State the equivalence principle.

A helium filled balloon is floating in air inside a spacecraft in outer space. The spacecraft begins to accelerate to the right.

Explain, with reference to the equivalence principle, the motion, if any, of the helium balloon relative to the spacecraft.

In an experiment, to verify the bending of light as it passes close to the Sun, the position of a star was measured during a total solar eclipse.

(i) Explain why the measurement of the star’s position was made during a total solar eclipse.

(ii) On the diagram above, draw lines to determine the apparent position of the star as seen from Earth. 

(iii) State what other measurement must be made in order to determine the angle by which rays from the star are bent by the Sun.

(iv) The angle of bending of a light ray from the star that just grazes the Sun’s surface is θ. State and explain the effect, if any, on θ if the Sun were to be replaced by another star of equal radius but larger mass.

a frame of reference accelerating in (outer space) is equivalent to a frame of reference at rest in a gravitational field / gravitational effects are indistinguishable from inertial effects;

balloon moves to the right;
rocket frame is equivalent to a rocket at rest in a gravitational field directed to the left;
helium balloons rise in gravitational fields;

(i) so that the star could be seen during the day;

(ii)

ray from star curving past the Sun towards the Earth and that ray extended backwards along a straight line to a position higher/lower than real position of star; 
Allow ray path to travel above or below the Sun.

(iii) the position of the star when light from the star reaches the Earth without going past the Sun; 

(iv) the angle of deflection will be greater;
a greater mass will cause a greater curvature of spacetime;

The equivalence principle was usually stated, but not always in unambiguous terms.

In (b) very few candidates could work out what would happen. Many identified that this was equivalent to a gravitational field, but did not state that the direction was to the left. Few mentioned that helium was less dense than air and so would move right, in the same direction as the acceleration of the spaceship. Admittedly it is counter-intuitive.

(c)(i) and (ii) were an easy two marks. But in (c)(iii) far too many candidates just stated that the position of the star should also be measured at night, without realizing that at night the star would be still be 'close' to the sun and so not in the night sky. It was expected that they would mention measuring the star’s position (at night!) when it is not 'close' to the sun - such as in six months time. More usually they referred, incorrectly, to measuring the distance to the star or measuring the mass of the sun. (c)(iv) was done well.