# Special Relativity - Relativistic Dynamics

1. Mar 16, 2012

### Jonmundsson

1. The problem statement, all variables and given/known data
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 $\gamma$.

2. Relevant 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
$p=0=m'v - q/c = p' - q/c$
$cp' = q$
3. 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.

Last edited: Mar 16, 2012
2. Mar 16, 2012

### tiny-tim

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