Functions: Moons

Functions for observing the natural satellites of Jupiter, Saturn, Uranus, and Mars. Each moon family uses a dedicated analytical theory for computing satellite positions relative to the parent planet, which is then transformed to Earth-based topocentric coordinates.

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galilean_observe

Computes the topocentric position of a Galilean moon of Jupiter as seen from an Earth-based observer. Uses the Lieske L1.2 theory (Lieske, 1998).

Signature

galilean_observe(moon_id int4, obs observer, t timestamptz) → topocentric

Parameters

Parameter	Type	Description
moon_id	int4	Galilean moon identifier (see table below)
obs	observer	Observer location on Earth
t	timestamptz	Observation time

Moon IDs

ID	Moon	Orbital Period
0	Io	1.769 days
1	Europa	3.551 days
2	Ganymede	7.155 days
3	Callisto	16.689 days

Returns

A topocentric with azimuth, elevation, range (km), and range rate (km/s).

Example

-- Current positions of all four Galilean moons
SELECT moon_id,
       CASE moon_id
         WHEN 0 THEN 'Io'       WHEN 1 THEN 'Europa'
         WHEN 2 THEN 'Ganymede' WHEN 3 THEN 'Callisto'
       END AS moon,
       round(topo_azimuth(t)::numeric, 4)   AS az,
       round(topo_elevation(t)::numeric, 4) AS el,
       round(topo_range(t)::numeric, 0)     AS range_km
FROM generate_series(0, 3) AS moon_id,
     galilean_observe(moon_id, '40.0N 105.3W 1655m'::observer, now()) AS t;

-- Track Io's position over one orbital period (1.769 days)
SELECT t,
       round(topo_azimuth(pos)::numeric, 4)   AS az,
       round(topo_elevation(pos)::numeric, 4) AS el
FROM generate_series(
       now(), now() + interval '1.769 days', interval '15 minutes'
     ) AS t,
     galilean_observe(0, '40.0N 105.3W 1655m'::observer, t) AS pos;

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saturn_moon_observe

Computes the topocentric position of a moon of Saturn as seen from an Earth-based observer. Uses the TASS17 theory (Vienne & Duriez, 1995) for the eight major Saturnian moons.

Signature

saturn_moon_observe(moon_id int4, obs observer, t timestamptz) → topocentric

Parameters

Parameter	Type	Description
moon_id	int4	Saturn moon identifier (see table below)
obs	observer	Observer location on Earth
t	timestamptz	Observation time

Moon IDs

ID	Moon	Orbital Period	Approx. Magnitude
0	Mimas	0.942 days	+12.9
1	Enceladus	1.370 days	+11.7
2	Tethys	1.888 days	+10.2
3	Dione	2.737 days	+10.4
4	Rhea	4.518 days	+9.7
5	Titan	15.945 days	+8.3
6	Iapetus	79.322 days	+10.2-11.9
7	Hyperion	21.277 days	+14.2

Note

Iapetus has a large brightness variation due to its two-toned surface — the leading hemisphere is much darker than the trailing hemisphere. The magnitude range reflects this dichotomy.

Returns

A topocentric with azimuth, elevation, range (km), and range rate (km/s).

Example

-- All eight Saturn moons' current positions
SELECT moon_id,
       CASE moon_id
         WHEN 0 THEN 'Mimas'     WHEN 1 THEN 'Enceladus'
         WHEN 2 THEN 'Tethys'    WHEN 3 THEN 'Dione'
         WHEN 4 THEN 'Rhea'      WHEN 5 THEN 'Titan'
         WHEN 6 THEN 'Iapetus'   WHEN 7 THEN 'Hyperion'
       END AS moon,
       round(topo_azimuth(t)::numeric, 4)   AS az,
       round(topo_elevation(t)::numeric, 4) AS el,
       round(topo_range(t)::numeric, 0)     AS range_km
FROM generate_series(0, 7) AS moon_id,
     saturn_moon_observe(moon_id, '40.0N 105.3W 1655m'::observer, now()) AS t;

-- Track Titan over one orbital period
SELECT t,
       round(topo_azimuth(pos)::numeric, 4) AS az,
       round(topo_elevation(pos)::numeric, 4) AS el
FROM generate_series(
       now(), now() + interval '15.945 days', interval '1 hour'
     ) AS t,
     saturn_moon_observe(5, '40.0N 105.3W 1655m'::observer, t) AS pos;

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uranus_moon_observe

Computes the topocentric position of a moon of Uranus as seen from an Earth-based observer. Uses the GUST86 theory (Laskar & Jacobson, 1987).

Signature

uranus_moon_observe(moon_id int4, obs observer, t timestamptz) → topocentric

Parameters

Parameter	Type	Description
moon_id	int4	Uranus moon identifier (see table below)
obs	observer	Observer location on Earth
t	timestamptz	Observation time

Moon IDs

ID	Moon	Orbital Period	Approx. Magnitude
0	Miranda	1.413 days	+16.5
1	Ariel	2.520 days	+14.2
2	Umbriel	4.144 days	+14.8
3	Titania	8.706 days	+13.9
4	Oberon	13.463 days	+14.1

Caution

The Uranian moons are faint. Miranda at magnitude +16.5 requires a large aperture telescope. Titania and Oberon are the most accessible at around magnitude +14.

Returns

A topocentric with azimuth, elevation, range (km), and range rate (km/s).

Example

-- All five Uranus moons' current positions
SELECT moon_id,
       CASE moon_id
         WHEN 0 THEN 'Miranda' WHEN 1 THEN 'Ariel'
         WHEN 2 THEN 'Umbriel' WHEN 3 THEN 'Titania'
         WHEN 4 THEN 'Oberon'
       END AS moon,
       round(topo_azimuth(t)::numeric, 4)   AS az,
       round(topo_elevation(t)::numeric, 4) AS el,
       round(topo_range(t)::numeric, 0)     AS range_km
FROM generate_series(0, 4) AS moon_id,
     uranus_moon_observe(moon_id, '40.0N 105.3W 1655m'::observer, now()) AS t;

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mars_moon_observe

Computes the topocentric position of a moon of Mars as seen from an Earth-based observer. Uses the MarsSat analytical theory.

Signature

mars_moon_observe(moon_id int4, obs observer, t timestamptz) → topocentric

Parameters

Parameter	Type	Description
moon_id	int4	Mars moon identifier (see table below)
obs	observer	Observer location on Earth
t	timestamptz	Observation time

Moon IDs

ID	Moon	Orbital Period	Approx. Magnitude
0	Phobos	0.319 days (7.66 hours)	+11.4
1	Deimos	1.263 days	+12.5

Note

Phobos and Deimos are extremely close to Mars and are typically overwhelmed by Mars’s glare. Observations are best attempted near Mars opposition when the planet is closest to Earth and the moons have maximum angular separation.

Returns

A topocentric with azimuth, elevation, range (km), and range rate (km/s).

Example

-- Phobos and Deimos positions from Boulder
SELECT moon_id,
       CASE moon_id
         WHEN 0 THEN 'Phobos'
         WHEN 1 THEN 'Deimos'
       END AS moon,
       round(topo_azimuth(t)::numeric, 4)   AS az,
       round(topo_elevation(t)::numeric, 4) AS el,
       round(topo_range(t)::numeric, 0)     AS range_km
FROM generate_series(0, 1) AS moon_id,
     mars_moon_observe(moon_id, '40.0N 105.3W 1655m'::observer, now()) AS t;

-- Track Phobos through one full orbit (~7.66 hours)
SELECT t,
       round(topo_azimuth(pos)::numeric, 4) AS az,
       round(topo_elevation(pos)::numeric, 4) AS el
FROM generate_series(
       now(), now() + interval '7.66 hours', interval '5 minutes'
     ) AS t,
     mars_moon_observe(0, '40.0N 105.3W 1655m'::observer, t) AS pos;