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Jonmundsson

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## 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 [itex]m_0[/itex] up to a fixed value of [itex]\gamma[/itex].

## Homework Equations

I usually define [itex]c=1[/itex] for convenience.

[itex]m'=m_o \gamma[/itex]

[itex]p = m_0v[/itex]

[itex]E = m_0c^2 = m'c^2+ q = E' + q[/itex] q is the energy of the photon(s) emitted

[itex]p=0=m'v - q/c = p' - q/c[/itex]

[itex]cp' = q[/itex]

## 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 [itex]\gamma[/itex] we get [itex]v = \gamma[/itex] so [itex]p' = m'v = m_0 \gamma ^2[/itex]. Also [itex]q = m_0 \gamma ^2[/itex]

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.

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