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

(1)

\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.

(2)

\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:

(3)

\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.

(5)

\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.