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:

$M = E - e \cdot \sin(E)$
$E_{k+1} = E_k - \frac{E_k - e \cdot \sin(E_k) - M}{1 - e \cdot \cos(E_k)}$

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

2. True Anomaly $\nu$ & Radial Distance $r$:

$r = a(1 - e \cdot \cos(E)) = \frac{a(1 - e^2)}{1 + e \cdot \cos(\nu)}$
$\tan(\nu/2) = \sqrt{\frac{1+e}{1-e}} \cdot \tan(E/2)$

3. Vis-Viva Orbital Velocity:

$v = \sqrt{\mu \left(\frac{2}{r} - \frac{1}{a}\right)}, \quad T = 2\pi \sqrt{\frac{a^3}{\mu}}$

4. Hohmann Transfer Delta-v ($\Delta v$):

$\Delta v_1 = \sqrt{\frac{\mu}{r_1}} \left(\sqrt{\frac{2r_2}{r_1+r_2}} - 1\right)$

$\Delta v_2 = \sqrt{\frac{\mu}{r_2}} \left(1 - \sqrt{\frac{2r_1}{r_1+r_2}}\right)$

$t_{\text{trans}} = \pi \sqrt{\frac{(r_1+r_2)^3}{8\mu}}$

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