This is the master list for equations!

## Δ v

Where:

• M t is total mass.
• M d is total mass minus fuel mass.
• "In" is the natural logarithm.

See the Δv page for a comprehensive explanation of Δv.

## Rocket Efficiency

According to Stef:

### Top to Bottom

Where

• E_r is Efficiency of the rocket, and
• M_n < is Mass in tonnes of the succeeding stages.

### Bottom to Top

, which simplifies to:

## Exhaust Velocity of Propellant

, where

is the exhaust velocity of your propellant, and

is the standard gravity, which on Earth  is:

## Thrust to Weight

, where

is force of thrust in kilonewtons (kN) and

is your rocket's mass in metric tons (t).

is the force of gravity. For example, on Earth , it is 9.80665 m / s 2 .

If the TWR is greater than or equal to 1 your rocket will lift off the ground.

## Average ISP

, where

• is the sum of all the forces, and
• is the fuel consumption rate in kg / s.

Average ISP can also be calculated from each engine:

, where

• is the force in kilonewtons of the nth engine, including duplicates,
• is the specific impulse of the nth engine, and
• is the number of engines.

## Fuel Consumption Rate

The same fuel flow rate.

## Suicide burn

The height D at which you should start your burn from sea level is

, where T is the time it will take to burn,

Where g is the surface gravity of the body upon which you're landing, Di is initial altitude, Vi is initial vertical velocity, mi is initial mass (with fuel) and FT is thrust. See this Desmos calculator.

## Kepler's Third Law of Planetary Motion

R = Required Δv for mission, x = Max Payload in tonnes

## Eccentricity

= Eccentricity

rmax = Apoapsis

rmin = Periapsis

Please allow a margin of error of 10% as well as user errors.