Rocket Launch
Law of Conservation of momentum.
- This is how the spaceship is able to propagate in space at all.
- The law states: "In a closed system, the sum of the momenta before a change is equal to the sum of momenta after the change."
- Before a launch, the spacecraft and its fuel are not moving, so their momenta add up to zero
\begin{equation} P_{rocket} + P_{fuel} = 0 \end{equation}
- As the rocket ejects the fuel, it will move in the opposite direction that the fuel was ejected at.
\begin{equation} P_{rocket} = - P_{fuel} \end{equation}
- Also, assuming the exhaust speed is constant, therefore the thrust of the rocket is also constant.
- Yet the rocket also has to also overcome gravity, so the net force on a rocket is given by:
\begin{equation} F_{net} = F_{thrust} - F_{gravity} \end{equation}
(4)
\begin{equation} F_{net} = F_{thrust} - mg \end{equation}
- From Newton's second law, we can find the acceleration on the rocket.
\begin{align} a = \frac{T-mg}{m} \end{align}
- However, as fuel is being ejected, mass decreases.
- And as shown by the previous equation, if mass decreases, acceleration increases exponentially
Forces on Astronauts.
page revision: 0, last edited: 03 Nov 2011 03:26