Essential Equations

Question 1

Tsiolkovsky Rocket Equation

Answer 1

ΔV = I_sp * g₀ * ln(m₀ / m_f)

• ΔV: total change in velocity
• I_sp: specific impulse (s)
• g₀: standard gravity (~9.806 m/s²)
• m₀: initial mass (with propellant)
• m_f: final mass (after burn)

Forms the foundation of all propellant budgeting and staging

Question 2

Propellant Mass Equation

Answer 2

m_prop = m₀ * (1 - e^(-ΔV / (I_sp * g₀)))

Required propellant mass based on ΔV and prop system performance.

Question 3

Thrust Equation

Answer 3

F = ṁ * v_e = I_sp * ṁ * g₀

• F: thrust (N)
• ṁ: mass flow rate (kg/s)
• v_e: exhaust velocity (m/s)

Understand performance, sizing, and burn time of engines.

Question 4

Center of Mass (COM) Shift

Answer 4

r_COM = (1/M) * Σ(m_i * r_i)

Changing propellant mass affects COM, impacting GNC & control authority

Question 5

Moment of Inertia (MOI) Change

Answer 5

I = Σ(m_i * r_i²)

Important for attitude control

Question 6

Ideal Gas Law (for Pressurization Systems)

Answer 6

PV = nRT or P = (ρRT) / M

Used in blowdown or regulated helium pressurization system modeling

Question 7

Specific Impulse

Answer 7

I_sp = F / (ṁ * g₀) or I_sp = v_e / g₀

Question 8

Mixture Ratio (MR)

Answer 8

MR = m_fuel / m_oxidizer

Question 9

What does MR impact?

Answer 9

• Tank Sizing
• Tank Pressurization
• Mass Distribution

Question 10

Why operate off optimal MR?

Answer 10

• Tank volume constraints (e.g., LH₂ takes a lot more volume than LOX)
• Thermal constraints
• Pressurization system limits
• Engine cooling needs (sometimes excess fuel is used for regenerative cooling)

Question 11

Formula: Orbital velocity for a circular orbit

Answer 11

Derive from centrigual acceleration = gravity

Question 12

Formula: Orbital velocity for a circular orbit

Answer 12

Derive from centrigual acceleration = gravity

Question 13

Formula: the Vis-Viva equation?

Answer 13

Question 14

Formula: Tsiolkovsky rocket equation?

Answer 14