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Physics

23.3 - Orbits

9 min

Why objects orbit

Acceleration in an orbit

Orbital radius and speed

note 1 of 6

Gravity provides the force that creates orbits

Planets orbit the Sun, and moons and artificial satellites orbit planets, in almost circular orbits.
An object moving in a circle is constantly changing direction, so even at a constant speed its velocity is constantly changing.
A changing velocity means the object is accelerating, which requires a resultant force.
This force acts towards the centre of the circle.

Gravity provides the inward force

For an orbiting object, this inward force is provided by gravity:
- The Sun's gravitational pull keeps planets and comets in orbit.
- A planet's gravitational pull keeps moons and artificial satellites in orbit.
Because the object is already moving, the gravitational pull doesn't pull it straight in - it constantly bends its path into a circle.

Four Earths sit on a grey dashed circle labelled orbit around a central sun, each with a green arrow labelled gravitational force pointing inwards and a pink arrow labelled velocity along the circle.

note 2 of 6

Orbital speed and the size of the orbit

For a circular orbit, the gravitational force acts at right angles to the object's motion.
This changes the object's direction without changing its speed.

Orbital speed depends on the radius

Gravitational pull is stronger the closer an object is to the body it orbits.
The stronger the pull, the faster the object must travel to maintain a stable orbit.
If the speed of an orbiting object changes, its radius must change too:
- A faster object orbits with a smaller radius.
- A slower object orbits with a larger radius.
This is why planets closer to the Sun travel faster and have shorter orbital periods than planets further out.

Two dashed circles ring a yellow sun, with Earth on the inner one labelled greater velocity and stronger gravity, and a small red planet on the outer one labelled weaker gravity and lower velocity.

note 3 of 6

Orbits can be circular or elliptical

Most planets and moons have slightly elliptical (stretched circular) orbits.
Comets have highly elliptical orbits, with the Sun near one end of the ellipse.
A comet's orbital period is much longer than a planet's because it travels far into the outer solar system.
A comet travels much faster near the Sun than far away, because the gravitational pull is stronger the closer it gets.

A labelled comet with a blue tail sits on a dashed ellipse; the sun is near the right end, with dots marked slowest point at the far left and fastest point beside it.

note 4 of 6

Why an object speeds up near the Sun

The change in speed of an object in an elliptical orbit is explained by the conservation of energy.
As the object moves closer to the Sun:
- Its gravitational potential energy store decreases.
- Energy is transferred to its kinetic energy store, so it speeds up.
As the object moves away from the Sun:
- Energy transfers from its kinetic store back to its gravitational potential store, so it slows down.

Two comets travel a dashed elliptical orbit round the sun, with a box marked moving away showing kinetic energy store arrowed to gravitational potential energy store, and a box marked moving closer showing the reverse.

note 5 of 6

Calculating orbital speed

In one complete circular orbit, an object travels a distance equal to the circumference ( $2 π r$ ).
Dividing this distance by the time for one orbit gives the orbital speed.

Formula for orbital speed

$T$

Where:

$v$ = Orbital speed, in metres per second (m/s)
$r$ = Orbital radius, in metres (m), the distance from the centre of the orbited body to the orbiting object
$T$ = Orbital period, in seconds (s), the time for one complete orbit

note 6 of 6

Worked example - Orbital speed of a satellite

A satellite orbits at an altitude of 800 km above the Earth's surface. The radius of the Earth is 6,400 km, and the satellite takes 100 minutes to complete one orbit. Calculate its orbital speed.

Step 1 - Find the orbital radius in metres

Add the altitude to the Earth's radius:

$\begin{matrix} r & = 6,400 + 800 \\ = 7,200 km \\ = 7,200,000 m \end{matrix}$

Step 2 - Convert the orbital period to seconds

$T = 100 \times 60 = 6,000 s$

Step 3 - Substitute into the orbital-speed equation

$\begin{matrix} v & = \frac{2 π r}{T} \\ = \frac{2 \times π \times 7,200,000}{6,000} = 7,540 m/s \\ = 7,500 m/s (to 2 s.f.) \end{matrix}$

key terms

TermDefinition

Orbital periodThe time taken for an object to complete one full orbit.

end of notes

Key points to remember

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23.4 - Solar System FormationNext up