What is specific orbital energy?

Specific orbital energy (ε) is the total mechanical energy — kinetic plus potential — per unit mass of an orbiting body. It is measured in J/kg (or equivalently m²/s²). Because it is mass-independent, it describes the orbit shape regardless of the spacecraft mass.

What does a negative specific orbital energy mean?

A negative value means the orbit is bound — the body does not have enough energy to escape and follows an elliptical (or circular) path. The more negative the value, the tighter and lower-energy the orbit.

What is the gravitational parameter (μ)?

The standard gravitational parameter μ = GM is the product of the gravitational constant G and the mass M of the central body. For Earth, μ ≈ 398,600 km³/s². Using μ directly avoids uncertainty in G and M individually.

How is the semi-major axis related to specific orbital energy?

For a bound orbit, the semi-major axis a = −μ / (2ε). This means that for any orbit with the same specific energy, the semi-major axis is identical regardless of eccentricity.

What are the units used in this calculator?

Inputs use km and km/s for compatibility with standard astrodynamics tables (μ in km³/s², distances in km). The output energy is displayed in MJ/kg (megajoules per kilogram) and km²/s².

Can I use this for interplanetary trajectories?

Yes. Simply enter the heliocentric velocity and heliocentric distance for the spacecraft, and use the Sun's gravitational parameter (μ_Sun ≈ 1.327 × 10¹¹ km³/s²) to get the heliocentric specific orbital energy.

Specific Orbital Energy Calculator

Calculate the specific orbital energy of a spacecraft or planet from its speed, orbital radius, and the central body gravitational parameter.

Orbital Parameters

Quick Presets

Orbital Speed (v)

km/s

Orbital Radius (r)

Gravitational Parameter (μ = GM)

km³/s²

Earth: 398,600 | Sun: 1.327 × 10¹¹ | Moon: 4,904.9

Results

Enter parameters or choose a preset, then click Calculate.

Orbit Type Reference

Bound Orbit (ε < 0)

Circle or ellipse. The body is gravitationally captured. Semi-major axis: a = −μ / (2ε).

Parabolic Escape (ε = 0)

Marginally unbound. Speed equals the local escape velocity. Semi-major axis is infinite.

Hyperbolic Flyby (ε > 0)

Unbound trajectory. Body escapes to infinity with residual speed v∞ = √(2ε).

Summary

Specific orbital energy (also called vis-viva energy) is the total mechanical energy per unit mass of an orbiting body. It equals the sum of kinetic energy per unit mass and gravitational potential energy per unit mass. A negative value indicates a bound (elliptical or circular) orbit, while zero means a parabolic escape trajectory and a positive value means a hyperbolic flyby.

How it works

Enter the orbital speed of the body in km/s.
Enter the current orbital radius (distance from the center of the primary body) in km.
Enter the standard gravitational parameter (GM) of the central body in km³/s².
The calculator applies the vis-viva formula: ε = v²/2 − μ/r.
The result shows specific orbital energy in MJ/kg, the orbit type, and derived orbital elements.

Use cases

Verify that a spacecraft is in a bound orbit after a burn.
Determine whether a comet or asteroid is on a hyperbolic trajectory.
Compute the semi-major axis of an elliptical orbit from energy alone.
Teach orbital mechanics and the vis-viva equation to students.
Cross-check trajectory simulations in mission design.
Quickly assess escape vs. capture conditions at planetary flybys.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu