Chapter 3 — Where a planet is located: celestial coordinates #

What you will learn #

In this chapter you will learn the three coordinate systems used in astronomy — ecliptic, equatorial and horizontal — and how to convert between them. You will also understand what reference frames are (J2000, ICRS), and the effects of precession, nutation and aberration.

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3.1 Ecliptic coordinates: longitude and latitude #

The most used coordinate system in astrology. The reference plane is the ecliptic (the Sun’s path), the zero point is the vernal equinox.

• Ecliptic longitude: 0°–360° along the ecliptic. It is the “zodiac sign”.
• Ecliptic latitude: distance from the ecliptic, from -90° to +90°.

The Sun always has a latitude of ~0° (by definition, it traces the ecliptic). The Moon can reach ±5.1° of latitude. The planets stay within a few degrees of the ecliptic, except Pluto which can reach ~17°.

import libephemeris as ephem

jd = ephem.julday(2024, 4, 8, 12.0)
pos, flag = ephem.calc_ut(jd, ephem.SE_MOON, 0)

lon = pos[0]   # ecliptic longitude (degrees)
lat = pos[1]   # ecliptic latitude (degrees)
dist = pos[2]  # distance (AU)

sign_num = int(lon / 30)
signs = ["Ari", "Tau", "Gem", "Cnc", "Leo", "Vir",
         "Lib", "Sco", "Sgr", "Cap", "Aqr", "Psc"]
print(f"Moon: {lon % 30:.2f}° {signs[sign_num]}, lat {lat:.2f}°")
# "Moon at 15° Cancer" = ecliptic longitude 105.x°

Moon: 15.43° Ari, lat -0.02°

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3.2 Equatorial coordinates: right ascension and declination #

The system used by telescopes. The reference plane is the celestial equator.

• Right Ascension (RA): 0°–360° along the celestial equator (sometimes expressed in hours: 0h–24h).
• Declination (Dec): distance from the celestial equator, from -90° to +90°.

Telescopes prefer this system because the celestial equator is aligned with the Earth’s rotation: it is enough to rotate around a single axis to track an object.

import libephemeris as ephem

jd = ephem.julday(2024, 4, 8, 12.0)

# Flag SEFLG_EQUATORIAL: returns RA and Dec instead of lon and lat
pos, flag = ephem.calc_ut(jd, ephem.SE_MOON, ephem.SEFLG_EQUATORIAL)

ra = pos[0]    # Right Ascension in degrees (0–360)
dec = pos[1]   # Declination in degrees (-90 to +90)

# RA conversion from degrees to hours:minutes:seconds
ra_hours = ra / 15.0
ra_h = int(ra_hours)
ra_m = int((ra_hours - ra_h) * 60)
ra_s = ((ra_hours - ra_h) * 60 - ra_m) * 60

print(f"Moon: RA = {ra_h}h {ra_m}m {ra_s:.1f}s, Dec = {dec:+.2f}°")

Moon: RA = 0h 56m 52.2s, Dec = +6.06°

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3.3 Horizontal coordinates: altitude and azimuth #

The “practical” system — where should I look to see an object in the sky? This system depends on the observer’s position and the time.

• Altitude: angle above the horizon. 0° = horizon, 90° = zenith. Negative values = below the horizon.
• Azimuth: direction on the horizon. In LibEphemeris: 0° = South, 90° = West, 180° = North, 270° = East.

The observer’s position is required and, optionally, pressure and temperature for atmospheric refraction.

import libephemeris as ephem

jd = ephem.julday(2024, 9, 15, 21.0)

# Jupiter in equatorial coordinates
pos, _ = ephem.calc_ut(jd, ephem.SE_JUPITER, ephem.SEFLG_EQUATORIAL)

# Rome (lon East, lat North, altitude in meters)
geopos = (12.4964, 41.9028, 50.0)

# From equatorial to horizontal (SE_EQU2HOR = 1)
hor = ephem.azalt(jd, ephem.SE_EQU2HOR, geopos, 1013.25, 15.0,
                  (pos[0], pos[1], pos[2]))

print(f"Azimuth: {hor[0]:.1f}° (from South)")
print(f"True altitude: {hor[1]:.1f}°")
print(f"Apparent altitude: {hor[2]:.1f}° (with refraction)")

# Inverse operation: from horizontal to equatorial
ra_dec = ephem.azalt_rev(jd, ephem.SE_HOR2EQU, geopos, hor[0], hor[1])
print(f"Recovered RA: {ra_dec[0]:.4f}°, Dec: {ra_dec[1]:.4f}°")

Azimuth: 235.7° (from South)
True altitude: -3.2°
Apparent altitude: -3.2° (with refraction)
Recovered RA: 79.6564°, Dec: 22.3890°

🌍 Real life #

“Is Jupiter visible tonight?” — calculate the altitude: if it is > 0°, it is above the horizon. If it is > 10°, it is high enough not to be disturbed by the atmosphere near the horizon. The azimuth tells you in which direction to look.

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3.4 Reference frames: ICRS, J2000, equinox of date #

The coordinates of a celestial object depend on the chosen reference frame. The zero point and axes can be defined in different ways:

• Equinox of date: the default in LibEphemeris. The coordinates take into account the current precession and nutation. The zero point is the vernal equinox of that moment. It is the system used in astrology.

• J2000.0: the coordinates are fixed to January 1, 2000, 12:00 TT. The zero point is the vernal equinox as it was in 2000. It is the standard for astronomical catalogs.

• ICRS: the modern system, based on the positions of very distant quasars (practically fixed). It is almost identical to J2000 — the difference (“frame bias”) is ~0.02".

import libephemeris as ephem

jd = ephem.julday(2024, 4, 8, 12.0)

# "Of date" ecliptic coordinates (default)
pos_date, _ = ephem.calc_ut(jd, ephem.SE_MARS, 0)

# J2000 ecliptic coordinates
pos_j2000, _ = ephem.calc_ut(jd, ephem.SE_MARS, ephem.SEFLG_J2000)

# ICRS equatorial coordinates
pos_icrs, _ = ephem.calc_ut(jd, ephem.SE_MARS,
                            ephem.SEFLG_EQUATORIAL | ephem.SEFLG_ICRS)

print(f"Mars of-date: {pos_date[0]:.4f}°")
print(f"Mars J2000:   {pos_j2000[0]:.4f}°")
print(f"Difference:   {pos_date[0] - pos_j2000[0]:.4f}° (≈ precession)")

Mars of-date: 342.8458°
Mars J2000:   342.5082°
Difference:   0.3376° (≈ precession)

The difference between “of date” and J2000 is mainly the precession accumulated from 2000 to today — about 0.34° in 2024.

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3.5 Precession, nutation and aberration #

Three physical effects influence celestial coordinates. It is important to know they exist, even if in practice the library handles them automatically.

Precession #

The Earth’s axis of rotation does not always point in the same direction: it draws a circle in the sky in about 26000 years, like a wobbling top. The effect is that the vernal point (0° Aries) shifts by about 50 arcseconds per year relative to the stars.

In 2000 years, precession has shifted the vernal point by about 28° — almost an entire zodiac sign. This is the reason why the tropical zodiac and constellations no longer coincide.

Nutation #

Superimposed on precession, the Earth’s axis makes small oscillations with a main period of ~18.6 years (linked to the cycle of the lunar nodes). The amplitude is ~9" in longitude and ~17" in obliquity.

The SEFLG_NONUT flag calculates “mean” coordinates (without nutation) instead of “true” ones:

import libephemeris as ephem

jd = ephem.julday(2024, 4, 8, 12.0)

# With nutation (default = "true" coordinates)
pos_true, _ = ephem.calc_ut(jd, ephem.SE_SUN, 0)

# Without nutation ("mean" coordinates)
pos_mean, _ = ephem.calc_ut(jd, ephem.SE_SUN, ephem.SEFLG_NONUT)

diff_arcsec = (pos_true[0] - pos_mean[0]) * 3600
print(f"Nutation effect: {diff_arcsec:.2f}\"")

Nutation effect: -5.30"

Aberration #

Light takes time to arrive, and meanwhile the Earth moves. The effect is an apparent shift up to ~20" in the direction of the Earth’s motion. The SEFLG_NOABERR flag disables it; SEFLG_TRUEPOS returns the pure geometric position (without correction for light-time nor for aberration).

import libephemeris as ephem

jd = ephem.julday(2024, 4, 8, 12.0)

# Apparent position (default: with aberration)
pos_app, _ = ephem.calc_ut(jd, ephem.SE_MARS, 0)

# True geometric position (without aberration nor light-time)
pos_true, _ = ephem.calc_ut(jd, ephem.SE_MARS, ephem.SEFLG_TRUEPOS)

diff = (pos_app[0] - pos_true[0]) * 3600
print(f"Aberration + light-time effect: {diff:.1f}\"")

Aberration + light-time effect: -33.3"

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3.6 Cartesian coordinates (XYZ) #

Sometimes positions are needed in Cartesian coordinates (X, Y, Z) instead of angular ones. Useful for 3D distance calculations, phase angles, or geometric problems.

The SEFLG_XYZ flag changes the meaning of the returned tuple: instead of (lon, lat, dist, vel_lon, vel_lat, vel_dist) you get (x, y, z, vx, vy, vz) in astronomical units and AU/day.

import libephemeris as ephem

jd = ephem.julday(2024, 4, 8, 12.0)

# Equatorial Cartesian position
pos, _ = ephem.calc_ut(jd, ephem.SE_MARS,
                       ephem.SEFLG_XYZ | ephem.SEFLG_EQUATORIAL)

x, y, z = pos[0], pos[1], pos[2]
import math
dist = math.sqrt(x**2 + y**2 + z**2)
print(f"Mars: X={x:.4f}, Y={y:.4f}, Z={z:.4f} AU")
print(f"Distance: {dist:.4f} AU = {dist * 149597870.7:.0f} km")

Mars: X=1.9696, Y=-0.5400, Z=-0.2829 AU
Distance: 2.0618 AU = 308436754 km

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3.7 Converting between systems #

LibEphemeris offers dedicated functions for conversions:

The sign of the obliquity in cotrans controls the direction: negative = ecliptic→equatorial, positive = equatorial→ecliptic.

Complete example: from ecliptic position to altitude in the sky #

import libephemeris as ephem

jd = ephem.julday(2024, 9, 15, 21.0)

# 1. Saturn's ecliptic position
pos, _ = ephem.calc_ut(jd, ephem.SE_SATURN, 0)
lon, lat, dist = pos[0], pos[1], pos[2]

# 2. Get the obliquity
nut, _ = ephem.calc_ut(jd, ephem.SE_ECL_NUT, 0)
obliquity = nut[0]

# 3. Ecliptic -> Equatorial (negative obliquity)
ra, dec, d = ephem.cotrans((lon, lat, dist), -obliquity)

# 4. Equatorial -> Horizontal (Rome)
geopos = (12.4964, 41.9028, 50.0)
hor = ephem.azalt(jd, ephem.SE_EQU2HOR, geopos, 1013.25, 15.0,
                  (ra, dec, d))

print(f"Saturn: lon={lon:.2f}°, lat={lat:.2f}°")
print(f"        RA={ra:.2f}°, Dec={dec:+.2f}°")
print(f"        Altitude={hor[2]:.1f}°, Azimuth={hor[0]:.1f}° (from S)")

Saturn: lon=345.44°, lat=-2.20°
        RA=347.46°, Dec=-7.76°
        Altitude=35.5°, Azimuth=329.5° (from S)

Shortcut: you can also pass ecliptic coordinates directly to azalt with SE_ECL2HOR, avoiding manual conversion. The explicit conversion via cotrans is useful when you need intermediate values.

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Summary #

• Ecliptic (lon, lat): system of astrology, based on the ecliptic. Default of calc_ut.
• Equatorial (RA, Dec): system of telescopes, based on the celestial equator. Flag SEFLG_EQUATORIAL.
• Horizontal (azimuth, altitude): practical system, depends on the location. Function azalt.
• Of date (default), J2000 (SEFLG_J2000), ICRS (SEFLG_ICRS): three reference frames for the coordinate zero point.
• Precession: slow shift of the zero point (~50"/year). Nutation: oscillation of the axis (~9"). Aberration: shift due to Earth’s motion (~20").
• cotrans converts between ecliptic and equatorial. azalt and azalt_rev convert from/to horizontal coordinates.

Introduced functions and constants #