Orbital Period Calculator
Calculate orbital periods for satellites and binary systems using Kepler's laws
Calculate Orbital Period
Mean density of the central body (e.g., Earth: 5.51 g/cm³)
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Kepler's Laws of Planetary Motion
First Law
Planets orbit in ellipses with the Sun at one focus
Second Law
Equal areas swept in equal times (planets move faster when closer)
Third Law
T² ∝ a³ (period squared proportional to distance cubed)
Common Orbital Types
Low Earth Orbit (LEO)
160-2000 km altitude, ~1.5-2 hour periods
Geostationary Orbit
35,786 km altitude, 24-hour period
Polar Orbit
Passes over both poles, sun-synchronous
Quick Facts
Earth has over 3,700 active satellites in orbit
ISS completes ~15.5 orbits per day
Binary stars can have periods from hours to thousands of years
Pluto-Charon system takes 6.39 days per orbit
Understanding Orbital Periods
What is an Orbital Period?
The orbital period is the time it takes for one celestial body to complete a full orbit around another. This fundamental concept governs the motion of planets around stars, moons around planets, and binary star systems.
Satellite Orbits
For satellites in low orbit around a massive central body, the period depends only on the central body's density. This simplified formula works when the satellite is much smaller than the central body and orbits close to its surface.
T = √(3π / (G·ρ))
- T: Orbital period
- G: Gravitational constant
- ρ: Central body density
Binary Systems
Binary systems involve two bodies of comparable mass orbiting their common center of mass. This applies to binary stars, double planets, and some asteroid systems. The calculation requires both masses and their separation distance.
T = 2π√(a³ / (G·(M₁+M₂)))
- T: Orbital period
- a: Semi-major axis
- M₁, M₂: Masses of both bodies
- G: Gravitational constant
Applications
- •Satellite mission planning and orbit design
- •Exoplanet detection and characterization
- •Binary star system analysis
- •Asteroid and comet orbit prediction