Orbital Period Calculator
Compute orbital period using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Formula
T = 2 pi sqrt(a^3 / (G M))
Where T is the orbital period in seconds, a is the semi-major axis in meters, G is the gravitational constant (6.674 x 10^-11 m^3 kg^-1 s^-2), and M is the mass of the central body in kilograms. This is derived from Kepler's Third Law combined with Newton's law of gravitation.
Frequently Asked Questions
What is Kepler's Third Law and how does it calculate orbital period?
Kepler's Third Law of Planetary Motion states that the square of a planet's orbital period is directly proportional to the cube of the semi-major axis of its orbit. Mathematically, T squared equals 4 pi squared times a cubed divided by G times M, where T is the orbital period, a is the semi-major axis (the average distance from the central body), G is the gravitational constant, and M is the mass of the central body. This elegant relationship means that if you know the distance of an orbiting body from its parent and the mass of the parent, you can calculate exactly how long one complete orbit takes. Johannes Kepler discovered this empirical relationship in 1619, and Isaac Newton later provided the theoretical foundation by deriving it from his law of universal gravitation, showing that it applies to any two gravitationally bound objects in the universe.
How are orbital periods used to discover exoplanets?
Orbital periods are fundamental to exoplanet detection through the transit method, where astronomers measure periodic dips in a star's brightness as a planet crosses in front of it. The time between transits directly gives the orbital period, and using Kepler's Third Law with the known stellar mass, scientists can calculate the planet's distance from its star. The Kepler Space Telescope discovered over 2,600 confirmed exoplanets using this technique. The radial velocity method also relies on orbital periods by detecting the periodic wobble of a star caused by an orbiting planet's gravitational pull. Shorter orbital periods are easier to detect because multiple transits can be observed in less time. This observational bias means that close-in hot Jupiters with periods of a few days were among the first exoplanets discovered, while detecting Earth-like planets with year-long periods requires years of continuous observation.
What determines the orbital period of satellites around Earth?
Satellite orbital periods around Earth depend entirely on their altitude above the surface, which determines the semi-major axis. Low Earth orbit satellites at 400 km altitude, like the International Space Station, complete one orbit in approximately 93 minutes traveling at 7.66 km/s. Medium Earth orbit GPS satellites at 20,200 km altitude have periods of about 12 hours. At exactly 35,786 km altitude, a satellite achieves geostationary orbit with a period matching Earth's 24-hour rotation, appearing stationary above a fixed point on the equator. This principle is used for communications and weather satellites. The Moon orbits at 384,400 km with a period of 27.3 days. For any circular orbit, doubling the altitude more than doubles the period because of the cube-root relationship in Kepler's law. No satellite can orbit below approximately 160 km altitude because atmospheric drag would quickly deorbit it.
How do orbital velocities relate to altitude?
Orbital velocity decreases with altitude: v = sqrt(GM/r), where G is the gravitational constant, M is Earth's mass, and r is orbital radius. Low Earth orbit (400 km) requires about 7.67 km/s. Geostationary orbit (35,786 km) requires only 3.07 km/s. Escape velocity from Earth's surface is 11.2 km/s.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
Is Orbital Period Calculator free to use?
Yes, completely free with no sign-up required. All calculators on NovaCalculator are free to use without registration, subscription, or payment.