Calculated orbital result
The calculator reports ideal circular orbit values for the selected body.
Orbit performance graph
The chart compares circular orbital velocity against altitude for the chosen body and marks your computed point.
Formula used
Orbital radius: r = R + h
Velocity relation: v = √(μ / r)
Period relation: T = 2π √(r³ / μ)
Altitude from radius: h = r − R
Where μ is gravitational parameter, R is mean body radius, r is orbital radius, and h is orbital altitude.
How to use this calculator
- Select whether altitude should be solved from orbital period, velocity, or orbital radius.
- Choose a preset body, or select a custom body and enter μ plus mean radius.
- Enter the input value and set the correct unit.
- Press submit to display the result block above the form.
- Review altitude, speed, period, local gravity, escape velocity, and specific energy.
- Use the graph and exports for quick engineering documentation.
Example data table
| Body | Known input | Value | Approximate altitude | Typical use |
|---|---|---|---|---|
| Earth | Period | 92 min | ~400 km | Crewed station operations |
| Earth | Radius | 42,164 km | 35,786 km | Geostationary communications |
| Mars | Velocity | 3.40 km/s | ~400 km | Mapping and relay studies |
| Moon | Period | 118 min | ~100 km | Lunar reconnaissance missions |
Orbital altitude and mission context
Orbital altitude is the distance between a spacecraft and the reference body's surface. Engineers use altitude to classify low and medium regimes, estimate atmospheric influence, and compare mission constraints. For Earth missions, typical low orbits extend from roughly 160 km to 2,000 km, while geostationary altitude is near 35,786 km above sea level.
Primary equations behind the calculator
The calculator applies circular orbit relations built from Newtonian gravitation. Orbital radius equals body radius plus altitude. Velocity follows v = √(μ/r), where μ is the standard gravitational parameter. Period follows T = 2π√(r³/μ). Rearranging these equations lets the tool solve altitude from radius, velocity, or period while keeping units consistent for engineering review.
Why body radius and gravity matter
Altitude alone does not define an orbit. A 500 km orbit above Earth behaves differently from a 500 km orbit above Mars or the Moon because body radius and μ change the resulting orbital radius, speed, and period. For example, a circular orbit near Earth at 400 km travels near 7.67 km/s with a period around 92 minutes.
Engineering uses during concept studies
Concept teams use orbital altitude estimates to size communications coverage, revisit intervals, eclipse exposure, and delta-v budgets for insertion and maintenance. The same altitude also influences payload heating, drag compensation, and debris exposure in crowded corridors. Early altitude screening helps compare observation missions, navigation architectures, transfer staging, and relay platforms before detailed trajectory design begins.
Interpreting output values correctly
The result panel reports altitude together with orbital radius, speed, period, local gravity, escape velocity, and specific orbital energy. Those outputs should be interpreted as ideal circular orbit values. Real operations may differ because of oblateness, atmospheric drag, stationkeeping, maneuver dispersions, and noncircular geometry. Use the calculator for preliminary sizing, then validate with higher fidelity mission analysis.
Example ranges for practical decisions
Very low Earth orbits below about 300 km can reduce latency and improve resolution, but they demand frequent drag management. Sun-synchronous observation missions commonly operate near 500 to 800 km. Medium Earth navigation systems work much higher, around 20,000 km. Geostationary services remain fixed relative to Earth’s rotation near 35,786 km, trading altitude for regional coverage.
FAQs
1. Does this calculator support elliptical orbits?
No. It assumes an ideal circular orbit. Use it for first-pass engineering estimates, then verify elliptical cases with higher fidelity trajectory tools.
2. What is the difference between altitude and orbital radius?
Orbital radius is measured from the body's center. Altitude is measured from the surface. The calculator converts between them using the selected body's mean radius.
3. Why can two bodies give different results at the same altitude?
Because gravitational parameter and body radius differ. Those values change orbital velocity, period, local gravity, and energy even when altitude is numerically identical.
4. Can I use custom planetary values?
Yes. Select the custom body option, then enter μ in m³/s² and mean body radius in kilometers to solve altitude for any spherical reference body.
5. What units are accepted?
The calculator accepts seconds, minutes, hours, meters per second, kilometers per second, meters, and kilometers depending on the selected solve mode.
6. Is atmospheric drag included?
No. The model ignores drag, oblateness, and perturbations. For very low orbits, actual operational altitude requirements may be higher than this estimate suggests.