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

6.1.2 The Solar System

Learning Objective

Explain why the Sun, which contains almost all of the mass of the Solar System, determines the orbital motion of the planets and other bodies.

Solar‑System Overview (Syllabus Requirement)

• The Sun
• Eight named planets (in order from the Sun)

  1. Mercury
  2. Venus
  3. Earth
  4. Mars
  5. Jupiter
  6. Saturn
  7. Uranus
  8. Neptune

• Dwarf (minor) planets – e.g. Pluto (re‑classified as a dwarf planet in 2006), Eris, Haumea, Makemake, Ceres
• Moons (natural satellites) – e.g. Earth’s Moon, Jupiter’s four Galilean moons, Saturn’s Titan
• Asteroids – mainly in the asteroid belt between Mars and Jupiter
• Comets – icy bodies from the Kuiper Belt or Oort Cloud that develop tails when near the Sun

Mass Distribution in the Solar System

Why Do the Planets Orbit the Sun?

1. Newton’s law of universal gravitation

   For two masses separated by a distance \(r\):

   \[

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

   \]

   • \(G = 6.674\times10^{-11}\ \text{N·m}^{2}\text{/kg}^{2}\)
   • \(M_{\text{sun}}\) – mass of the Sun (≈ 99.86 % of the Solar System)
   • \(m_{\text{planet}}\) – mass of the planet
   • \(r\) – centre‑to‑centre distance

   Because \(M{\text{sun}} \gg m{\text{planet}}\), the Sun’s gravitational pull dominates the dynamics of every Solar‑System body.

2. Balance of forces for an orbit (centripetal‑force condition)

   For a (near‑circular) orbit the required centripetal force is supplied by gravity:

   \[

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

   \]

   Canceling \(m_{\text{planet}}\) gives the orbital‑speed formula:

   \[

   v = \sqrt{\frac{GM_{\text{sun}}}{r}}

   \]

3. Average orbital speed

   For any closed orbit

   \[

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

   \]

   where \(T\) is the orbital period. Combining this with Kepler’s 3rd law (\(T^{2}\propto r^{3}\)) reproduces the same \(v\propto r^{-1/2}\) dependence as the formula above.

4. Result

   The Sun’s huge mass fixes the orbital speed and period for each body at a given distance, so the planets move in ellipses (or circles) with the Sun at one focus.

Worked Example – Orbital Speed of Earth

Given:

• \(r = 1.496\times10^{11}\ \text{m}\) (average Earth‑Sun distance)
• \(M_{\text{sun}} = 1.989\times10^{30}\ \text{kg}\)
• \(G = 6.674\times10^{-11}\ \text{N·m}^{2}\text{/kg}^{2}\)

Calculate:

\[

v = \sqrt{\frac{GM_{\text{sun}}}{r}}

= \sqrt{\frac{(6.674\times10^{-11})(1.989\times10^{30})}{1.496\times10^{11}}}

= \sqrt{8.87\times10^{8}}

\approx 2.98\times10^{4}\ \text{m s}^{-1}

= 29.8\ \text{km s}^{-1}

\]

Thus Earth travels around the Sun at about 30 km s⁻¹.

Consequences of the Sun’s Dominant Mass

• All planets and most other bodies follow conic‑section paths (primarily ellipses) with the Sun at one focus.
• Gravitational attractions between planets are tiny compared with the Sun’s pull; planetary positions are therefore governed mainly by their distances from the Sun.
• An object that passes sufficiently close to the Sun can be captured into orbit if its speed matches the required orbital speed for that distance.

Suggested Diagram

A scale illustration of the Solar System showing:

• The Sun’s relative size compared with the planets.
• Orbits of the eight planets (elliptical paths).
• Positions of dwarf planets, the asteroid belt, and the Kuiper Belt.
• Arrows on each body indicating the direction of the Sun’s gravitational force.

Quick‑Check Questions (Exam‑style)

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. State the orbital‑speed formula for a planet in a circular orbit.
4. Explain in one sentence why the planets do not orbit each other.
5. Calculate the orbital speed of Earth using the data given in the worked example (give your answer in km s⁻¹).
6. Diagram interpretation: In the diagram suggested above, an arrow points from a planet toward the Sun. Identify the physical quantity represented by this arrow and explain its role in keeping the planet in orbit.