Orbital Speed and Period

Objects in orbit around a star or planet are held in orbit by gravitational attraction. The orbital speed and period depend on the orbital radius.

Key relationships

For an object in a stable circular orbit:

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

where $v$ is the orbital speed, $r$ is the orbital radius, and $T$ is the orbital period (time for one complete orbit).

How radius affects speed and period

As orbital radius increases:

• Orbital speed decreases (the gravitational pull is weaker, so a slower speed is needed to maintain the orbit).
• Orbital period increases (the circumference is larger AND the speed is slower, so it takes much longer to complete one orbit).

Examples from the solar system

Planet	Orbital radius (AU)	Orbital period
Mercury	0.39	88 days
Earth	1.00	365 days
Mars	1.52	687 days
Jupiter	5.20	12 years
Neptune	30.1	165 years

Satellites around Earth

• Low Earth orbit (LEO): altitude ~200 to 2000 km. Period ~90 minutes. Used for Earth observation, ISS.
• Geostationary orbit: altitude ~36 000 km. Period = 24 hours (matches Earth’s rotation). Stays above the same point. Used for TV broadcasting and weather satellites.

Common errors and how to correct them

• Thinking faster orbits are at greater distances. The opposite is true: closer orbits are faster.
• Confusing orbital speed with rotational speed of the planet.

How to apply this in an exam

State the relationship between radius and speed/period. Use $v = 2\pi r/T$ for calculations. Know the difference between LEO and geostationary orbits.