Satellite Orbit Calculator

Orbit Input Form

Central body

Select a preset or enter custom mass and radius.

Orbit type

Distance input mode

Satellite mass (kg)

Custom body mass (kg)

Custom body radius (km)

Circular altitude (km)

Circular radius (km)

Periapsis altitude (km)

Apoapsis altitude (km)

Periapsis radius (km)

Apoapsis radius (km)

True anomaly (degrees)

Used for current radius, speed, and flight path angle.

Plotly Graph

The chart changes with the chosen orbit model. Circular mode plots speed against altitude. Elliptical mode plots speed against true anomaly.

Formula Used

Standard gravitational parameter: μ = G × M
Circular orbital velocity: v = √(μ / r)
Escape velocity: v_esc = √(2μ / r)
Elliptical semi-major axis: a = (r_p + r_a) / 2
Eccentricity: e = (r_a − r_p) / (r_a + r_p)
Vis-viva equation: v = √[μ(2/r − 1/a)]
Orbital period: T = 2π√(a³ / μ)
Specific orbital energy: ε = −μ / (2a)
Specific angular momentum: h = √[μa(1 − e²)]
Local gravitational acceleration: g = μ / r²

How to Use This Calculator

Select the central body, or choose Custom for your own mass and radius.
Pick Circular or Elliptical orbit mode.
Choose whether you want to enter altitude above the surface or full radius from the center.
Enter satellite mass to estimate energy and centripetal force values.
For elliptical orbits, provide periapsis and apoapsis values, then add a true anomaly to inspect the current state.
Press the calculate button to show results above the form.
Review the chart, then export the final results using CSV or PDF download buttons.

Example Data Table

Central Body	Orbit Type	Example Input	Approx Radius	Approx Speed	Approx Period
Earth	Circular	Altitude = 400 km	6,771 km	7.67 km/s	92.4 min
Moon	Circular	Altitude = 100 km	1,837.4 km	1.63 km/s	117.9 min
Mars	Circular	Altitude = 500 km	3,889.5 km	3.32 km/s	122.7 min
Earth	Elliptical	Periapsis 400 km, Apoapsis 1,200 km	a ≈ 7,171 km	7.87 / 7.02 km/s	100.7 min

FAQs

1) What does this calculator compute?

It computes orbital radius, semi-major axis, eccentricity, orbital period, velocity, escape velocity, specific energy, angular momentum, local gravity, centripetal force, and energy values for the selected orbit.

2) What is the difference between circular and elliptical orbit mode?

Circular mode assumes one constant orbital radius. Elliptical mode uses periapsis and apoapsis, then applies the vis-viva equation to show changing speed and position throughout the orbit.

3) Should I enter altitude or radius?

Use altitude when you know height above the body’s surface. Use radius when you already know the distance from the body’s center to the satellite.

4) Why is satellite mass included?

Mass does not change the orbit in the ideal two-body model, but it is needed to compute actual kinetic energy, potential energy, total mechanical energy, and centripetal force.

5) Why does orbital period increase with altitude?

Higher orbits have larger path lengths and lower orbital speeds. Together, those effects make the satellite take longer to complete one revolution.

6) Can I use this for planets not listed?

Yes. Choose Custom and enter the body’s mass and radius. The calculator will then apply the same orbit equations to your custom central body.

7) Does this include air drag or real mission effects?

No. It uses ideal Keplerian motion. Real missions may differ because of drag, thrust, non-spherical gravity, radiation pressure, and other perturbations.

8) Why is the satellite faster at periapsis?

In an elliptical orbit, the satellite moves fastest where it is closest to the central body. Gravity is stronger there, so orbital speed rises.