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Celestial object phenomena

• Object Types
• Object Phases
• Object Periods

Object Types

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

• Circumpolar (C)
  An object that never sets and thus is always visible; in naked eye astronomy: it is always above its extinction angle.
  
• Curtailed Passage (CP)
  For an object far north of the ecliptic.
  
• Arisen and Laying Hidden (ALH)
  For an object south of the ecliptic (ALHa) and somewhat northern and southern of ecliptic (ALHb). These sub Types have not been found/recognised in any literature. e.g Brady (2011 and pers. comm. 2017) (if wrong, let me know). But the underlying Phase sequences are clearly recorded by Ptolemy for many stars.
  
• Invisible (I)
  An object that never rises and thus is never visible; in naked eye astronomy: it is always below its extinction angle.

Object Phases

Naming phases

• Toomer's naming in Ptolemy's translation combines the sun's moment (dawn/evening) and the location of the visibility on the actual moment (east/west).
• Or should dawn/dusk be replaced by dawn/evening or morning/evening to use more equivalent concepts.
• Instead of east/west one could use rise/set.
• First/last is a pair of words that describes for a few Phases very well what happens on morning or evening (MF, ML, EF, EL).
  
• For some Phases the celestial object is still visible the day before and after the Phase (AR and CS), while for other Phases the celestial object is not visible the day before/after the Phase (MF, ML, EF, EL). So there are conceptually differences in observation.
  

Star and outer planet Phases

Apparent Phases

• Morning First (MF)
  "At a certain moment, the star (rise) becomes visible for the first time in the (rising) solar halo." (page 10)
  
• Evening Last (EL)
  "The light halo of the setting Sun approaches the star with every day. Then a day comes when the star (set) is so close to the solar halo that it is hardly visible. The next day the star is not visible at all." (page 14)
  
• Acronychal Rise (AR)
  The rising of the star is happening around sunset
  "You watch the place on the sky where the star appears in deep night. The last evening when the star appears on that place is the AR event [Phase]. The next day it appears higher." (Rumen Kolev, pers. communication [2009])
  'Appears in deep night' I assume to be the extinction angle of the star. According to Rumen ~0.5 degrees higher than the extinction angle (pers. comm. [2013]). I have the idea that this change of appearing place might be at the start of the transition from scotopic to photopic vision (change from darkness to astronomical twilight).
  An example of observation of Spica's rise, where the end of the black horizontal line is the date of Acronychal Rise (Julian Date Number: 2456377):
  
  
  
  
  
• Cosmical Set (CS)
  The setting of the stars is happening around sunrise
  You watch the place on the sky where the star appears in deep night. The first morning when the star appears on that place is the CS Phase. The next day it stays at same apparent altitude (analogue to Rumen Kolev's definition of AR).
  'Appears in deep night' can be seen as the extinction angle of the star.
  

• CP Type: the Phase pair (ML,EL) has the Phase sequence: MF and then EL
  
• ALH Types: the Phase pair (ML,EL) has the Phase sequence: EL and then MF
  

Topocentric Phases

Inner planet Phases

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

• Morning First (MF)
  At a certain moment, the inner planet becomes visible for the first time in the (rising) solar halo.
  
• Morning Last (ML)
  The light halo of the rising Sun approaches the inner planet with every day. Then a day comes when the inner planet (set) is so close to the solar halo that it is hardly visible. The next day the inner planet is not visible at all.
  
• Evening First (EF)
  At a certain moment, the inner planet becomes visible for the last time in the (setting) solar halo.
  
• Evening Last (EL)
  The light halo of the setting Sun approaches the inner planet with every day. Then a day comes when the inner planet (set) is so close to the solar halo that it is hardly visible. The next day the inner planet is not visible at all.

Some other definitions

• Meeus [1997]
  Heliacal Rise -> MF
  Heliacal Set -> EL
  
• Ptolemy ([1993], Section 4, page 5)
  Morning Rise Phase -> MF
  Morning Set Phase -> CS
  Evening Rise Phase -> AR
  Evening Set Phase -> EL
  
• Ptolemy ([1984], page 409-410)
  Dawn Easterly configuration -> MF
  Dawn Westerly configuration -> CS
  Evening Easterly configuration -> AR
  Evening Westerly configuration -> EL
• Evans/Autolytus ([1998], page 191) Robinson [2007, page 256]
  Morning rising phase -> MF
  Morning setting phase -> CS
  Evening rising phase -> AR
  Evening setting phase -> EL
• PLSV
  Fist Visibility -> MF
  Last Visibility -> EL
  Evening visibility begins -> EF
  Evening visibility ends -> EL
  Morning visibility begins -> MF
  Morning visibility ends -> ML
  
• Brady (pers. comm., 2012]
  Heliacal Rising (ALH) -> MF
  Morning Rising (CP) -> MF
  Morning Setting  (ALH) -> CS
  Heliacal Setting  (CP) -> CS
  Acronychal Setting (ALH) -> EL
  Evening Setting (CP) -> EL
  Evening Rising (ALH) -> AR
  Acronychal Rising (CP) -> AR
  Her terminology is also taking into account what the star does after the 'transitional event' (so combing Phase and Period). Her 'stage' (Brady, 2011, page 45) might be mapping the Period; her 'group' seems to be the Type; her 'transitional event' maps on the Phase; and her 'phase' is the full star's behavior over the mean periodicy of the star (so possibly includes 'stage', 'group' and 'transitional event').
• skyscapeR (version 0.2.2), looks to follow Brady for at least its 'events'
  phase -> Type
  event -> Phase???
  season -> Period
  Heliacal Rising -> MF
  Achronycal Setting -> EL
  Setting -> SS
  Rising -> RS
  Rising and Setting -> RSS
  Arising and Lying Hidden -> NS
  
• Swiss Ephemeris [2012]
  Does not have at this moment AR and CS in default mode, due to lack of scientific definition. This needs to be studied. If the helflag includes SE_HELIACAL_AVKIND_VR, one can calculate the AR and CS using Reijs' definition (see next bullet).
  
• ARCHAEOCOSMO
  It has similar code for MF, EL, AR and CS (finding the lowest object's altitude for these Phases). This does not fully map Kolev's definitions of AR and CS. This needs to be studied.
• Some unhelpful definitions of Acronychal Rising floating around:
  
• Swerdlow ([1998], page 24) quotes Neugebauer's Greek-letter phenomena:
  Acronychal rising, in the east just after sunset slightly before true opposition
• Quoted by R. van Gent (pers. communication [2009]) from other source:
  Traditionally, the (apparent) acronychal rising of a star is defined as the last evening when the star can be seen rising in the east just after sunset.
• Queried by Schaefer (Schaefer, 1987, page S31)
  ...how is the end of twilight defined?
  

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):

• Non visible Star all night (NS)
  
• Rising Star in night (RS)
  
• Rising and Setting Star in same night (RSS)
• Setting Star in night (SS)
  
• Setting and Rising Star in same night (SRS)
• Star All night visible (SA)
  

• C: only SA
  
• CP: SRS, RS, SA, SS,
  
• ALH: NS, RS, RSS, SS
• I: only NS

Examples

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):

Arcturus' visibility (using PLSV)

The naked eye apparent Phases and Periods are:

• EL (~Dec 1947)
  
• RS (~Dec 1947 to ~March 1948)
• AR (~April 1948)
• SA (~April 1948 to ~June 1948)
  
• CS (~July 1948)
  
• SS (~July 1948 to ~Oct. 1948)
  
• MF (~Oct. 1948)
  
• SRS (~Oct. 1948 to ~Nov. 1948)
  
• EL (~Dec. 1948)
  

Arcturus is of CP Type (as indicated by the sequence MF -> EL -> AR -> CS).

Remark:
***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' visibility (using PLSV)

The naked eye apparent Phases and Periods are:

• AR (~Feb 1947)
• SS (~Feb 1947 to ~April 1947)
• EL (~May 1947)
  
• NS (~May 1947 to ~Aug. 1947)
• MF (~Sep. 1947)
  
• RS (~Sep. 1947 to ~Nov. 1947)
• CS (~Nov 1947)
  
• RSS (~Nov 1947 to ~Feb. 1948)
  
• AR (~Feb. 1948)
  

Sirius is of ALHa Type (as indicated by the sequence: EL -> MF -> CS -> AR).

ALHb Type

Star's (RA=18h, DEC=-25) visibility (using PLSV)

• AR (~May -2294)
• RSS (~May -2294)
  
• CS (~June -2294)
  
• SS (~June -2294 to ~Sep. -2294)
  
• EL (~Oct. -2294)
  
• NS (~Oct. -2294 to ~Nov. -2294)
  
• MF (~Nov. -2294)
• RS (~Nov. -2294 to ~May. -2293)
• AR (~May -2293)

References

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.

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