Where can I find the formula for the relavistic rocket equation?

[Albertgauss]

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!

 

[PAllen]

Here is the page you want. See the section on fuel. It assumes much better than fusion - 100% conversion of mass to energy. The results are still pretty grim.

http://www.desy.de/user/projects/Physics/Relativity/SR/rocket.html

Note, a search of this forum would have readily turned up this link.

 

[DrStupid]

The classical rocket equation

$v_{class.} = p_{sp} \cdot \ln \frac{{m_0 }}{m}$

can be upgraded to a relativistic version by

$v_{rel.} = \frac{{v_{class.} }}{{\sqrt {1 + \frac{{v_{class.}^2 }}{{c^2 }}} }}$

and

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

where $d$ is the mass defect and $\eta$ the efficiency.

 

[Albertgauss]

Oh hey guys great! Thanks! I think that will do it.