Calculator Inputs
Example Data Table
| Example | Body | Semi-major Axis | Eccentricity | True Anomaly | Approx Speed |
|---|---|---|---|---|---|
| Near Earth orbit | Earth | 7000 km | 0.001 | 90° | 7.546 km/s |
| Molniya style apoapsis | Earth | 26600 km | 0.74 | 180° | 1.496 km/s |
| Mars transfer sample | Sun | 188800000 km | 0.207 | 0° | 32.709 km/s |
| Moon orbit sample | Moon | 5000 km | 0.20 | 120° | 0.926 km/s |
Formula Used
The main equation is the vis-viva equation:
v = √[ μ × (2 / r − 1 / a) ]
Here, v is orbital speed, μ is the gravitational parameter, r is current orbital radius, and a is the semi-major axis.
Radius from true anomaly is:
r = a(1 − e²) / (1 + e cos θ)
Periapsis and apoapsis radii are:
rₚ = a(1 − e) and rₐ = a(1 + e)
Orbital period is:
T = 2π√(a³ / μ)
How to Use This Calculator
- Select a central body, or choose custom and enter its gravitational parameter.
- Choose the distance unit used by your semi-major axis and radius values.
- Enter the semi-major axis of the ellipse.
- Enter eccentricity. It must be less than one for an elliptical orbit.
- Choose true anomaly or current radius as the position input.
- Press the calculate button to show results above the form.
- Download the result table as CSV or PDF for records.
Understanding Elliptical Orbit Speed
Elliptical motion is not uniform. A satellite moves fastest near periapsis. It moves slowest near apoapsis. This happens because gravity trades potential energy for kinetic energy. The vis-viva equation links speed, radius, semi-major axis, and gravitational parameter. It works for any point on a bound elliptical path.
Why Speed Changes
An ellipse has one focus occupied by the central body. The orbiting object falls inward as it approaches that focus. Its radius becomes smaller. Its speed increases. After periapsis, it climbs outward again. Radius grows. Speed drops. This constant exchange keeps total specific energy fixed, when drag and thrust are ignored.
Useful Planning Insight
Mission planners use orbit speed to check burns, transfer arcs, and timing. A small speed error can shift arrival time. It can also change apoapsis height. This calculator helps compare current speed with circular and escape speed at the same radius. That comparison gives a quick safety margin. It also shows whether an orbit is tight, stretched, or near escape.
Inputs That Matter
The semi-major axis sets orbit size. Eccentricity sets orbit shape. The gravitational parameter sets central body strength. The current position can be entered as true anomaly or radius. True anomaly is the angle from periapsis. Radius is the distance from the focus to the object. Both methods lead to the same vis-viva speed.
Reading The Results
Periapsis speed is the maximum bound speed in the orbit. Apoapsis speed is the minimum speed. Specific energy is negative for an ellipse. Angular momentum indicates turning strength. Flight path angle shows whether motion is mostly sideways or partly radial. Use all outputs together. Do not rely on one number alone for critical mission work.
Practical Limits
This tool assumes a two-body model. It ignores air drag, oblateness, solar pressure, third bodies, and maneuvers. Real spacecraft need higher fidelity propagation. Still, the model is excellent for learning, first estimates, classroom work, and quick design checks.
Good Data Habits
Use consistent units before comparing outputs. Check that eccentricity stays below one. Confirm radius is between periapsis and apoapsis. Save exports with notes about assumptions. Clear records make later reviews faster and safer for teams.
FAQs
1. What does elliptical orbit speed mean?
It is the instantaneous speed of an orbiting object at a chosen point on an elliptical path. The value changes because radius changes along the orbit.
2. Why is speed highest at periapsis?
At periapsis, the object is closest to the central body. Gravitational potential energy is lower, so kinetic energy and speed are higher.
3. Why is speed lowest at apoapsis?
At apoapsis, the object is farthest from the central body. More energy is stored as potential energy, so the orbital speed becomes lower.
4. What is the vis-viva equation used for?
The vis-viva equation calculates orbital speed from gravitational parameter, current radius, and semi-major axis. It is useful for two-body orbit estimates.
5. Can eccentricity be equal to one?
No, not for an ellipse. An eccentricity of one represents a parabolic path. Elliptical orbits require eccentricity values from zero up to below one.
6. Should radius include planet radius?
Yes. Use distance from the central body's center or focus. Do not enter altitude alone unless you add the body's radius first.
7. Why compare orbital speed with escape speed?
Escape speed shows the speed needed to leave the central body from that radius. The margin helps judge how bound the orbit remains.
8. Is this calculator accurate for real missions?
It is accurate for ideal two-body estimates. Real missions may also need drag, third-body gravity, radiation pressure, and detailed numerical propagation.