(a)[1]
Define gravitational field.
(b(i))[2]
At the probe position where $x = 1.47 \times 10^{11}\,\text{m}$, calculate $g$.
(b(ii))[2]
At the probe position where $x = 1.47 \times 10^{11}\,\text{m}$, determine the probe’s gravitational potential energy $E_P$.
(c(i))[3]
Show that, for any chosen value of $x$, the numerical values of $g$ and $F$ satisfy $g = \dfrac{4\pi G M}{L} F$, where $M$ is the mass of the Sun, $L$ is the luminosity of the Sun and $G$ is the gravitational constant.
(c(ii))[2]
Fig. 2.1 illustrates how $g$ changes with $F$. Find a value for the Sun’s luminosity $L$. Include a unit with your answer.
(c(iii))[2]
Use your answer in (c)(ii) to find the radius $r$ of the Sun.