The mechanism behind the repetition
A calendar year of three hundred and sixty five days is roughly a quarter of a day shorter than the time the Earth takes to go round the Sun. Each ordinary year, therefore, a given date catches the Sun about six hours further along its path.
Adding a day to February every fourth year hands those six hours back, four at a time, by pulling the date roughly eighteen hours earlier. The two effects nearly cancel, leaving a small sawtooth wobble rather than a steady march, and that wobble is the whole of the variation.
Over long spans the calendar reform shows up too. Dropping three leap days every four centuries keeps the average year closer to the orbit than a plain four year rule would, which is why the pattern holds steady over the century sampled here rather than slowly slipping.
What the stability is good for
It means a printed date range can stay usable for a century without revision, which is why the familiar tables survive. It also means that a rough position can be quoted for a date without knowing the year, provided the date is not near a boundary.
Where it fails is exactly at the edges. A degree and a bit of drift is invisible in the middle of a sign and decisive at its start or end, which is why boundary dates need a computed answer and dates like this one do not.
It also explains why the familiar date ranges are so nearly right and so confidently wrong at the edges. They encode an average, and an average is an excellent description of a stable middle and a poor one of a boundary that moves by a day between years.
Where twenty two degrees falls
Twenty two degrees is inside the final face of Gemini, the band from twenty to thirty. The Chaldean order gives that face to the Sun, while the triplicity count reads it as the Aquarius portion of Gemini and hands it to Saturn, or to Uranus in modern practice.
The sign itself is Mercury's throughout, mutable and air, and none of the face attributions disturb that. They are subdivisions used to tell one part of a sign from another, and they are marked as tradition rather than as anything measured.
The parts that do not repeat
Nothing else in a chart behaves like the Sun. The Moon returns to a given sign on a cycle of under a month, so it has no relationship at all to the calendar date, and a 13 June birth can place it in either of two signs depending on the hour.
The ascendant repeats daily rather than annually and depends on where you were born as well as when. The widget above takes those details, computes the solar degree for your own year rather than an average, and gives the distance to the nearest sign boundary.
Houses have no annual rhythm at all, being set by the rotation of the Earth. The result is that two people born on 13 June in different years share a solar degree to within a degree and a half and may share nothing else in the structure of their charts.
Questions people ask about this
Why is the solar degree almost the same every year?
Because the leap year cycle keeps the calendar in step with the orbit. The date drifts about six hours forward each ordinary year and jumps roughly eighteen hours back when February gains a day.
What degree is the Sun on 13 June?
Close to twenty two degrees of Gemini, with a noon range of about twenty one point five to twenty two point nine across 1930 to 2035.
Is the sign ever anything but Gemini?
No. Cancer begins at the June solstice, a week later, and the drift on this date is nowhere near large enough to reach it.
Which face of Gemini is this?
The third, twenty to thirty degrees, assigned to the Sun in the Chaldean order and to Aquarius, and so Saturn, in the triplicity scheme.
Does the degree matter for anything practical?
It sets which aspects the Sun makes to other planets and which face applies. Both depend on the exact position rather than on the sign label.
Do I still need my birth time?
For the Sun, barely. For the Moon, the rising sign and the houses, yes, and those are the placements that differ most between two people sharing a birthday.