How far past the line this sits
The Sun enters Aquarius on reaching three hundred degrees of ecliptic longitude, a moment that has fallen on 19, 20 or 21 January throughout the modern record. On 22 January the Sun has already been between about 1.3 and 2.7 degrees into Aquarius at noon in every year from 1930 to 2035.
Since the Sun covers just under a degree a day, that is between one and three days past the ingress. An unrecorded hour of birth is worth a fraction of a degree, and even the widest time zone difference is worth about one. Neither can carry the position back over the line.
The drift itself is regular rather than random. The ingress slips roughly six hours later through three ordinary years, then February gains a leap day and it jumps back about eighteen hours. Your place in that four year cycle is what decides whether you sit at the low or the high end of the range.
What an early degree does and does not mean
Being two degrees into a sign does not make the sign partial. At any instant the Sun has one longitude and that longitude lies inside one sign, with nothing shared across the edge. Two degrees of Aquarius is Aquarius in exactly the way twenty two degrees is.
What the early degree does change is the mechanics. Aspects are measured in degrees, so a Sun at two of Aquarius contacts a different set of points than one late in the sign. House placement follows the degree too, and in most house systems an early degree can land in a different house from a late one under the same ascendant.
It is also worth saying that nothing in the tradition treats an early degree as a lesser version of the sign. Where the older writers did grade degrees, they did so by other schemes entirely, the terms and the monomoiria, which cut the sign up on different lines and have nothing to do with proximity to the edge.
The first decan and its two rulers
Two degrees falls in the first decan of Aquarius, the band from zero to ten. The Chaldean order assigns that band to Venus, while the sign itself is ruled by Saturn in the older scheme and by Uranus in modern practice.
That leaves three planets in the frame at once, which sounds crowded but is only the ordinary layering of the tradition. Aquarius is fixed air, read as principled and detached at the same time, and the Venus decan is read as softening the detachment without changing the fixity. All of that is inherited interpretation. The decan itself is simply what follows from the measured longitude.
What the date does not reach
The Moon moves around thirteen degrees a day and changes sign every two and a half, so on any 22 January it can be in one of two or three signs depending on the year and the hour. No date table can supply it.
The ascendant is decided by the clock time and the latitude of the birthplace and runs through all twelve signs daily, so the calendar date contributes nothing at all. The widget above computes the Sun's exact longitude from your own details and reports the measured distance to the nearest boundary, which on this date will be a day or more.
Mercury and Venus are partly constrained by the date, since neither strays far from the Sun. On this birthday Mercury is generally within about a sign of Aquarius and Venus within two. Jupiter and Saturn are not constrained at all, because they answer to the birth year rather than the day.
Questions people ask about this
Is 22 January Capricorn or Aquarius?
Aquarius, in every year on record. The Sun crosses into the sign on 19, 20 or 21 January, so by the twenty second it is already one to three degrees in.
Could my birth time make me Capricorn?
No. A full day of uncertainty about the hour is worth about one degree of solar motion, and the position is further past the boundary than that in every year.
What degree is the Sun on 22 January?
Between roughly one and three degrees of Aquarius. The exact value depends on your year and hour, and the widget above will compute it along with the margin to the boundary.
Am I on the Capricorn Aquarius cusp?
No. The Sun sits at one longitude at any moment and that longitude is inside a single sign. The word cusp usually stands in for birth details that were never checked.
Which decan is a 22 January birthday?
The first decan of Aquarius, the zero to ten degree band, assigned to Venus in the Chaldean sequence. Saturn and Uranus remain in play as rulers of the sign itself.
Does an early degree weaken the sign?
No. Sign membership is not graded by position. The degree changes which aspects form and which house the placement falls in, not whether the sign applies.