Know that the strength of the Sun's gravitational field decreases and that the orbital speeds of the planets decrease as the distance from the Sun increases

6.1.2 The Solar System

In this section we explore how the Sun’s gravity and the planets’ orbital speeds change with distance. 🌞🚀

Gravitational Field Strength

The Sun’s gravitational field pulls on all objects in the Solar System. The strength of this pull, called gravitational field, is given by:

\$g = \frac{G M_{\text{Sun}}}{r^2}\$

Where \$G\$ is the gravitational constant, \$M_{\text{Sun}}\$ is the Sun’s mass, and \$r\$ is the distance from the Sun. As \$r\$ increases, the denominator grows faster, so \$g\$ becomes smaller. Think of it like a rubber band: the further you pull, the less force it exerts.

Orbital Speed of Planets

Planets orbit because the Sun’s gravity provides the centripetal force needed to keep them moving in a circle. Equating the gravitational force to the centripetal force gives:

\$\frac{G M_{\text{Sun}} m}{r^2} = \frac{m v^2}{r}\$

Solving for the orbital speed \$v\$:

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

Thus, the farther a planet is from the Sun, the slower it travels. Imagine a spinning track: the closer the ball to the center, the tighter the track and the faster it rolls. 🪐

PlanetAverage Distance (AU)Orbital Speed (km/s)
Mercury0.3947.9
Venus0.7235.0
Earth1.0029.8
Mars1.5224.1
Jupiter5.2013.1
Saturn9.589.7
Uranus19.206.8
Neptune30.055.4

Exam Tip 🚀

When asked to compare the gravitational pull or orbital speed of two planets, remember:

  1. Use the formula \$g = \dfrac{G M_{\text{Sun}}}{r^2}\$ to show that \$g\$ decreases with the square of the distance.
  2. Use \$v = \sqrt{\dfrac{G M_{\text{Sun}}}{r}}\$ to show that orbital speed decreases as the square root of the distance.
  3. State the trend clearly: “The farther a planet is from the Sun, the weaker the Sun’s pull and the slower the planet moves.”

Keep your answer concise and use the correct symbols. Good luck! 🎓