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## Homework Statement

A distant star at rest with respect to an observer on Earth emits light of frequency 6.690 x 10^14 Hz. The star breaks up into two remnants of equal mass, which are observed to emit light of frequency 7.135 x 10^14 Hz and 4.282 x 10^14 Hz

Find the velocities of the remnant and the angle between line of sight and their direction of motion.

## Homework Equations

[tex] v^{prime} = v \gamma [1 - \beta cos \theta] [/tex]

[tex] v^{prime} = v \sqrt{\frac{1 + \beta}{1 - \beta}} [/tex]

## The Attempt at a Solution

I have solved the first part, finding the speed, using:

[tex] v^{prime} = v \sqrt{\frac{1 + \beta}{1 - \beta}} [/tex]

assuming that since the star was initally at rest, teh centre of momentum will remain in the same polace, hence the two parts will fly away from each other.

I got [tex] \beta [/tex] to be 0.47, and the speed of the star remnants to be 0.235c

I am having a small problem with the second part, finding the angle. I am sure I need to use:

[tex] v^{prime} = v \gamma [1 - \beta cos \theta] [/tex]

with the v primke being the orginal stars frequency. but I am nto sure which of the othe frequencies to use as v, and I am not sure how to get a value of beta to use in this part, since I am sure it will be different to the value in part A.

Any ideas will be greatly appreciated,

TFM