# Problem 3 – Hint 3

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It is convenient to consider the following 4-momenta: (a) of the rocket at the moment when the direction of the engine was changed; (b) of all the photons sent in the initial direction (i.e. until the direction of the engine was changed); (c) of all the photons emitted after the direction was changed. With all the relativistic invariants based on these three 4-momenta (cf. Hint 1), the angle $\alpha$ can be conveniently expressed in terms of a parameter, for instance in terms of the time-component of the 4-momentum (b), as measured in the frame of the rocket at the moment when the direction of the engine was changed.