Keplerian Orbit Physics

60 FPS

Native Newton-Raphson orbital solver, Keplerian equations, and Hohmann transfer trajectory calculator.

Celestial Mechanics Formulas

1. Kepler's Equation & Solver:

M = E - e · sin(E)
E_{k+1} = E_k - (E_k - e · sin(E_k) - M) / (1 - e · cos(E_k))

Solved iteratively via Newton-Raphson root finding for Eccentric Anomaly E from Mean Anomaly M.

2. True Anomaly ν & Radial Distance r:

r = a(1 - e · cos(E)) = a(1 - e²) / (1 + e · cos(ν))
tan(ν/2) = √((1+e)/(1-e)) · tan(E/2)

3. Vis-Viva Orbital Velocity:

v = √(μ · (2/r - 1/a)), T = 2π · √(a³ / μ)

4. Hohmann Transfer Delta-v (Δv):

Δv_1 = √(μ/r_1) · (√(2r_2 / (r_1+r_2)) - 1)
Δv_2 = √(μ/r_2) · (1 - √(2r_1 / (r_1+r_2)))
t_trans = π · √((r_1+r_2)³ / (8μ))

Celestial Target / Preset

Semi-Major (a) (AU)

Eccentricity (e)

Time Warp (days/s)

Arg of Periapsis (°)

Departure Body

Arrival Target

Departure Burn (Δv₁): 2.94 km/s

Arrival Burn (Δv₂): 2.65 km/s

Total Mission Δv: 5.59 km/s

Flight Duration: 259 days

Required Lead Angle: 44.3°

ISS Velocity 27,580 km/h

Altitude 418.5 km

Coordinates 28.4°N, 80.5°W

Inclination 51.64° LEO

Active Body: Earth

Heliocentric Distance (r): 1.000 AU

Orbital Velocity (v): 29.78 km/s

True Anomaly (ν): 0.0°

Orbital Period (T): 365.25 days

Sun (1.0 M☉) Target Orbit Hohmann Ellipse | Pan: Drag • Zoom: Wheel