Orbital Speed Equation

Objects in nearly circular orbits (like planets and many satellites) move at an average speed that depends on how big the orbit is and how long one orbit takes. This is called average orbital speed.

The equation

Average orbital speed is given by

$$v = \frac{2\pi r}{T}$$

• v = average orbital speed
• r = average radius of the orbit (distance from the centre of the object being orbited)
• T = orbital period (time for one full orbit)

Why this works

In one complete orbit the object travels the circumference of a circle, which is $2\pi r$. Speed is distance divided by time, so distance $/$ time becomes $2\pi r / T$.

Units that match

• Use metres (m) for $r$ and seconds (s) for $T$ to get $v$ in m/s.
• If you use kilometres for $r$, keep $v$ in km/s, or convert: 1 km = 1000 m.
• Time conversions: 1 day = 86 400 s; 1 year ≈ 365 days.

Common mistakes

• Using $\pi r^2$ (area) instead of $2\pi r$ (circumference).
• Using diameter instead of radius. Remember: radius is half the diameter.
• Forgetting to convert days to seconds or km to m.
• Thinking speed changes a lot in a circular orbit. In a circular orbit, speed is constant; in an elliptical orbit it varies, so $v = 2\pi r/T$ gives an average value.

Real-world connections

• Satellites closer to Earth (smaller $r$) have shorter $T$ and must move faster to stay in orbit.
• Outer planets have larger $r$ and much longer $T$, so their average orbital speeds are lower.