The rogue starship Galaxa is being chased by the battlecruiser Millenia. The Mil

Question

The rogue starship Galaxa is being chased by the battlecruiser Millenia. The Millenia is catching up to the Galaxa at a rate of 0.53c when the captain of the Millenia decides it is time to fire a missile. First the captain shines a laser range finder to determine the distance to the Galaxa and then he fires a missile that is moving at a speed of 0.47c with respect to the Millenia.

(a) What speed does the Galaxa measure for the missile?
c

(b) What speed does the Galaxa measure for the the laser beam?

Explanation / Answer

a) The velocity of Millenia relative to Galaxa is vMG= 0.53c. The velocity of the missile relative to Millenia is vmM = 0.47c. The velocity of the missile relative to Galaxa is

vmG = (vmM+vMG)/(1+vmM.vMG/c2) = (0.47c+0.53c)/(1+0.47c*0.53c/c2) = c/1+0.2491 = c/1.2491 = 0.801c

b) The laser beam will be measured to have speed c.

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