Know that the Sun contains most of the mass of the Solar System and this explains why the planets orbit the Sun

Published by Patrick Mutisya · 8 days ago

Cambridge IGCSE Physics 0625 – 6.1.2 The Solar System

6.1.2 The Solar System

Learning Objective

Understand that the Sun contains the overwhelming majority of the mass in the Solar System and that this explains why the planets orbit the Sun.

Key Facts

  • The Sun accounts for about 99.86 % of the total mass of the Solar System.

  • All planets, dwarf planets, asteroids and comets together make up only about 0.14 % of the total mass.

  • Because the Sun is so massive, its gravitational pull dominates the motion of all other bodies.

Mass Distribution Table

ObjectMass (kg)Mass as % of Solar System
Sun1.989 × 103099.86 %
Jupiter1.898 × 10270.095 %
Saturn5.683 × 10260.028 %
All other planets combined≈ 2.5 × 1026≈ 0.012 %
All other bodies (asteroids, comets, etc.)≈ 3 × 1024≈ 0.001 %

Why Do Planets Orbit the Sun?

The motion of a planet around the Sun is governed by Newton’s law of universal gravitation and his second law of motion.

  1. Gravitational force between two masses:

    \$F = G\frac{M{\text{sun}}\,m{\text{planet}}}{r^{2}}\$

    where

    • \$G\$ is the universal gravitational constant (\$6.674\times10^{-11}\,\text{N·m}^2\text{/kg}^2\$),

    • \$M_{\text{sun}}\$ is the mass of the Sun,

    • \$m_{\text{planet}}\$ is the mass of the planet, and

    • \$r\$ is the distance between the centres of the two bodies.

  2. Because \$M{\text{sun}} \gg m{\text{planet}}\$, the force is essentially determined by the Sun’s mass.

  3. The planet’s centripetal acceleration needed for a circular (or elliptical) orbit is provided by this gravitational force:

    \$\frac{m{\text{planet}}v^{2}}{r}=G\frac{M{\text{sun}}\,m_{\text{planet}}}{r^{2}}\$

    Cancelling \$m_{\text{planet}}\$ gives the orbital speed:

    \$v = \sqrt{\frac{G M_{\text{sun}}}{r}}\$

  4. Thus the Sun’s large mass fixes the orbital speed and period for each planet at a given distance.

Consequences of the Sun’s Dominant Mass

  • All planets move in paths that are conic sections (mostly ellipses) with the Sun at one focus.

  • The relative positions of the planets are determined by their distances from the Sun, not by mutual attractions between the planets (which are comparatively tiny).

  • Any object that passes close enough to the Sun can become a satellite or be captured into orbit if its velocity matches the required orbital speed.

Suggested diagram: A scale diagram of the Solar System showing the Sun’s size relative to the planets and indicating the direction of gravitational force vectors pointing toward the Sun.

Quick Check Questions

  1. What percentage of the Solar System’s total mass is contained in the Sun?

  2. Write the expression for the gravitational force between the Sun and a planet.

  3. Explain in one sentence why the planets do not orbit each other.

  4. Calculate the orbital speed of Earth using \$r = 1.496\times10^{11}\,\text{m}\$ and \$M_{\text{sun}} = 1.989\times10^{30}\,\text{kg}\$ (use \$G = 6.674\times10^{-11}\,\text{N·m}^2\text{/kg}^2\$).