weight, you use a weighing machine. This weighing scale will show you what amount of gravity is acting on your body.

The theory of gravitation was discovered by Sir Isaac Newton in the 1680s. It was his discovery which stated that gravity acts on all matter plus it is a function of both mass distances.

Importance of Gravity

The law of gravity applies to almost everything that exists in the universes with a mass. Any two objects attract to one another just like any two galaxies. Moreover, the attractions become small even zero sometimes when the distance is large enough.

You can derive its importance from the way how all types of matter interact. For instance, you might have seen astronauts floating around in space. It is so because of the lack of gravity in space. Thus, you see you are able to walk on earth due to gravity.

Gravity Formula

As gravity is the force of attraction between two entities, the formula comes as this force of attraction times the gravitational constant which will inversely relate to the square of the distance between the entities. Therefore, our equation will come as:

Force = [gravitational constant x masses (\(m_{1}\) \(m_{2}\))] / (radius)²

F = [ \(m_{1}m_{2}\)] / r\(^{2}\)

F refers to the force of gravity, N/kg

G is the gravitational constant, 6.67  \(10^{-11}\) N- \(m^{2} / kg^{2}\)

\(m_{1}\) will be the 1^st mass, kg

\(m_{2}\) is the 2^nd mass, kg

r refers to the distance between two masses, m

Solved Examples on Gravity Formula

Question- Calculate the gravitational force which acts upon two objects of masses 15 g and 15 kg which are 11 m apart?

Answer- Looking at the question we see that we have the gravitational constant, G is 6.67 x 10^-11 N-m²/kg²

\(m_{1}\) = 15 g = 0.015 kg

r = 11 m

Therefore, we will apply the gravity formula here, which will be:

F = [ \(m_{1}m_{2}\)] / r\(^{2}\)

F= [6.67  \(10^{-11} N-m^{2}/kg^{2}\) (0.015 x 15)kg] / (11 \(m^{2}\))

F = 1.24 x \(10^{-13}\) N/kg

 Question- Calculate the distance between two objects whose gravitational force is to 1.1 x \(10^{-11}\) kg. Moreover, the mass of each object is 6 kg.

 Answer- We see here that we have got our force as, F = 1.1 x \(10^{-11}\) kg. Furthermore, our \(m_{1}\) and \(m_{2}\) comes as 6 kg. G is already defined as 6.67 x 10^-11 N-m²/kg²

Thus, when you put in the equation, you will get:

F = [ \(m_{1}m_{2}\)] / r\(^{2}\)

r² = [Gm₁m₂] / F

r² = [ 6.67 x 10^-11 N-m²M/kg² (6 kg)(6kg)] / 1.1 x 10^-11 N/kg

r² = 2.18 x 10 ^-20 m²

r = √(2.18 x 10 ^-20 m²)

r = 1.48 x 10^-10 m