State the meaning of a gravitational field.
In the Solar System, the planets may be treated as travelling in circular paths around the Sun. Fig. 1.1 gives the orbital radii of Earth and Jupiter about the Sun.
State Newton’s law of gravitation in words.
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 time for the Earth to complete one orbit around the Sun is $T$.
Use circular-motion ideas to show that the mass $M$ of the Sun is given by $M = \dfrac{4\pi^2 R^3}{G T^2}$, where $R$ is the radius of the Earth’s orbit about the Sun and $G$ is the gravitational constant. Show your working.
The Earth’s orbital period about the Sun is $3.16 \times 10^7\,\text{s}$. The radius of the Earth’s orbit is shown in Fig. 1.1. Use the expression in (i) to find the mass of the Sun.