Rocket equation

Biosyn

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

The following equation is known as the "Rocket Equation":

[itex]\frac{M+P}{M}[/itex]= e[itex]^{ΔV/C}[/itex] = mass ratio

M = dry mass
P = mass of propellant
C = exhaust velocity
ΔV = velocity change


e^1 = 2.72
e^2 = 2.74
e^3 = 20.4

As ΔV/C goes up, the mass of the spacecraft goes up faster than the exponential, so much so that depending on the lightness of the structural materials and the density of the propellants employed, somewhere between ΔV/C = 2 and ΔV/C = 3 the mass of a single spacecraft will go to infinity!


Please explain how and why the mass of the spacecraft will reach infinity?





2. Relevant equations

[itex]\frac{M+P}{M}[/itex]= e[itex]^{ΔV/C}[/itex]


3. The attempt at a solution


Shouldn't the mass ratio be equal to 1 if the mass is a really huge number?
Or, does the propellant mass have something to do with it. I know that the propellant mass needs to increase along with the dry mass of the rocket.

haruspex

It's unclear whether the question posed refers to M or M+P. If M is fixed, then M+P goes up exponentially with ΔV/C. But I don't get the bit about going to infinity between 2 and 3. I've no idea where that's coming from. Is this the whole question, or is something left out?
Btw, the quoted value for e^2 is wrong. Looks like a typo.

Biosyn

I think it's the total mass of the spacecraft (M+P). I'm not entirely sure. This is from a USAD Science section study guide.

haruspex

Can you provide a link or is it behind a paywall?

Biosyn

It's behind a paywall. :/