Formula used
This calculator uses standard two-body orbital mechanics with a central gravitational parameter μ and a satellite mass m. Radii are measured from the body center.
- Potential energy: U = − μm / r
- Total orbital energy: E = − μm / (2a)
- Kinetic energy: K = E − U
- Circular speed: v = √(μ / r)
- Vis-viva speed: v² = μ(2/r − 1/a)
- Orbital period: T = 2π √(a³ / μ)
How to use this calculator
- Select a central body or choose custom values.
- Pick circular or elliptical orbit calculation mode.
- Enter satellite mass with your preferred unit.
- Choose altitude mode or enter radius directly.
- For elliptical orbits, enter the semi-major axis.
- Optionally override the evaluation radius for perigee/apogee.
- Press Calculate to view energy, speed, and period.
- Use the export buttons to save your results.
Example data table
| Scenario | Body | Orbit type | Mass (kg) | Altitude (km) | a (km) | Energy unit |
|---|---|---|---|---|---|---|
| LEO imaging | Earth | Circular | 500 | 400 | — | MJ |
| Elliptical transfer check | Earth | Elliptical | 1200 | 300 | 12000 | MJ |
| Lunar orbit | Moon | Circular | 250 | 100 | — | MJ |
Orbital energy overview
Orbital energy is the mechanical energy that determines whether a satellite stays bound to a central body. In the ideal two‑body model (no drag or thrust), the total specific energy stays constant along the orbit. Negative energy means a bound ellipse, zero is the escape boundary, and positive energy implies a flyby trajectory.
Reference values and constants
Calculations typically use the gravitational parameter μ = GM because it is measured very accurately. For Earth, μ ≈ 3.986004418×1014 m³/s² and mean radius is about 6,371 km. The calculator converts your selected units to SI internally before computing energy, speed, and period.
Circular orbit interpretation
In a circular orbit the radius is constant, so speed is constant as well. The specific potential energy is U = −μ/r and the specific kinetic energy is K = v²/2. Their sum gives the total specific energy, which becomes less negative as the orbit radius increases.
Elliptical orbit behavior
Elliptical orbits trade speed for altitude. The satellite moves fastest near periapsis and slowest near apoapsis, but the total specific energy remains fixed. This is why a single orbit can have very different point‑by‑point speeds even when the overall energy is unchanged.
Energy tied to semi‑major axis
A key result is ε = −μ/(2a), where ε is specific orbital energy and a is the semi‑major axis. This means orbit size largely controls total energy. Raising a requires adding energy (and usually Δv), even if eccentricity changes during the maneuver.
Sanity‑check numbers for Earth
A ~400 km low Earth orbit has speed near 7.7 km/s and a period around 92 minutes. A geostationary orbit at r ≈ 42,164 km has speed near 3.1 km/s and a period of one sidereal day (~23 h 56 m). Use these as quick validation targets.
Design notes for real missions
Real satellites deviate from the ideal model due to drag, Earth’s oblateness, third‑body effects, and finite‑burn losses. Energy outputs are best treated as baseline estimates. For planning, engineers add margins and often compare orbits using Δv and transfer strategies, not energy alone.
Units and input tips
Energy formulas require distance from the body’s center, so altitude inputs are converted using r = R + h. Keep units realistic and consistent, especially for custom bodies. If results look odd, recheck the selected central body, orbit type, and whether your distances are radius or altitude.
FAQs
1) What does a negative total orbital energy indicate?
A negative total (specific) energy means the satellite is gravitationally bound, so the path is an ellipse (including a circle). It cannot escape without adding energy.
2) Why does the calculator use μ instead of G and mass?
μ = GM is measured with high precision for planets and moons. Using μ reduces rounding error and avoids mixing very large or very small constants.
3) How is altitude converted to orbital radius?
Orbital radius r is distance from the center: r = R + h, where R is mean radius and h is altitude above the surface. The energy and speed formulas require r.
4) Does eccentricity change the total orbital energy?
If the semi‑major axis stays the same, total specific energy stays the same. Eccentricity mainly changes how speed and radius vary around the orbit.
5) Why is speed highest at periapsis?
In the ideal model, angular momentum is conserved. When the satellite is closer to the body, it must move faster, increasing kinetic energy while potential energy becomes more negative.
6) Are results accurate for very low orbits?
They are ideal two‑body estimates. Very low orbits experience drag and stronger perturbations, so energy and period can drift over time. Use the outputs as a starting point.
7) Can I use this for custom planets or moons?
Yes. Enter custom μ and radius in SI units, then provide your orbit radius or altitude. Make sure the values describe the central body you are orbiting.