The Tyranny of the Rocket Equation
In spaceflight, there is no friction, but there is inertia. To move a spaceship, you need to throw mass out the back. That mass is fuel.
But here is the catch: fuel is heavy.
If you want to go faster, you need more fuel. But adding more fuel makes the ship heavier, which means you need *even more fuel* just to push the extra fuel you just added. This vicious cycle is known as the Tyranny of the Rocket Equation, formulated by Konstantin Tsiolkovsky in 1903.
How the Math Works
The calculator implements the ideal Tsiolkovsky rocket equation: $$ \Delta v = ve \ln \left( \frac{m0}{m_f} \right) $$
To find the required fuel mass, the formula is algebraically inverted. We take your target $ \Delta v $ (Delta-V) and your engine's exhaust velocity (derived from Specific Impulse or $I{sp}$). We calculate the mass ratio using an exponential function $ e^{\Delta v / ve} $. By subtracting the wet mass from your inputted dry mass, the script outputs the exact metric tonnage of propellant required to achieve the maneuver.