Satellite Orbit Calculator

Enter Orbit Inputs

Use the responsive input grid below. Large screens show three columns, smaller screens show two, and mobile shows one.

Central Body Choose a preset gravity source or use a custom body.

Orbit Type Circular uses one altitude. Elliptical uses perigee and apogee.

Inclination (deg) Displayed for mission context. It does not change scalar speed values here.

Circular Orbit Altitude (km) Height above the selected body's surface.

Perigee Altitude (km) Closest-point altitude above the body's surface.

Apogee Altitude (km) Farthest-point altitude above the body's surface.

Payload Mass (kg) Used for total and kinetic energy estimates.

Custom Body Radius (km) Required only when using a custom central body.

Custom Standard Gravitational Parameter (km³/s²) This value equals G × M for the selected body.

Example Data Table

These sample values illustrate typical outputs for common satellite cases.

Scenario	Body	Perigee Altitude (km)	Apogee Altitude (km)	Eccentricity	Period	Perigee Speed (km/s)	Apogee Speed (km/s)
Low Earth Circular Orbit	Earth	400	400	0.000000	92.41 minutes	7.67260	7.67260
Geostationary-Like Circular Orbit	Earth	35786	35786	0.000000	23.93 hours	3.07492	3.07492
Elliptical Earth Orbit	Earth	300	1000	0.049850	97.58 minutes	7.92022	7.16806

Formula Used

1) Orbital Radius

r = R + h, where R is body radius and h is altitude above the surface.

2) Semi-Major Axis

a = (r_p + r_a) / 2

3) Eccentricity

e = (r_a - r_p) / (r_a + r_p)

4) Orbital Period

T = 2π √(a³ / μ)

5) Vis-Viva Equation

v = √[ μ × (2/r − 1/a) ] gives orbital velocity at any radius r.

6) Escape Velocity

v_esc = √(2μ / r)

7) Specific Orbital Energy

ε = − μ / (2a)

8) Specific Angular Momentum

h = √[ μa(1 − e²) ]

How to Use This Calculator

Select the central body, such as Earth, Moon, Mars, or a custom object.
Choose either a circular or elliptical orbit model.
Enter altitude for a circular orbit, or enter perigee and apogee altitudes for an elliptical orbit.
Add payload mass if you want total energy estimates.
Enter inclination for mission reference and reporting.
For custom bodies, enter body radius and the standard gravitational parameter.
Press Calculate Orbit to display results above the form.
Review the output metrics, then download the report as CSV or PDF.

Frequently Asked Questions

1) What does this calculator estimate?

It estimates orbital period, perigee and apogee velocity, eccentricity, escape velocity, energy, angular momentum, and orbit class using standard two-body orbital mechanics formulas.

2) Can I model elliptical orbits?

Yes. Choose the elliptical option and enter separate perigee and apogee altitudes. The calculator then derives the semi-major axis, eccentricity, speeds, and period.

3) What is the standard gravitational parameter?

It is the product of the gravitational constant and body mass, written as μ. Orbital calculations often use μ directly because it is more practical than entering mass and G separately.

4) Why is inclination included?

Inclination is included for mission reporting and documentation. In this simplified two-body model, scalar speed and period are not changed by inclination alone.

5) Does the graph show a real orbit shape?

Yes. The Plotly graph uses the orbital conic equation with the central body at a focus. It marks periapsis and apoapsis for quick interpretation.

6) Are atmospheric drag and perturbations included?

No. This tool assumes an idealized two-body environment. It does not include drag, oblateness, third-body effects, solar pressure, or station-keeping corrections.

7) What units does the calculator use?

It uses kilometers, seconds, degrees, kilograms, joules, and kilometers per second. Keep every entry in the displayed unit system for correct results.

8) When should I use a custom body?

Use a custom body when working with asteroids, fictional worlds, or specialized research cases. Enter the body radius and gravitational parameter carefully.