Enter the mass and radius of a spherical object into the calculator to determine the gravitational binding energy (GBE).

## GBE Formula

The following formula is used to calculate gravitational binding energy (GBE).

GBE = 3 * G * M^2 / (5*R)

• Where GBE is the gravitational binding energy (J)
• G is the gravitational constant (6.674*10^-11 m^3/(kg*s^2))
• M is the mass of the sphere (kg)
• R is the radius of the sphere (m)

To calculate GBE (gravitational binding energy) multiply the gravitational constant by 3, then multiply by the mass square, and finally divide by 5 times the radius.

## What is GBE?

Definition:

GBE stands for gravitational binding energy. It is a measure of the total amount of energy that needs to be added to a system in order for that system to no longer be in a gravitationally bound state.

## How to calculate GBE?

Example Problem:

The following example problem outlines how to calculate GBE.

First, determine the mass of the sphere. In this example, the sphere has a mass of 100,000,000 kg.

Next, determine the radius of the object. This sphere is measured to have a sphere of 1,000 m.

Finally, calculate the GBE using the formula above:

GBE = 3 * G * M^2 / (5*R)

GBE = 3 * 6.674*10^-11 * 100,000,000^2 / (5*1000)

GBE = 400 .44 Joules