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# Gravity Calculator

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Gravity calculator is used to find out the gravitational force between the two objects. If we know the masses of the objects and the distance between them, we can easily calculate gravitational force using the given formula.

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

where,
F is the gravitational force
G is gravitational constant
$m_{1}$ and $m_{2}$ are different masses of objects
r is the distance between these objects

## Steps

Step 1 : Note down the given parameters.

Step 2 : Substitute these parameters in the given equation,

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

Step 3 : Find out the unknown variable.

## Problems

Problems based on gravity is discussed below:

### Solved Examples

Question 1: Calculate the gravitational force of a 100 kg objects on earth. This object is 8$\times10^{8}$ m apart from the center of the earth? Given that the mass of the earth is 6.87$\times10^{29}$ kg.

Solution:

Given that,
$m_{1}$ = 6.87$\times10^{29}$ kg
$m_{2}$ = 100 kg
r = 8$\times10^{8}$ m
G = 6.6726$\times10^{-11}$
The formula to find out the gravitational force is,

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

F = $\frac{6.6726 \times 10^{-11} \times 6.87 \times 10^{29} \times100}{{8 \times 10^{8}}^{2}}$

F = 7162.6 N

Question 2: The gravitational force acting between two objects is 550$\times10^{-10}$ N. One mass is given as 5$\times10^{5}$ kg and the other situated at a distance of 18 km apart. Calculate the mass of the other object?

Solution:

Given that,
$m_{1}$ = 5$\times10^5$ kg
$m_{2}$ = ?
r = 18 km = 18000 m
G = 6.6726$\times10^{-11}$
F = 550$\times10^{-10}$ N
The formula to find out the gravitational force is,

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

$m_{2}$ = $\frac{Fr^{2}}{Gm_{1}}$

$m_{2}$ = $\frac{550\times10^{-10}\times18000^{2}}{6.6726\times10^{-11}\times50\times10^{5}}$

$m_{2}$ = 53.4$\times10^{4}$ kg