- #1
Dopplershift
- 59
- 9
The problem states:
Typical chemical fuels yield exhaust speeds of the order of 103 m/s. Let us imagine we had a fuel that gives v0 = 3 × 105 m/s. What initial mass of fuel would the rocket need in order to attain a final velocity of 0.1c for a final mass of 1 ton?
I derived the equation in the first part of the problem:
\begin{equation}
v - v_0 = v_e \ln(\frac{m_0}{m})
\end{equation}
Solving for the initial mass, m, yields
\begin{equation}
m_0 = me^{\frac{\Delta v}{v_e)}}
\end{equation}
I plug in that.
0.1c = 3.0*10^7
v0 = 3.0*10^5
vee = 1.0*10^3
v - v0 = 3.0 *10^7 - 3.0*10^5 = 2.97*10^7
m = 1000 kg
I plug in these numbers and I am getting infinity. What am I doing wrong?
Thanks!
Typical chemical fuels yield exhaust speeds of the order of 103 m/s. Let us imagine we had a fuel that gives v0 = 3 × 105 m/s. What initial mass of fuel would the rocket need in order to attain a final velocity of 0.1c for a final mass of 1 ton?
I derived the equation in the first part of the problem:
\begin{equation}
v - v_0 = v_e \ln(\frac{m_0}{m})
\end{equation}
Solving for the initial mass, m, yields
\begin{equation}
m_0 = me^{\frac{\Delta v}{v_e)}}
\end{equation}
I plug in that.
0.1c = 3.0*10^7
v0 = 3.0*10^5
vee = 1.0*10^3
v - v0 = 3.0 *10^7 - 3.0*10^5 = 2.97*10^7
m = 1000 kg
I plug in these numbers and I am getting infinity. What am I doing wrong?
Thanks!