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Days of heliacal rising and setting of a star

Days of heliacal rising and setting of a star

In the eyes of the terrestrial observer, the Sun in the daytime, the stars at night,
follow one another in the sky, describing circular trajectories.
At a given moment, some objects are visible, others not.
This is due to their apparent luminosity, their distance from the Sun, ...
With the help of modern tools, let's determine the time of their (in)visibility ...

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point In brief

At intermediate terrestrial latitudes (between -66°33' and +66°33'), star rises and star sets follow one another. Some of these events occur at dusk (shortly after sunset), others in the dark night, and still others in the light of dawn (shortly before sunrise). The day and the moment at which these events occur depend mainly on the geographical latitude of the observer, on his/her visual acuity (his/her capacity to distinguish contrasting objects), on the apparent magnitude of the star sighted, on its position on the celestial vault at the historical period considered, as well as on the local atmospheric conditions.

Lever héliaque de l'étoile Sirius
Simulation of the heliacal rising of the star Sirius in the sky of the Occitanie region, southern France:
shortly after appearing in the southeastern corner of the sky it will disappear, fading into the glow of the rising Sun.


This software designed during my PhD thesis invites you to accurately determine the days and instants of heliacal rising and setting of any star visible to the naked eye of the Hipparcos catalog (5043 stars in total) since the year 4713 before our era. To do this, it combines various algorithms of astrometry (relative to the positioning of the stars on the sky) and photometry (relative to the brightness of the observed object and the local visibility conditions) borrowed from the scientific publications mentioned below.

The access to the user interface of this software is made on payment : 20 euros, which can be paid via the Paypal secured paiement system (payment by PayPal account or by credit card). This amount includes an unlimited access to the user interface and a free access to any future updates. Free tests of this software are available within the Culture Diff' Client Area.

Price : 20,00 euros

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point In detail

The celestial vault is filled with several thousand stars visible to the naked eye. Some of them can be observed all year long - these are the stars located in the northern circumpolar area of the sky for an observer based in the northern hemisphere, such as the stars defining the outlines of the Big Dipper, the Little Dipper and the Dragon constellations. Others, however, remain inaccessible to the observer located in the northern hemisphere - these are the stars populating the southern circumpolar area of the sky, such as those defining the outlines of the Southern Triangle and the Octans. Thus, circumpolar stars are constantly visible or invisible to the terrestrial observer (located below or above the equatorial latitudes). They never disappear below the horizon - which is why the ancient Egyptians qualified them as imperishable - or appear on the surface of the local horizon. Their trajectories are parallel to the circle of the horizon. Therefore, they do not rise or set at dawn or dusk, nor do they rise or set at night (in the dark). In any case, at a given historical period. Because the proper movements of the stars, the movements of precession and nutation which drive the rotation axis of the Earth as well, result in slow but inexorable displacements of stars on the celestial vault over the centuries. So that some stars, today circumpolar, may no longer be so in a few centuries ... and the « pole star » changes over time: alpha Draconis materialized the direction of the celestial north pole 5,000 years ago, in the era of the Egyptian and Mesopotamian civilizations; today, it is the star alpha Ursae Minoris.


Northern and southern circumpolar areas of the sky


Mapping of the circumpolar areas of the sky

The stars in the northern circumpolar region of the sky are constantly visible from the northern hemisphere, but remain invisible to the terrestrial observer located in the southern hemisphere. On the contrary, the stars filling the southern circumpolar area of the sky are constantly visible from the southern hemisphere, but remain invisible to the terrestrial observer located in the northern hemisphere. From equatorial latitudes, all the stars in the sky are visible - including the stars in the northern and southern circumpolar zones; their movements are perpendicular to the local horizon. (see the numerical simulation of the succession of day and night on Earth).

Portion of the sky visible from the Earth's surface

Trajectories of stars at an intermediate latitude

At intermediate latitudes (around 45 degrees north in this case), the sky appears to be populated by two types of stars: circumpolar stars, which never disappear below the northern horizon and thus remain visible throughout the year; and stars that, due to their apparent rotation, describe longer trajectories - partly below the horizon. In turn, these stars appear in the eastern sky, culminate in the local meridian and then disappear in the west. They remain invisible for part of the day (or night) and part of the year. Further south are other stars, whose rotation is constantly below the local horizon circle. For this reason, they remain invisible all year long from the northern hemisphere.


Between the northern and southern circumpolar areas of the sky are thousands of stars (first and foremost the Sun) whose appearances in the eastern sky, culminations in the local meridian and disappearances below the circle of the horizon follow one another, throughout the hours of the day. Some of these events occur at dusk (shortly after sunset), others on a dark night, others again in the light of dawn (shortly before sunrise), and finally some in daylight. At a given moment, some celestial objects are visible to the terrestrial observer, others not. Their visibility depends mainly on the time of year, the geographical latitude of the observer, the celestial location and apparent magnitude of the observed star, as well as local atmospheric conditions.

Because the Earth rotates on itself in less than 24 hours - 23 h 56 min 04 sec to be exact - the moments at which a star appears in the eastern sky, culminates in the local meridian and disappears from the local celestial vault are shifted over the days of the year. Because the Earth makes a revolution around the Sun in about 365.25 days, the Sun gives the impression of moving among the stars in the sky: during its apparent annual course, the star of the day seems to approach and then move away from each of them, indeed. On their day of conjunction with the Sun, most stars are invisible to the naked eye. Days, weeks, even months later, when their apparent distance to the Sun will have increased sufficiently, they will make their heliacal rising, that is to say their reappearance in the eastern sky, in the light of dawn. This heliacal rising will put an end to their annual period of invisibility, which began on their heliacal setting day - the day on which the star disappears, in the west of the sky, in the light of the setting Sun.


Heliacal rising of the star of Sirius

Simulation of the heliacal rising of the star Sirius in the sky of the Occitanie region, southren France:
shortly after appearing in the southeastern corner of the sky it will disappear, fading into the glow of the rising Sun.


The yearly period of invisibility of a star - or the time elapsing between its days of heliacal setting and rising - depends mainly on its apparent magnitude, its distance from the ecliptic, the latitude and altitude of the observation site, the local atmospheric conditions and the visual acuity of the observer. It is necessarily comprised between 0 and 365 days: a star whose yearly period of invisibility is equal to 0 or 365 days is a circumpolar star; it neither appears nor disappears from the local celestial vault. Any other star makes an heliacal rising and setting during the year.

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This software designed during my PhD thesis invites you to accurately determine the days and instants of heliacal rising and setting of any star visible to the naked eye of the Hipparcos catalog (5043 stars in total) since the year 4713 before our era. To do this, it combines various algorithms of astrometry (relative to the positioning of the stars on the sky) and photometry (relative to the brightness of the observed object and the local visibility conditions) borrowed from the scientific publications mentioned below.

The access to the user interface of this software is made on payment : 20 euros, which can be paid via the Paypal secured paiement system (payment by PayPal account or by credit card). This amount includes an unlimited access to the user interface and a free access to any future updates. Free tests of this software are available within the Culture Diff' Client Area.

Price : 20,00 euros

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point Bibliography

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