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:

- Yet the rocket also has to also

\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