Know that planets, minor planets and comets have elliptical orbits, and recall that the Sun is not at the centre of the elliptical orbit, except when the orbit is approximately circular

6.1.2 The Solar System

Learning Objective

Know that planets, minor planets and comets have elliptical orbits, and recall that the Sun is not at the centre of the elliptical orbit, except when the orbit is approximately circular.

Key Concepts

Elliptical Orbits

According to Kepler’s First Law, the path of any body that orbits the Sun is an ellipse with the Sun at one focus.

The general equation of an ellipse centred at the origin is

\$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\$

where a is the semi‑major axis and b is the semi‑minor axis. The distance from the centre to each focus is

\$c=\sqrt{a^{2}-b^{2}}\$

For a circular orbit, a = b and therefore c = 0; the Sun lies at the centre of the circle.

Sun’s Position in an Ellipse

• In a true ellipse the Sun occupies one of the two foci, not the geometric centre.
• Only when the eccentricity is very small (orbit nearly circular) does the Sun appear to be at the centre for practical purposes.

Types of Solar‑System Objects

All of the following follow elliptical paths around the Sun:

1. Planets
2. Minor planets (asteroids, dwarf planets)
3. Comets

Typical Orbital Eccentricities

Why the Sun Is Not at the Centre

Because the Sun and the orbiting body both exert gravitational forces on each other, they actually orbit their common centre of mass (barycentre). For the Sun–planet system the barycentre lies inside the Sun, but it is offset from the Sun’s geometric centre, which corresponds to one focus of the ellipse.

Implications for Observation

• Planetary distances from the Sun vary throughout the year.
• Speed of a planet changes – faster at perihelion (closest point) and slower at aphelion (farthest point).
• For highly eccentric comets, the Sun’s apparent motion across the sky is rapid near perihelion.

Summary

All major bodies in the Solar System travel in elliptical orbits with the Sun at one focus. Only when the eccentricity is very small does the orbit appear circular, allowing the Sun to be treated as if it were at the centre. Understanding this geometry is essential for interpreting orbital speed, distance variations, and the behaviour of different classes of objects (planets, minor planets, comets).