How To Calculate Acceleration Due To Gravity

A short tutorial on how to calculate the acceleration due to gravity at the surface of the earth with simple examples.

Acceleration Due To Gravity Calculation

The acceleration due to gravity is the force acting upon an object because of gravitational force. It is measured in SI unit m/s². The acceleration due to gravity at the surface of Earth is represented as "g" and has a standard value of 9.80665 m/s². Follow the below tutorial which guides on how to calculate acceleration due to gravity.

Acceleration Due To Gravity Formula:
g = G*M/R²
where,
g = Acceleration due to Gravity
G = Universal Gravitational Constant
M = Mass
R = Distance

This formula is calculated based on Newtons Second Law of Motion and Newtons Law of Universal Gravitation.

Newtons Second Law of Motion states that an object is accelerated whenever a net external force acts on it and this net force is equal to the mass of the object times its acceleration, and is given as F = m*a, where F is the net force acting on the object, m is the mass of the object, and a is the acceleration.

Newtons Law of Universal Gravitation states that every object exerts a gravitational force on every other object, and this gravitational force is proportional to the masses of both objects and inversely proportional to the square of the distance between their centers. It is given as F = G*(m1*m2/d²), where F is the force, G is the universal gravitational constant, m1 is the mass of object 1, m2 is the mass of object 2, and d is the distance between their centers.

Acceleration Due To Gravity Example:
Step 1:
Calculating the acceleration due to gravity on the surface of Earth.
Mass of Earth is 5.979 * 10²⁴ kg. Radius of Earth is 6.376 * 10⁶ m. Universal Gravitational Constant is 6.67408 * 10^-11 m³ kg^-1 s^-2.

Step 2:
Substitute the values in the formula,
g = 6.67408 * 10^-11 (5.979 * 10²⁴ / (6.376 * 10⁶)²
Acceleration Due to Gravity, g = 9.80665 m/s²

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