Elliptical Orbits

Planets, minor planets, and comets travel around the Sun in elliptical orbits. An ellipse is a squashed circle. The Sun is at one focus of the ellipse, not at the centre. Many planetary orbits are almost circular, but they are still ellipses.

Key Features of an Ellipse

• Perihelion: the closest point to the Sun.
• Aphelion: the furthest point from the Sun.
• If you imagine two pins (the foci) and a loop of string, keeping the string tight and tracing a path draws an ellipse.

Why Orbits Happen

The Sun contains most of the Solar System’s mass, so its gravity keeps objects in orbit. Gravity gets weaker as distance increases, so outer planets feel a smaller pull and generally move more slowly.

Speed Changes in an Elliptical Orbit

An object in an elliptical orbit moves faster when it is closer to the Sun and slower when it is further away. This can be explained using conservation of energy: the total energy stays constant, but energy shifts between kinetic (movement) and gravitational potential (position).

$$E_{\text{total}} = \text{KE} + \text{GPE} = \text{constant}$$

• Near perihelion: it is deeper in the Sun’s gravity well, so GPE decreases and KE increases → speed increases.
• Near aphelion: it is higher in the gravity well, so GPE increases and KE decreases → speed decreases.

Average Orbital Speed (nearly circular)

For near-circular orbits, or when using an average orbital radius $r$, the average speed is:

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

Real-World Connections

• Comets have very stretched ellipses; they move very fast near the Sun and very slowly far away.
• Satellites around planets also follow ellipses; lower orbits mean higher speeds.

Common Misconceptions

• “The Sun is at the centre of the ellipse.” It is at a focus.
• “Planets move at constant speed.” Speed changes along an ellipse.
• “Engines push planets around the Sun.” Gravity provides the inward force; no engines are needed.