8.7 Introduction to Rocket Propulsion

Rocket Propulsion Fundamentals

Rocket propulsion is a direct application of Newton's third law: a rocket pushes exhaust backward, and the exhaust pushes the rocket forward. This same principle explains how spacecraft launch, accelerate, and maneuver even in the vacuum of space where there's nothing to "push off" of.

Newton's Third Law in Rocket Propulsion

Newton's third law states that for every action, there is an equal and opposite reaction. In a rocket, the "action" is hot exhaust gases being expelled at high speed out the back. The "reaction" is an equal force pushing the rocket forward, called thrust.

This also connects to conservation of momentum. The total momentum of the system (rocket + exhaust) stays constant. As exhaust flies backward with high velocity, the rocket gains momentum in the opposite direction. The rocket's acceleration depends on how fast the exhaust leaves and how quickly mass is being expelled.

Rockets vs. Jet Engines

Both rockets and jets generate thrust by expelling hot gases through a nozzle, but they differ in one critical way: where they get their oxidizer.

• Rocket engines carry both fuel and oxidizer onboard. Because they don't need outside air, they work in the vacuum of space and at any altitude. This is what makes moon landings and satellite deployment possible.
• Jet engines pull in surrounding air and use it as the oxidizer. They compress the incoming air, mix it with fuel, and ignite the mixture. This means they only work within the atmosphere and perform best at lower altitudes where air is denser. Commercial airliners and military jets use this approach.

Factors in Rocket Acceleration

Rocket acceleration is given by:

$a = \frac{v_e}{m} \frac{dm}{dt}$

where:

• $v_e$ = exhaust velocity (how fast the gases leave the nozzle)
• $m$ = the rocket's instantaneous mass (total mass at that moment)
• $\frac{dm}{dt}$ = mass flow rate (how quickly propellant is being expelled)

Three things drive how quickly a rocket accelerates:

1. Higher exhaust velocity produces greater thrust for the same mass flow rate.
2. Higher mass flow rate means more propellant is expelled per second, generating more force.
3. Decreasing mass matters a lot. As the rocket burns fuel, $m$ drops, so the same thrust produces greater acceleration over time. This is why astronauts on the Saturn V experienced increasing g-forces as the rocket ascended.

Specific impulse measures how efficiently a rocket uses its propellant. Higher specific impulse means you get more thrust per unit of propellant consumed.

Key Performance Metrics

• Thrust-to-weight ratio tells you whether a rocket can overcome gravity. A ratio greater than 1 means the rocket can lift off; below 1, it stays on the ground.
• Propellant mass fraction is the proportion of the rocket's total mass that is propellant. Most rockets are overwhelmingly propellant by mass, often 85–90%.
• Delta-v ($\Delta v$) is the total change in velocity a rocket can achieve with its onboard propellant. Mission planners use delta-v budgets to determine whether a rocket can reach orbit, transfer to another planet, or land on the Moon.

Space Shuttle Propulsion System

The Space Shuttle used multiple propulsion systems that worked together at different stages of flight. Each component had a specific role during launch, orbit, and reentry.

Components of Space Shuttle Propulsion

• External Tank (ET) held liquid hydrogen (fuel) and liquid oxygen (oxidizer) that fed the main engines. It was the large orange tank visible during launch and detached after its fuel was depleted, breaking apart during reentry over the ocean.
• Solid Rocket Boosters (SRBs) provided roughly 71% of the total thrust during the first two minutes of flight. After burnout, they separated from the shuttle and parachuted into the ocean, where they were recovered and refurbished for reuse.
• Space Shuttle Main Engines (SSMEs) were mounted at the rear of the orbiter and burned the liquid hydrogen and oxygen supplied by the ET. These engines were throttleable, meaning controllers could adjust thrust levels to manage acceleration and structural loads during ascent.
• Orbital Maneuvering System (OMS) used smaller engines for tasks after the main engines shut down: inserting into orbit, making orbital corrections, and performing the deorbit burn to begin reentry. The OMS used hypergolic propellants (monomethylhydrazine and nitrogen tetroxide), which ignite spontaneously on contact with each other, eliminating the need for an ignition system.