Enter the orbital angular velocity (rad/s), the radius of orbit (m), and the mass (kg) into the calculator to determine the Orbital Energy. 

Orbital Energy Formula

The following equation is used to calculate the Orbital Energy.

Eo = (w*r)^2*m
  • Where Eo is the Orbital Energy (J)
  • w is the orbital angular velocity (rad/s) 
  • r is the radius of orbit (m) 
  • m is the mass (kg) 

To calculate orbital energy, square the product of the orbital velocity and the radius, then multiply the result by the mass.

How to Calculate Orbital Energy?

The following example problems outline the steps and information needed to calculate Orbital Energy.

Example Problem #1

  1. First, determine the orbital angular velocity (rad/s). In this example, the orbital angular velocity (rad/s) is determined to be 58.
  2. Next, determine the radius of orbit (m). For this problem, the radius of orbit (m) is measured to be 49.
  3. Next, determine the mass (kg). In this case, the mass (kg) is found to be 39.
  4. Finally, calculate the Orbital Energy using the formula above: 

Eo = (w*r)^2*m = (J)

Inserting the values from above and solving the equation yields: 

Eo = (58*49)^2*39 = 315001596 Joules

Example Problem #2

Using the same method as above, first, we need to measure or determine the variables required by the equation. For this example problem, these are provided as follows: 

orbital angular velocity (rad/s) = 959

radius of orbit (m) = 295

mass (kg) = 430

Enter these given values into the calculator or above yields: 

Eo = (959*295)^2*430 = 3.4415153e+13 (J)