Special Relativity - Relativistic Dynamics

[Jonmundsson]

Homework Statement

A.P. French 6.8
A thrust-beam space vehicle works bearing a sort of sail which feels the push of a strong steady laser light beam directed at it from Earth. If the sail is perfectly reflected, calculate the mass of light required to accelerate a vehicle of rest mass $m_0$ up to a fixed value of $\gamma$.

Homework Equations

I usually define $c=1$ for convenience.
$m'=m_o \gamma$
$p = m_0v$
$E = m_0c^2 = m'c^2+ q = E' + q$ q is the energy of the photon(s) emitted
$p=0=m'v - q/c = p' - q/c$
$cp' = q$

The Attempt at a Solution

Since the sail is perfectly reflective I view as if the vehicle is emitting photons. Since it is accelerated to $\gamma$ we get $v = \gamma$ so $p' = m'v = m_0 \gamma ^2$. Also $q = m_0 \gamma ^2$

Honestly, I have little idea what I'm doing. I'm following French's book (Emission of photons p.177) and I keep running into dead ends. Any help would be appreciated.

 

[tiny-tim]

Hi Jonmundsson!

A thrust-beam space vehicle works bearing a sort of sail which feels the push of a strong steady laser light beam directed at it from Earth. If the sail is perfectly reflected, calculate the mass of light required to accelerate a vehicle of rest mass $m_0$ up to a fixed value of $\gamma$.

Hint: if a photon has "mass" m, by how much does its momentum change?