# Relavistic Rocket Equation

1. Jan 13, 2012

### 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!

Last edited: Jan 13, 2012
2. Jan 13, 2012

### PAllen

3. Jan 13, 2012

### 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.

4. Jan 13, 2012

### Albertgauss

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