An orbit is a continuous state of falling — and missing. The International Space Station isn’t floating; it’s falling toward Earth at the same rate that the Earth’s surface curves away beneath it. That’s what an orbit is.

Orbital velocity

For a circular orbit at altitude $r$ from the centre of a body with mass $M$:

$$v = \sqrt{\frac{GM}{r}}$$

At Low Earth Orbit (LEO, ~400 km altitude): $v \approx$ 7.7 km/s — that’s 27,500 km/h, circling the Earth every 92 minutes.

The counterintuitive result: to go to a higher orbit, you need to speed up. But once you’re there, you’re moving slower. Orbital velocity decreases with altitude. The Moon orbits at just 1 km/s.

Escape velocity

To leave a body’s gravitational influence entirely:

$$v_{\text{esc}} = \sqrt{\frac{2GM}{r}} = \sqrt{2} \cdot v_{\text{circular}}$$

From Earth’s surface: 11.2 km/s. From the Moon: 2.4 km/s. From Jupiter: 59.5 km/s.

Key orbits

Geostationary orbit (GEO) is special: the period exactly matches Earth’s rotation, so the satellite appears stationary in the sky. That’s why satellite TV dishes point at a fixed spot.

The manoeuvre paradox

To catch up with something ahead of you in orbit, you don’t speed up (that would raise your orbit, making you slower). You slow down — dropping to a lower, faster orbit — then speed up again at the right moment. Orbital mechanics is deeply counterintuitive: the fastest way to catch something is to fall behind it first.

This counterintuitive logic extends to everything in orbital mechanics. Every manoeuvre is a trade between altitude and speed, governed by the conservation of energy.