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Acceleration due to Gravity Formula

The acceleration observed in any body due to gravity is called Acceleration due to gravity.

The force due to gravity is given by,
Where m = mass of the body and
g = gravity.

The Universal Law of gravitation gives,
Where G is a constant equal to 6.67 $\times$ 10-11 N-m2/kg2,
m = mass of the body 1,
M = mass of body 2,
r = radius between the two bodies.

Equating both the force formula we get

Hence Acceleration due to gravity formula is given as

The above formula can also be called Gravitational Acceleration Formula. It is used to find the acceleration due to gravity any where in space. On earth the acceleration due to gravity is 9.8 m/s2.

Related Calculators
Acceleration due to Gravity Calculator Acceleration Formula Calculator
Calculating Gravity force of gravity calculator
 

Acceleration due to gravity Problems

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Below are given some problems based on acceleration due to gravity using the above formula.

Solved Examples

Question 1: Calculate the acceleration due to gravity for a planet having mass 4 $\times$ 1023 Kg and is 3 $\times$ 106 m away from sun?
Solution:
 
Given: Mass of planet M = 4 $\times$ 106 Kg,
          Radius r = 3 $\times$ 106 m,
          Gravitational Constant G = 6.67 $\times$ 10-11 N-m2/kg2
Acceleration due to gravity g = $\frac{GM}{r^{2}}$
                                          =  $\frac{6.67 \times 10^{-11} \times 4 \times 10^{23}}{3 \times 10^{6} m}$
                                          = 2.964 m/s2.
 

Question 2: Calculate the acceleration due to gravity for the planet pluto if it is having mass of 1.22 $\times$ 1022 Kg and radius is 1.15 $\times$ 106 m.
Solution:
 
Given: Mass M = 1.22 $\times$ 1022 Kg and
          Radius r = 1.15 $\times$ 106 m
The acceleration due to gravity g = $\frac{GM}{r^{2}}$
                                                = $\frac{6.67 \times 10^{-11} \times 1.22 \times 10^{22}}{(1.15 \times 10^{6})^{2}}$
                                                = 0.61m/s2.

 

More topics in Acceleration due to Gravity Formula
Gravitational Acceleration Formula
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