Orbit total energy calculator

This orbit total energy calculator finds the combined kinetic and gravitational potential energy of a satellite moving in a circular orbit. Enter the central body's mass, the satellite's mass, and the orbital radius measured from the central body's center. The negative result expresses that the satellite is gravitationally bound: energy must be added for it to escape to an infinitely distant point with zero remaining speed.

What total mechanical energy means in a circular orbit

A satellite in orbit has positive kinetic energy because it is moving, and negative gravitational potential energy because it is bound to the central body. For a circular orbit, gravity supplies exactly the centripetal force required to keep the satellite at a constant radius. Here, G is the gravitational constant, M is the central body's mass, m is the satellite's mass, and r is the distance from the central body's center to the satellite.

The answer is negative for every valid set of positive inputs. That sign is physically important rather than a bookkeeping convention: it says the orbiting object does not possess enough mechanical energy to reach infinity. A result with a larger negative magnitude represents a more tightly bound orbit.

Moving the same satellite to a larger circular radius makes the energy less negative, while increasing either mass makes its magnitude larger. The calculator reports joules when masses are in kilograms, radius is in meters, and G uses its default SI value.

Enter radius and masses with consistent units

Use the orbital radius, not merely the altitude above a planet's surface. For a satellite at a stated altitude, add the central body's mean radius before entering the value. This distinction is often the largest source of error in low-orbit calculations because altitude and center-to-center distance can differ by thousands of kilometers.

With the default gravitational constant, enter the central mass and satellite mass in kilograms and radius in meters; the resulting total mechanical energy is in joules. You may provide a different positive gravitational constant for another internally consistent unit system or for a classroom convention, but every input must then follow that same system. Both masses must be positive and finite.

Radius must also be positive and finite. In particular, a zero radius produces an input error because the formula would divide by zero and because a point at the central body's center cannot describe a circular orbit. These checks prevent an apparently precise but physically meaningless result.

Interpret the result and understand the model limits

The returned value is the total mechanical energy of the satellite under the standard circular two-body approximation. It is not the gravitational potential energy alone. In a circular orbit, potential energy is -GMm/r, kinetic energy is +GMm/(2r), and their sum is therefore -GMm/(2r).

This relationship makes the calculator useful for checking textbook work, estimating the ideal energy difference between circular orbits, and validating simulation output. To compare two circular orbits, calculate each total separately and subtract the initial value from the final value. A transfer to a higher orbit normally requires a positive energy increase because the final total is closer to zero.

Real missions also depend on transfer trajectories, propulsion efficiency, staging, atmospheric drag, and the central body's rotation, so the difference in ideal orbital energies is not by itself a launch fuel requirement. The model further assumes that the central mass dominates, the orbit is circular, bodies can be treated as point masses or spherical masses, and disturbances from other bodies are negligible. For an elliptical orbit, use the semi-major-axis form of orbital energy instead of substituting a changing instantaneous radius into this circular formula.