The Power of Action and Reaction
Newton's Third Law of Motion states: For every action, there is an equal and opposite reaction.
This is the fundamental principle behind all jet engines and rockets. To push a 2,000,000-pound Saturn V rocket upward into space, you cannot push against the ground. Instead, the rocket takes a mass of chemical propellants, ignites them, and violently throws that mass out of the bottom nozzle at supersonic speeds.
The action is the engine throwing the hot gas downward. The equal and opposite reaction is the gas pushing the engine—and the entire rocket attached to it—upward. This upward pushing force is called Thrust.
The Two Components of Thrust
In aerospace engineering, total engine thrust is composed of two distinct parts:
- Momentum Thrust ($\dot{m} \cdot v_e$): This is the main source of power. It is calculated by multiplying the mass flow rate (how many kilograms of fuel you are burning and throwing out per second) by the exhaust velocity (how incredibly fast that gas is moving when it leaves the nozzle).
- Pressure Thrust ($(p_e - p_0) \cdot A_e$): This occurs if the pressure of the exhaust gas leaving the nozzle ($p_e$) is different from the ambient atmospheric pressure outside the rocket ($p_0$). This pressure difference pushing against the area of the nozzle exit ($A_e$) provides a slight bonus (or penalty) to total thrust.
The Formula
Example: Rocket Engine in a Vacuum
Imagine a rocket engine in the vacuum of space (meaning ambient pressure $p_0 = 0$). The engine pumps and burns $150 , \text{kg}$ of fuel every single second. It ejects this blazing gas at an exhaust velocity of $4,000 , \text{m/s}$. The exhaust pressure at the nozzle ($0.5 , \text{m}^2$ area) is $50,000 , \text{Pa}$.
- Momentum Thrust: $150 , \text{kg/s} \cdot 4000 , \text{m/s} = 600,000 , \text{Newtons}$.
- Pressure Thrust: $(50000 - 0) \cdot 0.5 = 25,000 , \text{Newtons}$.
- Total Thrust: $600,000 + 25,000 = \mathbf{625,000 , \text{Newtons}}$ (or $625 , \text{kN}$).
This engine generates 625 kilonewtons of pushing force, easily enough to accelerate a massive spacecraft through the void.