State the meaning of a gravitational field.
In the Solar System, the planets may be treated as moving in circular orbits about the Sun. Figure 1.1 gives the orbital radii of Earth and Jupiter about the Sun: Earth has radius $1.50 \times 10^8\ \text{km}$ and Jupiter has radius $7.78 \times 10^8\ \text{km}$.
State Newton’s law for gravitation.
Use Newton’s law to find the ratio $\dfrac{\text{gravitational field strength due to the Sun at orbit of Earth}}{\text{gravitational field strength due to the Sun at orbit of Jupiter}}$.
The Earth’s orbital period around the Sun is $T$.
Use ideas from circular motion to show that the Sun’s mass $M$ is given by $M = \frac{4\pi^2 R^3}{G T^2}$, where $R$ is the radius of Earth’s orbit around the Sun and $G$ is the gravitational constant. Show your working.
The Earth’s orbital period $T$ around the Sun is $3.16 \times 10^7\,\text{s}$. Figure 1.1 gives the radius of the Earth’s orbit. Use the expression in (i) to determine the Sun’s mass.