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Relavistic Rocket Equation

  1. Jan 13, 2012 #1
    Hi all,

    Does anyone know where I can find the formula for the relavistic rocket equation? That is, I want to know the mass of fuel required to accelerate a rocket from 0 to β, for a given acceleration A, assuming the rocket (with no fuel) has a mass of M. All of this would be in the frame of the Earth. I know there are several types of proposed Sci-Fi fuels but I think fusion is the most promising. A reliable webpage would be great. Thanks!
    Last edited: Jan 13, 2012
  2. jcsd
  3. Jan 13, 2012 #2


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  4. Jan 13, 2012 #3
    The classical rocket equation

    [itex]v_{class.} = p_{sp} \cdot \ln \frac{{m_0 }}{m}[/itex]

    can be upgraded to a relativistic version by

    [itex]v_{rel.} = \frac{{v_{class.} }}{{\sqrt {1 + \frac{{v_{class.}^2 }}{{c^2 }}} }}[/itex]


    [itex]p_{sp.} = c \cdot \sqrt {\left[ {2 + \left( {\eta - 2} \right) \cdot d} \right] \cdot \eta \cdot d}[/itex]

    where [itex]d[/itex] is the mass defect and [itex]\eta[/itex] the efficiency.
  5. Jan 13, 2012 #4
    Oh hey guys great! Thanks! I think that will do it.
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