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

Name: Specific Orbital Energy Calculator
Availability: InStock
Author: Nham Vu

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

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

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