Gravity Formula

Gravity Formula - Definitions and Examples

Gravity or Gravitation is a phenomenon which gives an idea about the existence of a force between any two objects having some mass. The force due to gravity is always attractive.
Law of Gravity states that if two masses m1 and m2 are kept at distance of r from each other then force due to gravity is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
If ‘F’ is the force due to gravity then mathematically:
$F \propto {m_1}{m_2}\,\,\,\,\,and\,\,\,\,\,F \propto \frac{1}{{{r^2}}}$
Therefore, $F \propto \frac{{{m_1}{m_2}}}{{{r^2}}}$ OR $F = G\frac{{{m_1}{m_2}}}{{{r^2}}}$
Where G = Gravitational constant = 6.673 x 10-11 N-m2/Kg2 (or) m3/Kg-s2
On earth the force due to gravity between Earth and an object on earth can also be related to the same formula.
Let mass of the Earth is M and mass of the object is m and radius of earth is r. So, force due to gravity on an object on Earth’s surface is the force between both the masses is given by:
$F = G\frac{{Mm}}{{{r^2}}}$
$mg = G\frac{{Mm}}{{{r^2}}}$
$g = G\frac{M}{{{r^2}}}$= 9.8 m/s2
Thus, is the relation between acceleration due to gravity, mass of Earth and radius of earth.

Example:
An object of mass 40 Kg experience a force of 200N towards the center of a planet from a distance of 20Km. Find the mass of the planet.
Solution:
Let mass of the planet = M
Mass of the object (m) = 40Kg
Distance between both the masses (r) = 20000m
Force due to gravity (F) = 200N
Therefore, $F = G\frac{{Mm}}{{{r^2}}}$
$200 = 6.673 \times {10^{ - 11}} \times \frac{{{\text{M}} \times 40}}{{{{\left( {20000} \right)}^2}}}$
${\text{M}} = \frac{{200 \times {{\left( {20000} \right)}^2}}}{{40 \times 6.673 \times {{10}^{ - 11}}}}$
M = 2.997 x 1019 Kg
Mass of the planet is 2.997 x 1019 Kg
Question:
Force between mass of two objects is 40N. If one of their mass is 2 kg and distance between them is 1m, find the mass of the other object.
Solution:
Force = $G\frac{{{m_1}{m_2}}}{{{r^2}}}$
$40 = 6.673 \times {10^{ - 11}}\frac{{m \times 2}}{1}$
m = 2.99 x 1011 Kg.