Rocket Propulsion: Momentum, Thrust, and Gravity

All flashcards

Why is momentum conserved for a rocket and its exhaust in deep space?

When external forces are negligible, internal momentum transfers do not change the total momentum of the complete system.

What does $dm_g=-dm$ express?

The exhaust gains the mass that the rocket loses, so their mass changes have opposite signs.

What is the ideal rocket equation for constant exhaust speed?

$\Delta v=u\ln(m_0/m)$, where $m_0$ and $m$ are the total rocket masses before and after the burn.

How does gravity affect an upward burn at constant $g$?

It reduces the velocity change by $g\Delta t$ over a burn lasting $\Delta t$.

Why does acceleration rise under constant thrust during a burn?

The rocket's mass decreases while the thrust remains constant, so $a=F/m$ increases.

Quiz questions

1. When expanding the momentum equation for a small rocket mass ejection, why can the term $dm_g\,dv$ be neglected?Answer: It is a product of two infinitesimal changes and is second order.
2. A rocket moves at velocity $v$ in an inertial frame and ejects gas backward at speed $u$ relative to itself. What is the gas velocity in that frame?Answer: $v-u$
3. A rocket ejects gas at relative speed $u$ with positive exhaust mass flow rate $\dot m_g$. What is the magnitude of its thrust?Answer: $F=u\dot m_g$
4. A rocket has constant thrust while its mass decreases during a burn. How does its acceleration change?Answer: It increases because the same force acts on decreasing mass.
5. After a spacecraft stops firing its thrusters, what is its acceleration in the absence of external forces?Answer: Zero, although the spacecraft can continue moving.