Celestial object phenomena

Several aspect (differentia) of celestial objects (stars and inner- and outer planets) movements along the sky are important:

Object Types

The following object Types (depending on location and meteorological conditions) can be defined:

An object of a certain Type will exhibit certain sequence of Phases and in between the Phases there are Periods forming the mean periodicy of the object.

Below picture shows the Object Type changing depending on the RA/DEC of the object (for location London, 1948CE and AEC=0.25). The number in the cells refer to the Type Code mentioned in the table below:
      Types in the sky

The Type of an object can change to another (neighboring) Type depending on the atmospheric conditions.

The calendar entries of Ptolemy show the above mentioned (sub) Types: CP, ALHa and ALHb.
Looking at Ptolemy's calendar entries the following Type changes are seen for the same star when decreasing the geo. latitude:
ALHa -> ALHb: Alphard, Betelgeuse, Rukbat
CP -> ALHb: Alpheratz, Altair, Menkalinan,

Object Phases

Naming phases

What would be a good way to name object (apparent) Phases for stars, outer- and inner planets?
So for these reasons this web site will use the six terms: MF, ML, EF,  EL, AR and CS. These will be defined in a below section.

Star and outer planet Phases

Apparent Phases

(Apparent) Phases** (Ptolemy, 1993, start Section 2, page 3 and end Section 4, page 5; Ptolemy, 1984, page 409 to 410 [called 'configurations']) that occur during mean periodicy of the star (and outer planets [Mars, Jupiter and Saturn]) are (depending on location and meteorological conditions) described by Kolev [2006] as follows:
MF and EL (or swapped) Phases are following each other up, same with AR and CS (or swapped) Phases.
Furthermore the Type is also indicative for the sequence of Phases (Lehoux [2000, 12], who paraphrases Neugebauer [1975, 759-60]):
Below is a table that shows the (apparent) Phase and Period sequence for each Type (in this graph is a graphical representation of the Types an object goes through):
Type Description Ptolemy
Phase and Period sequence Type Code
C Circumpolar
SA 1
CP Curtailed Passage(b)*** All year long
MF   EL   CS   AR   MF 3
ALHa Arisen and Laying Hidden(a) Night pathed
EL   MF   AR   CS   EL 4
ALHb Arisen and Laying Hidden(b) Dock pathed
EL   MF   CS   AR   EL 5
I Invisible
NS 6

** Many people name these Phases: Heliacal Events. Both terms will be used interchangeable on this web site.

Topocentric Phases

Above (apparent) Phases have been mentioned, but of course Topocentric or Geocentric (ture) Phases can also be recognised. In the Topocentric Phases the meteorology and refraction are not included, while the star's and Sun centre's topo/geocentric altitude are zero (in PLSV: one puts all Visibility parameters to zero). Ptolemy talks in that case about True simultaneous phases (page xiii-xiv) (Toomer, page 410-413).
This website does not use by default the Topocentric (true) Phases but (apparent) Phases, unless the word 'Topocentric' is explicitly added.

Inner planet Phases

The inner planets (Mercury and Venus) have the following four Phases:

Some other definitions

Multiple other terms are utilised in literature, here are some of the mappings (for apparent event) used on this website (MF, ML, EF,  EL, AR and CS):

Object Periods

The following star Periods (Ptolemy, Section 5, page 5) can be seen in the sky during one night (this is depending on location and meteorological conditions):

These Object Periods are between Object Phases (Ptolemy, Section 5, page 5). The Periods that a certain Object Type can exhibit are limited and have one of the following sequences:


CP Type***

Ptolemy also recognises this sub Type: CP as double visible (Evans, 1998, pp 196-197).
This is an example for Arcturus (RA= ~14.5h:DEC= ~19; including refraction [Apparent], but no detailed meteorological conditions as PLSV does not include this):
Acrturus in London
Arcturus' visibility (using PLSV)

The naked eye apparent Phases and Periods are:
Arcturus is of CP Type (as indicated by the sequence MF -> EL -> AR -> CS).

***Theoretically there could be a CPa(Type Code=2) and CPb(Type Code=3); the difference that the sequence AR - CS is swapped. No calculations resulted consistently in the MF -> EL -> CS -> AR sequence. This sub phase (Type Code=2) might though happen, see above picture. There are only CP(Type Code=3) Ptolemy's calendar entries also, no CPa(Type Code=2).

ALH Types

There are two sub types of ALH (Arisen and Laying Hidden): ALHa (south of the ecliptic) and ALHb (somewhat northern and southern of ecliptic). Ptolemy also recognises these two sub Types: ALHa as night-pathed and ALHb as dock-pathed (Evans, 1998, pp 193-196).

ALHa Type star

This is an example for Sirius (RA= ~7h:DEC= ~17; including refraction [Apparent], but no detailed meteorological conditions as PLSV does not include this):
sirius in London
Sirius' visibility (using PLSV)

The naked eye apparent Phases and Periods are:
Sirius is of ALHa Type (as indicated by the sequence: EL -> MF -> CS -> AR).

ALHb Type

This is an example for a star (RA=18h:DEC=-25; including refraction [Apparent], but no detailed meteorological conditions as PLSV does not include this):
ALH2 type
        of star
Star's (RA=18h, DEC=-25) visibility (using PLSV)

The naked eye apparent Phases and Periods are:
This star is ALHb Type (as indicated by the sequence: EL -> MF -> AR -> CS).


Bernadette Brady. "The Egyptian ascension mythology of the Old Kingdom and the phenomenon of star phases." Paper presented at the Current research in Egyptology Durham University, UK, 2011.
Evans, James, The history and practice of ancient astronomy: Oxford University Press, USA, 1998.
Rumen Kolev. The Babylonian astrology & astronomy: The heliacal phases. Vol. 1, 2006.
Rumen Kolev. "Acronychal Rising." Pers. comm: Aug 2009.
Rumen Kolev, "The Babylonian astrolabe: The calendar of creation", Neo Assyrian text corpus project, 2013.
Lehoux, Daryn Rosario. 2000. 'Parapegmata: Astrology, Weather, and Calendars in the Ancient World', University of Toronto.
Jean Meeus. "Heliacal rising and setting." In Mathematical astronomy morsels, 289-96: Willmann-Bell, 1997.
Neugebauer, Otto. 1975. History of ancient mathematical astronomy (New York: Springer Science).
Planetary, Lunar and Stellar Visibility Version 3.1.0. Alcyone.
Ptolemy, Claudius, Ptolemy's Almagest. Translated by G.J. Toomer: Springer-Verlag, 1984.
Claudius Ptolemy. "The phases of the fixed stars." ed Robert Hand, The Golden Hind Press, 1993
Schaefer, Brad E., 'Heliacal rise phenomena', Journal for the History of Astronomy 11, no. xviii (1987): S19-S33.
N.M. Swerdlow. The Babylonian Theory of the Planets: Princeton University Press, 1998.
Swiss Ephemeris Version 1.78. Astrodienst.
Robinson, Matthew. 2007. 'Ardua et astra: On the calculation of the dates of the rising an setting of stars', Classical Philology, Vol 104: pp. 254-75.


I would like to thank the following people for their help and constructive feedback: Bernadette Brady, Dieter Koch, Rumen Kolev, Frank Prendergast and all other unmentioned people. Any remaining errors in methodology or results are my responsibility of course!!! If you want to provide constructive feedback, let me know.

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Major content related changes: Sept. 19, 2012