Astronomy & Astrophysics / Subcategory
Orbital Mechanics
Orbital mechanics calculators and formulas for orbits, escape velocity, and gravitation. Covers orbital period, escape velocity, and Kepler's laws calculations for spacecraft.
21Formulas
All levels Difficulty
Updated Oct 2026
← All Astronomy & Astrophysics (43) Orbital Mechanics (21)
Fundamental
Hour Angle from Local Solar Time
H = 15° * (LST_hours - 12)
Fundamental
Kepler's Third Law (AU-Year Simplified Form)
T² = a³ (T in years, a in AU, orbiting the Sun)
Fundamental
Precession Period of the Equinoxes
P ≈ 360° / (rate of precession per year)
Fundamental
Moonrise/Moonset Daily Shift (Approx.)
Δt ≈ 50 minutes/day
Fundamental
Synodic Period (Planetary Opposition Interval)
1/S = |1/T_1 - 1/T_2|
Fundamental
Solar Altitude Angle
sin(a) = sin(φ)sin(δ) + cos(φ)cos(δ)cos(H)
Fundamental
Solar Declination (Approximate)
δ ≈ 23.44° * sin(360°/365 * (N_day - 81))
Fundamental
Day Length (Daylight Hours)
N = (2/15) * arccos(-tan(φ)*tan(δ))
Fundamental
Local Sidereal Time (Approx.)
LST = GST + Longitude/15
Fundamental
Julian Date (Simplified)
JD = 367*Y - INT(7*(Y+INT((M+9)/12))/4) + INT(275*M/9) + D + 1721013.5
Fundamental
Minimum Orbital Inclination from Launch Latitude
i_min = latitude of launch site
Fundamental
Kepler's Equation & Orbital Anomaly Calculator
M = E - e*sin(E)
Fundamental
Orbit Equation (Semi-Latus Rectum Form)
r = p / (1 + e*cos(θ))
Fundamental
Specific Orbital Angular Momentum
h = r * v * cos(γ)
Fundamental
Specific Orbital Energy
ε = v^2/2 - μ/r = -μ/(2a)
Fundamental
Geostationary Orbit Radius
r = (μ * T^2 / (4π^2))^(1/3)
Fundamental
Hohmann Transfer Time of Flight
t = π * sqrt(a_t^3 / μ)
Fundamental
Vis-Viva Equation
v = sqrt(μ * (2/r - 1/a))
Fundamental
Circular Orbital Velocity
v = sqrt(μ / r)
Fundamental
Escape Velocity
v_esc = √(2GM / r)
Fundamental
Kepler's Third Law
T² = (4π² / GM) a³