Orbits and Orbital Speed

Why anything orbits. Gravity provides the force that keeps an orbiting body moving in its curved path. Without it the body would travel in a straight line, as Newton's first law requires.

The force always acts towards the centre of the orbit — towards the Sun for a planet, towards the Earth for the Moon or a satellite.

An orbiting body is accelerating even at constant speed, because its direction is constantly changing. Acceleration is a change in velocity, and velocity includes direction. This is worth being precise about, because a question asking whether a satellite accelerates has a counter-intuitive answer of yes.

Orbital speed:

v = 2 π r / T

where v is the orbital speed in m/s, r the orbital radius in metres and T the orbital period in seconds. The reasoning is simply that the body travels one circumference, 2πr, in one period.

Watch the units. Periods are usually quoted in days or years and must be converted to seconds; radii are often in kilometres and must be converted to metres. Almost every error in this topic is a conversion error rather than a physics one.

1 day = 86 400 s

1 year ≈ 3.15 × 10⁷ s

Bigger orbits are slower. A planet further from the Sun has a longer period and a lower orbital speed, because gravity is weaker further out and less speed is needed to maintain the orbit. Neptune takes 165 years to go round once; Mercury takes 88 days.

Gravitational field strength depends on the mass of the body producing it and the distance from it. It is stronger close to a massive body and weakens with distance. This is why the Sun's grip on Neptune is far weaker than on Mercury.

Example: the Moon orbits at a radius of 3.8 × 10⁸ m with a period of 27.3 days. Converting: T = 27.3 × 86 400 = 2.36 × 10⁶ s. So v = 2π × 3.8 × 10⁸ ÷ 2.36 × 10⁶ ≈ 1.0 × 10³ m/s, about 1 km/s.