Jyotisha 3D

Interactive Astronomical Orbits & Vedic Astrological Engine

Current Engine Mode100% Dependency-Free / WebGL Powered

Enter Natal Birth Details

Location Preset:
Drag: Rotate view | Scroll: Zoom

3D Viewport Controls

Rotate the solar system by clicking and dragging inside the canvas. Pinch or scroll to zoom in/out.

Coordinate System Model

Geocentric Model (Vedic Astrology Perspective):

The Earth is locked at the center. The orbital trails show the apparent motion of the Sun, Moon, and planets against the sidereal Zodiac ring (30° segments).

Notice the red spiral trail of the selected planet—it shows retrogrades and epicycles relative to the Earth!

Target Sandbox EntityuseAstrologyStore.selectedSandboxPlanet = 'Mercury'

Educational Math Sandbox: Base Parameters

Julian Date (JD)JD = f(Year, Month, Day, Hour UTC)
2449852.875000
Baseline count of days since Jan 1, 4713 BC. Standard coordinate for orbital theories.
Julian Centuries (T)T = (JD - 2451545.0) / 36525
-0.04632786 centuries
Number of Julian centuries (36,525 days) elapsed since the J2000.0 epoch.
Obliquity of Ecliptic (ε)ε = 23.4392911 - 0.0130042 * T ...
23.439894° (23° 26' 23")
Axial tilt of the Earth at birth epoch, used for equatorial/ecliptic coordinate shifts.
Lahiri Ayanamsa (α)α = 23.85708 + 1.39697 * T + 0.0003086 * T²
23.792362° (23° 47' 32")
Sidereal shift offset between Western Tropical and Vedic Sidereal zodiacs due to Equinox precession.
Local Sidereal Time (LST)LST = (GMST + Longitude) % 360
84.831070°
Astronomical time mapping the observer's meridian against the stars, required for Ascendant (Lagna).

CONSOLE_LOG://MERCURY_SOLVER

Live Math Trace
--- Heliocentric Keplerian Elements for Mercury at epoch ---
Semi-major axis (a): 0.387099 AU
Eccentricity (e): 0.205635
Inclination (i): 7.005255°
Mean Longitude (L): -6672.4984°
Longitude of Perihelion (ϖ): 77.4504°
Longitude of Asc. Node (Ω): 48.3366°
Mean Anomaly (M = L - ϖ): 90.0512°
Solving Kepler's Transcendental Equation (E - e * sin E = M):
Initial guess E0: 90.0512° + e * sin(M)
Newton-Raphson Iterations: converged in 3 steps.
Resolved Eccentric Anomaly (E): 101.5929°
Orbital Plane Vector coordinates (x', y'):
x' = a * (cos E - e) = -0.157391 AU
y' = a * sqrt(1 - e²) * sin E = 0.371099 AU
Rotate to Ecliptic Plane via Inclination (i) and Ascending Node (Ω):
Heliocentric Mercury [X_h, Y_h, Z_h]: [-0.395050, -0.074225, 0.030202] AU
Heliocentric Earth [X_e, Y_e, Z_e]: [-0.592119, -0.819283, -0.000008] AU
Geocentric Vector Projection (Subtract Earth):
X_geo = X_h - X_e = 0.197069 AU
Y_geo = Y_h - Y_e = 0.745058 AU
Z_geo = Z_h - Z_e = 0.030210 AU
Final Coordinates (Spherical Projection):
Tropical Longitude (atan2(Y_geo, X_geo)): 75.1844°
Latitude (atan2(Z_geo, projected)): 2.2448°
Subtract Ayanamsa: 75.1844° - 23.7924° = 51.3921°
Vedic Coordinates: 21° 23' 31" inside Taurus (Vrishabha)