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**m**_{1} and **m**_{2} and the distance between them is **d **as shown in figure.

Every mass exerts an attractive force on every other mass.

If there are two masses

Where,

G is a constant equal to 6.67 $\times$ 10^{-11} N-m^{2}/kg^{2},

mG is a constant equal to 6.67 $\times$ 10

m

r = radius or distance between the two bodies.

The

Related Calculators | |

Calculating Gravity | Acceleration due to Gravity Calculator |

force of gravity calculator | gravity water pressure calculator |

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 m_{1} = 2 Kg,

Mass m_{2} = 5 Kg,

Radius r = 5 cm.

Gravitational Constant G = 6.67 $\times$ 10^{-11} Nm^{2}/Kg^{2}

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 $\times$ 10^{6} 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 $\times$ 10^{16} N.

We know that gravitational constant is 6.67 $\times$ 10^{-11} Nm^{2}/Kg^{2}, the mass of the planet is given by

m_{2} = $\frac{F r^{2}}{m_{1}}$

= $\frac{2.25 \times 10^{16} \times (8 \times 10^{6})}{2000 \times 10^{3}}$

= $\frac{2.25 \times 10^{16} \times (8 \times 10^{6})}{2000 \times 10^{3}}$

= 9 $\times$ 10^{16} Kg.

The mass of the planet is 9 $\times$ 10^{16} Kg.

Given: Mass m

Mass m

Radius r = 5 cm.

Gravitational Constant G = 6.67 $\times$ 10

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

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 $\times$ 10

We know that gravitational constant is 6.67 $\times$ 10

m

= $\frac{2.25 \times 10^{16} \times (8 \times 10^{6})}{2000 \times 10^{3}}$

= $\frac{2.25 \times 10^{16} \times (8 \times 10^{6})}{2000 \times 10^{3}}$

= 9 $\times$ 10

The mass of the planet is 9 $\times$ 10