Orbital Period Calculator – Calculate Orbital Period

Calculate the orbital period of a satellite or planet using Kepler's third law. Enter the semi-major axis and central body mass.

Semi-major Axis (m)

Central Body Mass (kg)

How to Use This Orbital Period Calculator

Enter semi-major axis

Input the average distance from the orbiting body to the central body in meters.

Input central body mass

Enter the mass of the body being orbited (Earth, Sun, etc.) in kilograms.

Calculate orbital period

Click Calculate Period to see the time for one complete orbit in seconds, days, and years.

Orbital Periods in Our Solar System

Body	Semi-major Axis	Orbital Period
Mercury	57.9 million km	88 days
Venus	108.2 million km	225 days
Earth	149.6 million km	365.25 days
Mars	227.9 million km	687 days
Jupiter	778.5 million km	11.86 years
Neptune	4.5 billion km	165 years

Understanding Orbital Mechanics

Kepler's Third Law

The square of the orbital period is proportional to the cube of the semi-major axis. This means planets farther from the Sun take much longer to orbit. Double the distance and the period increases by about 2.8 times. This relationship holds for any orbiting system — moons around planets, satellites around Earth, or exoplanets around stars.

What Is Semi-major Axis?

The semi-major axis is half the longest diameter of an elliptical orbit. For nearly circular orbits like planets, it equals the average distance from the central body. For highly elliptical orbits like comets, it is the average of closest and farthest approach distances.

Why Mass Matters

More massive central bodies create stronger gravity, requiring faster orbital speeds. A satellite orbiting Jupiter at the same distance as one orbiting Earth would complete its orbit much faster because Jupiter is 318 times more massive. The formula accounts for this through the gravitational parameter GM.

Satellite Orbit Tips

Low Earth Orbit (LEO)

200-2,000 km altitude. Period: 90-120 minutes. Used by ISS, Hubble, and many satellites.

Geostationary Orbit (GEO)

35,786 km altitude. Period: exactly 24 hours. Satellites appear stationary over one point on Earth.

Medium Earth Orbit (MEO)

2,000-35,786 km altitude. GPS satellites orbit at about 20,200 km with 12-hour periods.

Escape velocity

To leave Earth orbit entirely, spacecraft must reach 11.2 km/s — about 40,000 km/h.

Frequently Asked Questions

What is the orbital period formula?

T = 2π × √(a³/GM), where T is period, a is semi-major axis, G is the gravitational constant (6.674×10⁻¹¹), and M is the central body mass. This comes from equating gravitational force to centripetal force for circular motion.

Does satellite mass affect orbital period?

No — not when the satellite is much less massive than the central body. A 1 kg satellite and a 1000 kg satellite at the same altitude have identical orbital periods. Only the central body mass matters. This is why all objects fall at the same rate in a vacuum.

Why do geostationary satellites orbit at 35,786 km?

That specific altitude gives exactly 24-hour orbital period, matching Earth's rotation. Lower orbits are faster; higher orbits are slower. At 35,786 km above the equator, satellites stay fixed over one point — perfect for communications and weather monitoring.

How accurate is this calculator?

Very accurate for ideal two-body systems. Real orbits have perturbations from other bodies, atmospheric drag (for LEO), and non-spherical gravity fields. For most educational and planning purposes, the two-body approximation is sufficient.

Can I use this for binary star systems?

For binary systems, use the sum of both masses as M and the separation distance as a. The formula still applies but both bodies orbit their common center of mass. For equal-mass binaries, each star orbits at half the separation distance.

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