What is Kepler's Third Law?

Kepler's Third Law states T² ∝ a³. Around the Sun: T² (years) = a³ (AU). The full formula is T = 2π × √(a³/(GM)).

What is the ISS orbital period?

The ISS orbits at about 408 km altitude (semi-major axis ≈ 6779 km from Earth's center), giving an orbital period of approximately 92.7 minutes.

What is geosynchronous orbit?

A geosynchronous orbit has a 24-hour period matching Earth's rotation. For a circular equatorial orbit this is geostationary at ~35,786 km altitude.

What is synodic period?

The synodic period is the time between successive alignments of two orbiting bodies. 1/P_syn = |1/P₁ − 1/P₂|.

How do I use AU and years?

For orbits around the Sun, T² = a³ where T is in years and a is in AU. Mars (a=1.524 AU): T = 1.524^1.5 ≈ 1.88 years = 687 days.

Orbital Period Calculator

Calculate orbital period using Kepler's Third Law (T = 2π√(a³/GM)). Supports AU/years shortcut, Earth orbits, solar system presets, and synodic period.

Semi-major Axis a (m)

Central Body Mass M (kg)

Orbital Period (s)

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Orbital Period (days) —

Orbital Period (years) —

Extended More scenarios, charts & detailed breakdown ▾

Semi-major Axis a (m)

Central Body Mass (kg)

Period (days)

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Period (years) —

Professional Full parameters & maximum detail ▾

Semi-major Axis a (m)

Central Body Mass (kg)

Second Body Axis a₂ (m)

Primary Orbit

Orbital Period —

Circular Orbital Speed —

Relative & Transfer

Synodic Period (vs body 2) —

Hohmann Transfer Time (to body 2) —

Reference

Geosync Altitude (Earth) —

How to Use This Calculator

Enter the semi-major axis in meters and central body mass in kg for the general formula.
Use Around Sun tab for the AU/years shortcut.
Use Around Earth for satellite altitudes.
The Professional tier adds synodic period, geosynchronous altitude, and Hohmann transfer time.

Formula

T = 2π × √(a³ / (GM))

Around Sun: T² (yr) = a³ (AU)

Synodic: 1/P_syn = |1/P₁ − 1/P₂|

Example

Earth around Sun: a = 1 AU = 1.496×10¹¹ m, M_Sun = 1.989×10³⁰ kg → T = 2π√(a³/GM) = 365.25 days

Frequently Asked Questions

Kepler's Third Law states T² ∝ a³. Around the Sun: T² (years) = a³ (AU). The full formula is T = 2π × √(a³/(GM)).
The ISS orbits at about 408 km altitude (semi-major axis ≈ 6779 km from Earth's center), giving an orbital period of approximately 92.7 minutes.
A geosynchronous orbit has a 24-hour period matching Earth's rotation. For a circular equatorial orbit this is geostationary at ~35,786 km altitude.
The synodic period is the time between successive alignments of two orbiting bodies. 1/P_syn = |1/P₁ − 1/P₂|.
For orbits around the Sun, T² = a³ where T is in years and a is in AU. Mars (a=1.524 AU): T = 1.524^1.5 ≈ 1.88 years = 687 days.

Related Calculators

Sources & References (5) ▾

Kepler's Laws — NASA Space Place — NASA
JPL Horizons — Orbital Elements — NASA Jet Propulsion Laboratory
University Physics Vol. 1, Ch. 13.5: Kepler's Laws — OpenStax
NIST Physical Constants — G — NIST CODATA
Orbital Mechanics — Wikipedia — Wikipedia