Planet Position Calculator

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Planet Position Calculator

Calculate the approximate heliocentric ecliptic longitude and distance of a solar system planet for a given date using simplified Keplerian orbital elements (J2000.0 epoch).

Planet

Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune

Date (UTC)

Calculate Enter a date and select a planet to calculate its position.

// Keplerian orbital elements at J2000.0 epoch and their rates (per Julian century) // Source: NASA JPL "Keplerian Elements for Approximate Positions of the Major Planets" // https://ssd.jpl.nasa.gov/planets/approx_pos.html // Elements: [a0, adot, e0, edot, I0, Idot, L0, Ldot, lp0, lpdot, Om0, Omdot] // a = semi-major axis (AU), e = eccentricity, I = inclination (deg), // L = mean longitude (deg), lp = longitude of perihelion (deg), Om = longitude of ascending node (deg) const PLA_ELEMENTS = { mercury: [0.38709927, 0.00000037, 0.20563593, 0.00001906, 7.00497902, -0.00594749, 252.25032350, 149472.67411175, 77.45779628, 0.16047689, 48.33076593, -0.12534081], venus: [0.72333566, 0.00000390, 0.00677672, -0.00004107, 3.39467605, -0.00078890, 181.97909950, 58517.81538729, 131.60246718, 0.00268329, 76.67984255, -0.27769418], earth: [1.00000261, 0.00000562, 0.01671123, -0.00004392, -0.00001531, -0.01294668, 100.46457166, 35999.37244981, 102.93768193, 0.32327364, 0.0, 0.0], mars: [1.52371034, 0.00001847, 0.09339410, 0.00007882, 1.84969142, -0.00813131, -4.55343205, 19140.30268499, -23.94362959, 0.44441088, 49.55953891, -0.29257343], jupiter: [5.20288700, -0.00011607, 0.04838624, -0.00013253, 1.30439695, -0.00183714, 34.39644051, 3034.74612775, 14.72847983, 0.21252668, 100.47390909, 0.20469106], saturn: [9.53667594, -0.00125060, 0.05386179, -0.00050991, 2.48599187, 0.00193609, 49.95424423, 1222.49362201, 92.59887831, -0.41897216, 113.66242448, -0.28867794], uranus: [19.18916464, -0.00196176, 0.04725744, -0.00004397, 0.77263783, -0.00242939, 313.23810451, 428.48202785, 170.95427630, 0.40805281, 74.01692503, 0.04240589], neptune: [30.06992276, 0.00026291, 0.00859048, 0.00005105, 1.77004347, 0.00035372, -55.12002969, 218.45945325, 44.96476227, -0.32241464, 131.78422574, -0.00508664] };

function plaCalc() { const planet = document.getElementById('pla-planet').value; const dateStr = document.getElementById('pla-date').value; const resultDiv = document.getElementById('pla-result');

if (!dateStr) { resultDiv.innerHTML = 'Please select a valid date.'; return; }

const date = new Date(dateStr + 'T12:00:00Z'); if (isNaN(date.getTime())) { resultDiv.innerHTML = 'Invalid date.'; return; }

// Julian Date const JD = date.getTime() / 86400000.0 + 2440587.5;

// Julian centuries from J2000.0 const T = (JD - 2451545.0) / 36525.0;

const el = PLA_ELEMENTS[planet]; const a = el[0] + el[1] * T; // AU const e = el[2] + el[3] * T; const I = el[4] + el[5] * T; // deg const L = el[6] + el[7] * T; // deg const lp = el[8] + el[9] * T; // deg const Om = el[10] + el[11] * T; // deg

// Argument of perihelion const w = lp - Om;

// Mean anomaly (degrees), normalized to [-180, 180] let M = L - lp; M = M % 360; if (M > 180) M -= 360; if (M ' + '' + 'Julian Date' + JD.toFixed(2) + '' + 'T (Julian centuries from J2000)' + T.toFixed(6) + '' + 'Semi-major axis (a)' + a.toFixed(6) + ' AU' + 'Eccentricity (e)' + e.toFixed(6) + '' + 'Mean Anomaly (M)' + M.toFixed(4) + '°' + 'Eccentric Anomaly (E)' + (E * 180 / Math.PI).toFixed(4) + '°' + 'True Anomaly (ν)' + nu.toFixed(4) + '°' + 'Heliocentric Distance (r)' + r.toFixed(6) + ' AU (' + (r * 149597870.7).toFixed(0) + ' km)' + 'Ecliptic Longitude (λ)' + lon.toFixed(4) + '°' + 'Ecliptic Latitude (β)' + lat.toFixed(4) + '°' + 'Zodiac Position' + signDeg.toFixed(2) + '° ' + signs[signIdx] + '' + 'Light Travel Time from Sun' + lightMin.toFixed(2) + ' minutes' + ''; }

#### Formulas Used

1. Julian Date: JD = (Unix timestamp in days) + 2440587.5

2. Julian Centuries from J2000.0: T = (JD − 2451545.0) / 36525

3. Orbital Elements (linearly interpolated): a(T) = a₀ + ȧ·T | e(T) = e₀ + ė·T | I(T) = I₀ + İ·T L(T) = L₀ + L̇·T | ϖ(T) = ϖ₀ + ϖ̇·T | Ω(T) = Ω₀ + Ω̇·T

4. Argument of Perihelion: ω = ϖ − Ω

5. Mean Anomaly: M = L − ϖ (normalized to [−180°, 180°])

6. Kepler's Equation (Newton-Raphson iteration): E − e·sin(E) = M ΔE = (M − E + e·sin(E)) / (1 − e·cos(E)) → E ← E + ΔE (until |ΔE| < 10⁻¹⁰)

7. Heliocentric Coordinates in Orbital Plane: x' = a·(cos E − e) y' = a·√(1 − e²)·sin E

8. Heliocentric Distance: r = √(x'² + y'²)

9. True Anomaly: ν = atan2(y', x')

10. Heliocentric Ecliptic Coordinates: xecl = r·[cos Ω·cos(ν+ω) − sin Ω·sin(ν+ω)·cos I] yecl = r·[sin Ω·cos(ν+ω) + cos Ω·sin(ν+ω)·cos I] zecl = r·sin(ν+ω)·sin I

11. Ecliptic Longitude & Latitude: λ = atan2(yecl, xecl) (normalized to [0°, 360°]) β = arcsin(zecl / r)

#### Assumptions & References

Orbital elements are from the NASA JPL "Keplerian Elements for Approximate Positions of the Major Planets" table, valid for dates within ~3000 years of J2000.0 (2000-Jan-1.5 TT). Accuracy is typically within ~1–2 arcminutes for inner planets and a few arcminutes for outer planets.
The epoch is J2000.0 (Julian Date 2451545.0, i.e., 2000 January 1, 12:00 TT).
Positions are heliocentric ecliptic (referenced to the mean ecliptic and equinox of J2000.0), not geocentric. To get geocentric positions, Earth's position vector must be subtracted.
Kepler's equation is solved iteratively using Newton-Raphson with convergence threshold 10⁻¹⁰ radians.
The zodiac sign is determined by dividing the ecliptic longitude into 12 equal 30° sectors starting at 0° Aries — this is the tropical zodiac, not the sidereal zodiac.
Reference: E.M. Standish, "Keplerian Elements for Approximate Positions of the Major Planets," NASA JPL Solar System Dynamics, 1992. ssd.jpl.nasa.gov

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