Rocket equation

Definition

The rocket equation, also known as the Tsiolkovsky rocket equation, relates the velocity change of a rocket to the effective exhaust velocity and the initial and final mass of the rocket. It is a fundamental principle in understanding how rockets move and accelerate in space.

5 Must Know Facts For Your Next Test

1. The rocket equation is given by $\Delta v = v_e \ln\left(\frac{m_i}{m_f}\right)$, where $\Delta v$ is the change in velocity, $v_e$ is the effective exhaust velocity, $m_i$ is the initial mass, and $m_f$ is the final mass.
2. The natural logarithm function ($\ln$) in the equation accounts for the exponential nature of mass loss due to fuel consumption.
3. The effective exhaust velocity ($v_e$) is a measure of how fast exhaust gases are expelled from the rocket engine.
4. A higher exhaust velocity or a greater ratio of initial to final mass results in a larger change in velocity ($\Delta v$).
5. The rocket equation assumes that external forces like gravity and atmospheric drag are negligible or constant during propulsion.

Review Questions

• What does $\Delta v$ represent in the context of the rocket equation?
• How does an increase in effective exhaust velocity affect a rocket's change in velocity?
• Why does the rocket equation use a natural logarithm function?

Related terms

Thrust: The force exerted by a rocket engine to propel it forward, typically measured in newtons (N).

Specific Impulse: A measure of how efficiently a rocket uses its propellant, defined as thrust per unit weight flow rate of propellant.

Propellant Mass Fraction: The ratio of propellant mass to total initial mass of the rocket; crucial for determining performance using the rocket equation.