Structural Analysis
Normal Stress
σ = F / A
Euler Buckling
Pcr = π²·E·I / (K·L)²
Safety Factor
n = σy / σapplied
Beam Deflection (Cantilever)
δ = F·L³ / (3·E·I)
Aerodynamics
Lift Force
L = ½ · ρ · v² · S · C_L
Drag Force
D = ½ · ρ · v² · S · C_D
Mach Number
M = v / a (a = √(γ·R·T))
Dynamic Pressure
q = ½ · ρ · v²
Propulsion
Thrust
F = ṁ·v_e + A_e·(p_e − p_a)
Specific Impulse
Isp = F / (ṁ · g₀)
Delta-V (Tsiolkovsky)
Δv = Isp · g₀ · ln(m₀ / m_f)
Thrust-to-Weight Ratio
TWR = T / (m · g)
Orbital Mechanics
Orbital Velocity
v = √(G·M / r)
Escape Velocity
v_e = √(2·G·M / r)
Hohmann Transfer
Δv₁, Δv₂, T_transfer
Sphere of Influence
SOI = a · (m_planet / m_star)^(2/5)
Power Systems
Solar Panel Power
P = η · A · G · PR
Battery Capacity
E = V · Ah = P · t
Power Budget
P_gen vs P_load → Margin
Mass Budget
Mass Budget Breakdown
Sum all components + margins
Mass Fraction
μ = m_struct / m_total
Algebra
Quadratic Equation
ax² + bx + c = 0 → x = (-b ± √(b²-4ac)) / 2a
Linear System (2×2)
a₁x + b₁y = c₁
a₂x + b₂y = c₂
a₂x + b₂y = c₂
Exponential / Logarithm
y = b^x | x = log_b(y)
Matrix Determinant (2×2)
det = a·d − b·c
Trigonometria
Trigonometric Functions
sin(θ), cos(θ), tan(θ)
Law of Sines
a/sin(A) = b/sin(B) = c/sin(C)
Law of Cosines
c² = a² + b² − 2ab·cos(C)
Angular Conversion
deg ↔ rad ↔ rev
Vector Decomposition
Vx = V·cos(θ), Vy = V·sin(θ)
Physics
Newton's Second Law
F = m · a
Kinematics (Projectile)
y = v₀t − ½gt² | v² = v₀² − 2gy
Work / Energy / Power
W = F·d | P = W/t
Ohm's Law
V = I·R | P = V·I = I²R = V²/R
Gravitational Force
F = G·m₁·m₂ / r²
Wave Calculator
v = f · λ | T = 1/f
Chemistry
Molar Mass Calculator
Enter formula: H2O, NaCl, C6H12O6
Ideal Gas Law
PV = nRT
Molarity
M = moles / Volume(L)
pH Calculator
pH = -log₁₀[H⁺] | [H⁺] = 10^(-pH)
Launch Routes & Seasons — Solar System + Exoplanets
Hohmann Transfer Calculator
Select origin → destination to compute Δv, transfer time, and launch window
Launch Window Season
Optimal departure based on synodic period
Planet Database