Altitude and Period: Kepler's third law, made interactive
Delta-V Academy / Learn / Lesson 2
Higher orbits move slower. Drag the altitude slider and watch why.
Kepler's third law says the square of an orbit's period is proportional to the cube of its size: T² ∝ a³. In plain English, bigger orbits take longer. A satellite at 400 km altitude orbits Earth in 92 minutes. One at 20,200 km (GPS altitude) takes 12 hours. One at 35,786 km (geostationary altitude) takes exactly 23 hours 56 minutes 4 seconds, matching Earth's rotation. That last number isn't a coincidence — it's why we have geostationary satellites at all.
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What you'll learn
- Kepler's third law: T² = (4π²/μ) × a³, where μ = 398,600 km³/s² for Earth
- Why geostationary orbit is exactly 35,786 km above the equator
- The relationship between orbit size and orbital speed
- How altitude trades off against signal latency and coverage area
- Why Starlink (550 km) and OneWeb (1,200 km) sit at different altitudes
Kepler's third law in numbers
For Earth orbits, plug in μ = 398,600 km³/s² and you get T (in seconds) = 2π × √(a³ / μ). A 400 km altitude (a ≈ 6,778 km) gives T = 5,550 s = 92.5 minutes. A 20,200 km altitude (a ≈ 26,578 km) gives T = 43,200 s = 12 hours. A 35,786 km altitude (a ≈ 42,164 km) gives T = 86,164 s = one sidereal day. The math is exact; the only reason GEO is at that specific altitude is because that's where the period equals Earth's rotation period.
Why geostationary orbit exists at exactly one altitude
For a satellite to appear stationary in the sky, it needs three things: (1) its orbital period must equal one sidereal day (23h 56m 4s, not 24 hours), (2) its orbit must be circular (eccentricity = 0), (3) its orbit must be exactly in the equatorial plane (inclination = 0°). Only the altitude that satisfies Kepler's third law for that exact period works. That altitude is 35,786 km above Earth's surface, or 42,164 km from Earth's center. Above or below, the satellite drifts east or west relative to the ground.
Why this matters for satellite design
Orbital period drives many design decisions. Low orbits (LEO) give low signal latency (Starlink at 550 km has ~20ms ping vs GEO's ~600ms) but each satellite covers only a small patch of ground at a time, requiring large constellations for global coverage. High orbits (GEO) cover a third of Earth from a single satellite but with much higher latency. Medium orbits (MEO, where GPS lives) compromise: 12-hour periods, moderate latency, and enough coverage that 24 satellites give global service.
Frequently asked questions
What is Kepler's third law?
Kepler's third law states that the square of an orbital period is proportional to the cube of the semi-major axis: T² ∝ a³. For Earth orbits, T² = (4π²/μ) × a³ where μ = 398,600.4418 km³/s² is Earth's gravitational parameter.
Why does GEO sit at 35,786 km exactly?
Because that's the altitude where Kepler's third law gives an orbital period equal to one sidereal day (23h 56m 4s). At that altitude in a circular equatorial orbit, the satellite's angular rate matches Earth's rotation rate, making it appear stationary in the sky.
How long does the ISS take to orbit Earth?
About 92.5 minutes. At an average altitude of 400 km, the ISS completes 16 orbits per day. Astronauts on board see 16 sunrises and 16 sunsets every day.
How long do GPS satellites take to orbit Earth?
GPS satellites are in roughly 12-hour orbits at 20,200 km altitude (more precisely, 11 hours 58 minutes, which is exactly half a sidereal day). Each satellite passes over the same ground track twice per day.
Is a higher orbit faster or slower?
Slower. Counterintuitive but true: ISS at 400 km moves at 7.66 km/s; GEO at 35,786 km moves at 3.07 km/s. Higher means slower because gravity is weaker at higher altitudes and less centripetal acceleration is needed.
Related lessons
- Lesson 1: Orbit Basics — Drag the sliders, watch what happens. Real Keplerian physics in your browser.
- Lesson 7: Orbital Regimes — Four altitude bands. Four totally different design philosophies.
- Lesson 3: Eccentricity and Speed — Same orbit, different speeds. Drag eccentricity, watch the satellite race through perigee and crawl through apogee.
Open it in the simulator
Delta-V Academy is a free interactive orbital mechanics simulator that runs entirely in your browser. The 10-lesson curriculum covers everything from these basics through space domain awareness, with three difficulty levels (novice, intermediate, advanced) plus a kid-friendly mode. Launch the simulator and try Lesson 2 interactively.
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