Archaeoastronomy at megalithic sites

The vast majority of observable stars are binary or multiple star systems. In these systems, two or more stars share a common focus of revolution and are gravitationally bound to each other in defined orbits. This is such a common observation such that the gravitational interaction of multiple stars appears to be the "normal" mode of stellar system formation...

...Is the idea of a solar companion to our Sun unprecedented? Not at all, in fact there have been numerous scientific publications examining the evidence for a "dark star", literally speaking, to which our Sun could be gravitationally bound in a definite orbit [3]. This alternate dark star is known as Nemesis, and its proposition comes primarily from observed perturbations of orbiting objects such as the planet-sized Kuiper belt object named Sedna [4]...

...Walter Cruttenden of the Binary Star research institute has propounded that a solar companion need not necessarily be of the "dark star" variety. Given the paucity of empirical observations and measurements of the movement of many of the bright stars within our own local galactic sector, it is with some justification that visible stars be examined to see if any may share a common focal point with our own Solar System [5]. At the heart of the poly-solar system theory is a simplification of the mechanics of constellation precession (precession observable) with a more logical model, one that does not rely on a putative wobble of the Earth but instead explains the precession observable with the movement of the Solar System itself...

...Is there a candidate for binary revolution among the visible stars? Logically we could begin with the closest star to our own, which is Alpha Centauri. At a distance of 4.37 light years, it is the third brightest star and, as is common, it is itself a binary system.

Another star that shows evidence of being gravitationally bound within the system and is called Alpha Proxima. Alpha Proxima is 0.2 light years from Alpha Centauri AB, about 400 times the distance of Neptune's orbit from the Sun. This shows that a dual or poly star system does not have to necessarily be in close orbital interaction. However Alpha Centauri lies at a declination of -60°, which is well out of the plane of the Solar System, and as such, has a near circumpolar motion in the sky.

A more suitable candidate would be a star closer to the plane of the Solar System, or celestial equator. Sirius meets this criteria, at a declination of -17°. It is also the brightest star in the night sky, three times brighter than Alpha Centauri and twice as bright as the next brightest star Canopus. Sirius is also the 5th closest system of stars to our own [6]. More significant is the fact that The Sirius Research Group has been recording the position of Sirius for approximately 20 years now and has not recorded any measurable alteration in its location relative to the precession [7]....

According to the source the Solstice actually occurred 3 weeks off ie 10th of July not 21st of June as it is now, that would appear to me to be a classic example of the effects of Precession.
No?

Arithmetic and astronomical calendars

An astronomical calendar is based on ongoing observation; examples are the religious Islamic calendar and the old religious Jewish calendar in the time of the Second Temple. Such a calendar is also referred to as an observation-based calendar. The advantage of such a calendar is that it is perfectly and perpetually accurate. The disadvantage is that working out when a particular date would occur is difficult.
An arithmetic calendar is one that is based on a strict set of rules; an example is the current Jewish calendar. Such a calendar is also referred to as a rule-based calendar. The advantage of such a calendar is the ease of calculating when a particular date occurs. The disadvantage is imperfect accuracy. Furthermore, even if the calendar is very accurate, its accuracy diminishes slowly over time, owing to changes in Earth's rotation. This limits the lifetime of an accurate arithmetic calendar to a few thousand years. After then, the rules would need to be modified from observations made since the invention of the calendar.

Not all calendars use the solar year as a unit. A lunar calendar is one in which days are numbered within each lunar phase cycle. Because the length of the lunar month is not an even fraction of the length of the tropical year, a purely lunar calendar quickly drifts against the seasons, which don't vary much near the equator. It does, however, stay constant with respect to other phenomena, notably tides. An example is the Islamic calendar. Alexander Marshack, in a controversial reading,[3] believed that marks on a bone baton (c. 25,000 BC) represented a lunar calendar. Other marked bones may also represent lunar calendars. Similarly, Michael Rappenglueck believes that marks on a 15,000-year old cave painting represent a lunar calendar.[4]

Stand somewhere that you have a clear view of the eastern horizon
Every day when the sun comes up, mark the point in the direction of where you see it.
The furthest point north will be the longest day of the year (in the northern hemisphere). It'll be back to the same point the next year on the longest day.

The average calendrical month, which is 1⁄12 of a year, is about 30.44 days, while the Moon's phase (synodic) cycle repeats on average every 29.53 days.