(i)     \({f_{\text{C}}}\)

(ii)     \({f_{\text{P}}}\)

Newton explained the motion of a planet around the Sun in terms of a force of gravitation between the Sun and the planet. Describe how Einstein’s theory of general relativity explains the motion of the planet around the Sun.

(i)     the box is equivalent to an inertial frame of reference (far from any masses);

so \({f_{\text{C}}} = {f_0}\);

(ii)     the energy of a photon is \(h{f_{\text{P}}}\);

light loses energy as it rises;

so \({f_{\text{P}}} < {f_0}\);

or

P’s frame of reference is equivalent to a frame accelerating upwards (far from any masses);

P moves away from the emitted light / the “space” between P and original source increases;

so (by the Doppler effect) \({f_{\text{P}}} < {f_0}\);

the mass of the Sun bends the spacetime around it;

particles follow paths of least length/geodesics (when no forces act on them);

paths of least length/geodesics are curves in the bent spacetime;

The equivalence principle was usually stated, but not always in unambiguous terms. In (b) the two situations were often confused. Candidates were less sure of the frequency in the free fall situation and usually did not recognise the box as an inertial frame. Many were able to explain why the frequency received by P was less than \({f_0}\). Most were able to refer to the sun 'bending' spacetime. Fewer referred to geodesics or the fact that they corresponded to the circular/elliptical orbit of a planet.

The equivalence principle was usually stated, but not always in unambiguous terms. In (b) the two situations were often confused. Candidates were less sure of the frequency in the free fall situation and usually did not recognise the box as an inertial frame. Many were able to explain why the frequency received by P was less than \({f_0}\). Most were able to refer to the sun 'bending' spacetime. Fewer referred to geodesics or the fact that they corresponded to the circular/elliptical orbit of a planet.