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I am dealing with math and physics only at amateur level and I am writing regarding my question on relativistic aberration of light. Reading "Realtivity and Common Sense" by Hermann Bondi and some other texts I discovered that the following aberration formula is being used

$$\cos a' = \frac{\cos a + v/c}{1+ (\cos a) v/c}$$

However in other physics websites the following aberration formula is being used

$$\cos a' = \frac{\cos a - v/c}{1 - (\cos a) v/c}$$ I am sure that both they are correct and something I have missed. Could you help me?

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The two formulae obviously differ by the convention for the sign of $v$. If you rename $v$ as $-v$, you switch from the first equation to the second and vice versa. Changing the sign of the velocity depends on the question which system is moving respect to the other, whether you consider passive or active transformations, etc. One must be careful about the sign when doing detailed calculations but at the general level, the forms of the equations are the same.

I have TeXified your equations, by the way.

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thank you about the equations and your valuable help. sometimes i see x= -c cos a and some others x= c cos a . What does the sign mean with respect to c? – kostis Jan 19 '12 at 17:19
Apologies, I probably don't understand this question of yours. If the two equations - regardless of the physical interpretations - differ by a sign, it either means that $x$ in one language means $-x$ in the other, or $c$ means $-c$ in the other, or $a$ means $\pi\pm a$ in the other, or all these three things combined. Depending on the context, some of the 4 options may be impossible. – Luboš Motl Jan 19 '12 at 19:42
thank you for the answer. Iam trying to find out the derivation of the aberration formula reading Hermann Bondi's Relativity and Common Sense pp. 125 but still having problems relating to the algebraic steps (mainly the signs). please any help is welcome – user7213 Jan 19 '12 at 23:21
Good luck, Kostis, but maybe you're taking some details too seriously. The signs (plus or minus) either follow from the text in a way you may understand, or you should ignore them if you just "roughly read" the text. In a broad variety of situations, the changed signs are just changes in conventions and both options may be equally valid assuming that other signs are adjusted as well. One must be careful which of the signs are really variable and which of them would be mistake if one changed them. Much of the structure beyond the signs is more important and characteristic about the equations. – Luboš Motl Jan 21 '12 at 7:12

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