Satellite Orbital Period Calculator

How Satellite Orbital Period Is Calculated

The orbital period of a satellite depends only on its altitude and the mass of the body it orbits — not on the satellite’s own mass. This is Kepler’s Third Law applied to circular orbits.

Orbital Period Formula: T = 2π × √(r³ / GM)

Where:

• T = orbital period in seconds
• r = orbital radius (planet radius + altitude) in meters
• G = gravitational constant = 6.674 × 10⁻¹¹ N·m²/kg²
• M = mass of the central body (Earth = 5.972 × 10²⁴ kg)

Worked Example: International Space Station:

• Altitude: ~408 km = 408,000 m
• Earth radius: 6,371,000 m
• r = 6,371,000 + 408,000 = 6,779,000 m
• GM = 6.674×10⁻¹¹ × 5.972×10²⁴ = 3.986×10¹⁴ m³/s²
• T = 2π × √((6,779,000)³ / 3.986×10¹⁴) = 2π × √(3.115×10²⁰ / 3.986×10¹⁴)
• T = 2π × √(781,234) = 2π × 883.9 = 5,552 seconds ≈ 92.5 minutes

Common Orbital Periods:

• Low Earth Orbit (400–600 km): ~90–97 minutes
• GPS satellites (20,200 km): 12 hours
• Geostationary orbit (35,786 km): exactly 24 hours
• Moon: 27.3 days (at 384,400 km)

Geostationary Orbit Calculation: Set T = 86,400 s and solve for r: r = (GM × T² / 4π²)^(1/3) = 42,164 km from Earth’s center (35,786 km altitude).