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Gravity Formula

Gravity, also called gravitation, is a force that exists among all material objects in the universe. For any two objects or particles having nonzero mass , the force of gravity tends to attract them toward each other. The Universal law of gravitation states that:

Every mass exerts an attractive force on every other mass.

If there are two masses m1 and m2 and the distance between them is d as shown in figure.

The gravity formula is given by
Where,
G is a constant equal to 6.67 $\times$ 10-11 N-m2/kg2,
m1 = mass of the body 1,
m2 = mass of body 2,
r = radius or distance between the two bodies.

The gravitational force formula is very helpful in finding larger radius, larger mass, gravity values etc.

Related Calculators
Calculating Gravity Acceleration due to Gravity Calculator
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Gravity Problems

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Below are some problems on gravity which helps you to understand the use of this formula.

Solved Examples

Question 1: Find the force due to gravitation acting on two bodies of mass 2 Kg and 5 Kg separated by the distance 5cm?
Solution:
 
Given: Mass m1 = 2 Kg,
          Mass m2 = 5 Kg,
          Radius r = 5 cm.
          Gravitational Constant G = 6.67 $\times$ 10-11 Nm2/Kg2
          The Force due to gravity are given by formula F = $\frac{G m_{1} m_{2}}{r^{2}}$
                                                                               = $\frac{6.67 \times 10^{-11} \times 2 \times 5}{5 \times 10^{-2}}$
                                                                               = 2.668 $\times$ 10-7 N.
 

Question 2: A spaceship is moving round the planet having mass of 2000 Kg. If it is at the distance 8 $\times$ 106 m from the planet. Calculate the mass of the planet?
Solution:
 
The Force due to gravity is given by F = $\frac{m_{1} v^{2}}{r}$
                                     
= $\frac{2000 \times 10^{3} \times (3 \times 10^{8})^{2}}{8 \times 10^{6}}$
                                                        = 2.25 $\times$ 1016 N.

We know that gravitational constant is 6.67 $\times$ 10-11 Nm2/Kg2, the mass of the planet is given by
m2 = $\frac{F r^{2}}{m_{1}}$
     = $\frac{2.25 \times 10^{16} \times (8 \times 10^{6})}{2000 \times 10^{3}}$
     = $\frac{2.25 \times 10^{16} \times (8 \times 10^{6})}{2000 \times 10^{3}}$
     = 9 $\times$ 1016 Kg.
The mass of the planet is 9 $\times$ 1016 Kg.


 

More topics in Gravity Formula
Acceleration due to Gravity Formula Escape Velocity Formula
Specific Gravity Formula Free Fall Formula
Projectile Motion Formula Gravitational Potential Energy Formula
Inverse Square Law Formula Air Resistance Formula
Gravitational Field Formula Universal Gravitation Formula
Relative Motion Formula
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