Orbital mechanics is the branch of physics that describes how objects move under the influence of gravity. It's the foundation of every satellite mission, every Moon landing, and every interplanetary probe. The good news: you don't need calculus to understand it.
Kepler's Three Laws
In the early 1600s Johannes Kepler distilled decades of planetary observations into three elegant rules that still govern every orbit today:
- Law 1 — Orbits are ellipses. Not perfect circles. The body being orbited sits at one focus of the ellipse.
- Law 2 — Equal areas in equal times. A satellite moves faster when closer to Earth (perigee) and slower when farther (apogee).
- Law 3 — Bigger orbits take longer. Specifically, the square of the orbital period is proportional to the cube of the orbit's size.
That third law is why a low-orbit satellite zips around Earth in 90 minutes while a geostationary satellite at 35,786 km altitude takes a full day.
Orbital Velocity
The required speed for a circular orbit depends only on altitude. At the Earth's surface (ignoring the atmosphere) it would be about 7.9 km/s. At the ISS's 408 km it drops to 7.66 km/s, and at GEO it's only 3.07 km/s. Higher orbits are slower, not faster.
Six Numbers Define Any Orbit
Engineers describe an orbit using six "Keplerian elements":
- Semi-major axis — the size of the orbit.
- Eccentricity — how stretched the ellipse is (0 = circle).
- Inclination — the tilt of the orbital plane against the equator.
- Right ascension of the ascending node — where the orbit crosses the equator going north.
- Argument of perigee — where in the orbit the closest approach occurs.
- True anomaly — where the satellite is right now along the orbit.
Maneuvers and Delta-v
Changing an orbit requires energy, measured in "delta-v" — the change in velocity. Raising orbit, changing inclination, or rendezvousing with another spacecraft all cost delta-v, which translates directly to fuel. Mission planners agonize over delta-v budgets because every kilogram of propellant is a kilogram that wasn't science payload.
Watch It Happen
The live tracker shows Kepler's second law beautifully — watch elliptical orbits speed up at perigee. Then read about the ISSto see real numbers in action.