Velocity Equation Derivation For Radiation Beaming

[ZAU]

Homework Statement

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Radiation beaming (cone) from an object traveling towards you at some velocity 'v'
with the observed flux enhanced by an amplification factor 'a'.

Derive an equation for the velocity 'v' needed to produce an amplification factor 'a'.

Thank you

Homework Equations

Beaming angle = Theta (rad) = SQRT(1-(v/c)^2)

v=velocity
c= speed of light

Amplification factor = a=4/Theta (rad)^2

The Attempt at a Solution

From previous attempts z (red-shift) and Theta (beaming angle) are not in the
derived equation.
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[Asim Riaz]

Using the equation for the amplification factor 'a':a = 4/Theta (rad)^2Rearranging the equation for Theta (rad):Theta (rad) = SQRT(4/a)Substituting in the equation for beaming angle:SQRT(1-(v/c)^2) = SQRT(4/a)Rearranging the equation for velocity:v = SQRT((1-4/a)*c^2)