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
Cambridge IGCSE Physics 0625 – Topic 6.1.2: The Solar System
Learning Objective
Understand that the strength of the Sun’s gravitational field decreases with distance and that the orbital speeds of the planets decrease as their distance from the Sun increases.
Key Concepts
The Sun’s gravitational field follows an inverse‑square law: \$g{\text{Sun}} = \frac{GM{\text{Sun}}}{r^{2}}\$ where \$G\$ is the universal gravitational constant, \$M_{\text{Sun}}\$ is the mass of the Sun and \$r\$ is the distance from the Sun’s centre.
For a planet in a circular orbit, the required centripetal force is provided by gravity, giving the orbital speed: \$v = \sqrt{\frac{GM_{\text{Sun}}}{r}}\$
Both equations show that as \$r\$ (the orbital radius) increases, \$g_{\text{Sun}}\$ and \$v\$ decrease.
Why Does the Gravitational Field Decrease?
The gravitational field strength depends on the distance from the source mass. Because the field spreads out over a larger spherical surface as the radius grows, the same amount of force is distributed over a larger area, leading to the inverse‑square relationship.
Why Do Orbital Speeds Decrease?
From the orbital speed equation \$v = \sqrt{GM_{\text{Sun}}/r}\$, the speed is proportional to \$r^{-1/2}\$. Thus, a planet farther from the Sun needs a lower speed to remain in a stable orbit because the gravitational pull is weaker.
Illustrative Data
Planet
Mean Distance from Sun (×10⁶ km)
Orbital Speed (km s⁻¹)
Mercury
57.9
47.4
Venus
108.2
35.0
Earth
149.6
29.8
Mars
227.9
24.1
Jupiter
778.5
13.1
Saturn
1,433.5
9.7
Uranus
2,872.5
6.8
Neptune
4,495.1
5.4
The table clearly shows that as the distance from the Sun increases, the orbital speed of each planet decreases, confirming the inverse relationship.
Practical Implications
Spacecraft leaving Earth must increase speed to climb out of Earth’s gravity, then reduce speed to match the slower orbital speed of the target planet.
Planetary periods (orbital times) increase with distance because \$T = 2\pi r/v\$ and \$v\$ decreases.
Suggested Diagram
Suggested diagram: A schematic of the Solar System showing the Sun at the centre, planetary orbits as concentric circles, and arrows indicating decreasing gravitational field strength and orbital speed with increasing distance.