Two space stations X and Y are at rest relative to each other. The separation of X and Y as measured in their frame of reference is 1.80×10¹¹m.

State what is meant by a frame of reference.

A radio signal is sent to both space stations in (a) from a point midway between them. On receipt of the signal a clock in X and a clock in Y are each set to read zero. A spaceship S travels between X and Y at a speed of 0.750c as measured by X and Y. In the frame of reference of S, station X passes S at the instant that X’s clock is set to zero. A clock in S is also set to zero at this instant.

(i) Calculate the time interval, as measured by the clock in X, that it takes S to travel from X to Y.

(ii) Calculate the time interval, as measured by the clock in S, that it takes S to travel from X to Y.

(iii) Explain whether the clock in X or the clock in S measures the proper time.

(iv) Explain why, according to S, the setting of the clock in X and the setting of the clock in Y does not occur simultaneously.

a set of coordinates that can be used to locate events/position of objects;

(i) \(\frac{{1.80 \times {{10}^{11}}}}{{0.750 \times 3 \times {{10}^8}}}\);
=800(s);
Award [2] for a bald correct answer.

(ii) \(\gamma  = \left( {\frac{1}{{\sqrt {1 - {{0.750}^2}} }} = } \right)1.51\);
\({\rm{time}} = \left( {\frac{{800}}{{1.51}} = } \right)530\left( {\rm{s}} \right)\);

Watch for ECF from (b)(i) or first marking point in (b)(ii).
Award [2] for a bald correct answer.

(iii) only S’s clock measures proper time;
because S’s clock is at both events / events occur at same place in S’s frame;

(iv) according to S, Y moves towards/X moves away from the radio signal;
the signal travels at the same speed/at the speed of light in each direction;
therefore according to S’s clock the signal reaches Y before it reaches X/X after reaching Y;

or

S’s frame is different/moving relative to the X and Y frame;
the two events/arrival of signals are separated in space;
so if simultaneous for XY, cannot be simultaneous for S;