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

FAQ

What factors influence the Orbital Energy of an object?
Orbital Energy is influenced by three main factors: the orbital angular velocity, the radius of the orbit, and the mass of the object in orbit. Changes in any of these parameters can significantly alter the Orbital Energy.

How does increasing the mass of an object affect its Orbital Energy?
Increasing the mass of an object in orbit directly increases its Orbital Energy. Since Orbital Energy is proportional to the mass (Eo = (w*r)^2*m), a larger mass results in higher energy, assuming orbital angular velocity and radius remain constant.

Can Orbital Energy be negative, and what would that imply?
Orbital Energy is typically positive, as it is calculated using the square of the product of orbital angular velocity and radius, then multiplied by mass. A negative Orbital Energy, in theoretical discussions, might imply an object is bound to a system (like a planet in a stable orbit around a star), where gravitational potential energy is considered, but this is not directly applicable to the formula provided.