In this section we explore how the Sun’s gravity and the planets’ orbital speeds change with distance. 🌞🚀
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.
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. 🪐
| Planet | Average Distance (AU) | Orbital Speed (km/s) |
|---|---|---|
| Mercury | 0.39 | 47.9 |
| Venus | 0.72 | 35.0 |
| Earth | 1.00 | 29.8 |
| Mars | 1.52 | 24.1 |
| Jupiter | 5.20 | 13.1 |
| Saturn | 9.58 | 9.7 |
| Uranus | 19.20 | 6.8 |
| Neptune | 30.05 | 5.4 |
When asked to compare the gravitational pull or orbital speed of two planets, remember:
Keep your answer concise and use the correct symbols. Good luck! 🎓