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1.3.5 Peculiar Velocities

If a star is ejected from a galaxy with a velocity \(V\) at right angles to its line of sight from Earth, its resulting velocity is \(c =\sqrt{c_o^2+V^2}\). Its expansion is now no longer in the radial direction, but at an angle \(\alpha\) to it, where \(tan\ \alpha = V/c_o\). As time passes, normal expansion velocity, \(c_o\), increases, whereas the expulsion velocity \(V\) remains constant. Hence the angle \(\alpha\), will decrease asymptotically to zero as the star approaches a new expansion vector which has a separation angle \(\alpha\) with the galaxy from which it was originally ejected. Many stars and galaxies have this kind of local (peculiar) motion, and this explains why it is almost always relatively small.

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