1. What is the Tsiolkovsky Rocket Equation?

The Tsiolkovsky rocket equation, also called the ideal rocket equation, describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself by expelling part of its mass with high velocity, thereby moving due to the conservation of momentum.

2. How Does the Calculator Work?

The calculator uses the Tsiolkovsky rocket equation:

Where:

• \( \Delta v \) — Change in velocity (m/s)
• \( I_{sp} \) — Specific impulse (seconds)
• \( g \) — Standard gravity (9.81 m/s²)
• \( m_0 \) — Initial total mass including propellant (kg)
• \( m_f \) — Final mass after propellant is expended (kg)

Explanation: The equation shows that the delta-v depends on the specific impulse of the engine and the natural logarithm of the ratio of initial to final mass.

3. Importance of Delta V Calculation

Details: Delta-v is crucial in mission design as it determines what maneuvers a spacecraft can perform, including orbit insertion, orbit changes, and interplanetary transfers.

4. Using the Calculator

Tips: Enter specific impulse in seconds, masses in kilograms. Initial mass must be greater than final mass. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is specific impulse?
A: Specific impulse (I_sp) measures how effectively a rocket uses propellant. Higher I_sp means more efficient propulsion.

Q2: What are typical delta-v requirements?
A: For example: Low Earth Orbit requires ~9.4 km/s, Moon landing ~15 km/s, Mars mission ~13 km/s from LEO.

Q3: Why is the natural logarithm used?
A: The ln(m₀/m_f) term accounts for the exponential nature of mass ratio to delta-v.

Q4: What are limitations of this equation?
A: Assumes constant exhaust velocity, no external forces (gravity, drag), and instantaneous burns.

Q5: How to increase delta-v?
A: Either increase specific impulse (better engine) or mass ratio (more propellant or lighter structure).