Understanding the

Tsiolkovsky Rocket Equation

$$\Delta V = I_{SP} \cdot g_0 \cdot \ln \Big( {M_0 \over M_1} \Big)$$

$$\Delta V = Change \; in \; Velocity \; (m/s)$$

$$I_{SP} = Specific \; Impulse \; (s)$$

$$g_0 = Standard \; Gravity \; (9.80665\;m/s^2)$$

$$\ln () = Naural \; Logarithm \; Function$$

$$M_0 = Starting \; Mass \; (any \; mass \; units)$$

$$M_1 = Ending \; Mass \; (any \; mass \; units)$$

Note: ISP is a way to quantify how effective a rocket engine is at turning fuel into thrust. Measured in units of time: "seconds," the way to understand ISP is that it represents how many seconds one kilogram of propellant produces one kilogram-force of thrust.

Note: g0 is always standard gravity (~9.8 m/s2) even when the rocket is experiencing different gravity. This is because standard gravity is baked into the calculation of ISP.

Note: ISP * g0 can be substituted with Ve, the exhaust gas velocity of the burned propellant in m/s. From this, you can see that higher velocity exhaust produces better efficiency.

Solver

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Use any three terms to solve the fourth term.

M0:     
M1:     
ISP:      
ΔV:        

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