Orbital Period & Gravity Field Calculator
Calculate orbital periods using Kepler's third law and evaluate gravity field quantities. Compare satellites around Earth, Moon, Mars, Jupiter, Sun, or custom celestial bodies.
Compare Orbits and Gravity Around Planets and Moons
Choose Earth, Moon, Mars or a custom body, set altitude or semi-major axis, and we'll compute orbital period, gravity at that radius, and circular orbital speed using simple two-body physics.
T = 2π√(a³/μ) — Kepler's third law
g(r) = μ/r² — Gravitational acceleration
vcirc = √(μ/r) — Circular orbital velocity
Start with a low Earth orbit around 400 km and compare it to a geostationary orbit.
Understanding Orbital Period and Gravity Fields
Two-Body Orbits in a Nutshell
In the two-body problem, a small object orbits a much more massive central body (like a satellite around Earth). The massive body's gravity dominates, and we can ignore other forces.
Under these conditions, orbits are conic sections: circles, ellipses, parabolas, or hyperbolas. Bound orbits (those that don't escape) are ellipses, with circles being a special case of zero eccentricity.
Kepler's Third Law
The orbital period T depends only on the semi-major axis a and the gravitational parameter μ = G·M. Remarkably, it doesn't depend on the orbit's eccentricity!
Two orbits with the same semi-major axis have the same period, regardless of how elliptical or circular they are.
Semi-Major Axis
The semi-major axis a is half the longest diameter of an ellipse:
- Circular orbit: a = rorbit = R + h (body radius plus altitude)
- Elliptical orbit: a = (rp + ra) / 2 (average of closest and farthest distances)
The semi-major axis determines both the orbital energy and the orbital period.
Gravity Field vs Radius
g(r) = μ / r² — Gravitational acceleration
Φ(r) = − μ / r — Gravitational potential
vcirc = √(μ/r) — Circular orbit velocity
Gravity weakens as the inverse square of distance. At double the radius, gravity is only 1/4 as strong. Orbital velocity also decreases with radius, but more slowly (inverse square root).
Common Orbital Examples
| Orbit | Altitude | Period |
|---|---|---|
| Low Earth Orbit (ISS) | ~400 km | ~92 min |
| GPS Satellites | ~20,200 km | ~12 hours |
| Geostationary (GEO) | ~35,786 km | ~24 hours |
| Moon's Orbit | ~384,400 km | ~27.3 days |
Limitations & Assumptions
- Two-body only: No effects from other bodies (Moon, Sun, other planets).
- Spherical body: No oblateness effects (J2 perturbation) that cause orbit precession.
- No drag: Atmospheric drag affects LEO satellites significantly.
- No radiation pressure: Solar pressure affects high-altitude orbits.
- Educational only: Real mission design needs full perturbation models.
Frequently Asked Questions
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