A boundary that is close but not a sign boundary
Decans divide each sign into three bands of ten degrees. The first decan of Libra ends at ten degrees, and on 2 October the noon Sun stands between 8.4 and 9.7 degrees, depending on the year. Every year in the range from 1930 to 2035 is inside the first decan at noon, with the later years within a fraction of a degree of leaving it.
Because the margin is that thin, the hour of birth becomes relevant. The Sun advances about a degree a day, so a birth late in the evening in a year at the top of the range can carry a longitude past ten degrees and therefore sit in the second decan, while a morning birth in the same year does not. On this date the decan is a year and hour dependent answer rather than a flat one, which is unusual and worth calculating rather than assuming.
What each side of the line carries
Under the Chaldean order the first decan of Libra belongs to the Moon and the second to Saturn, with Venus ruling the sign throughout. That is a substantial difference in traditional terms, moving from a lunar sub ruler read as responsive and mood led to a Saturnian one read as reserved and structural.
The triplicity scheme draws the same line and labels the bands differently, giving the first to Libra under Venus and the second to Aquarius under Saturn in traditional rulership. Both schemes therefore place a real change at ten degrees, which is why a birth this close to it should be resolved rather than rounded.
The sign ruler is untouched by any of this. Venus governs Libra across all thirty degrees, and the decan sub ruler is an additional layer rather than a replacement. What changes at the ten degree mark is which second planet the tradition reads across the position, not which sign the Sun is in.
The sign, by contrast, is not in question
Libra opened at the September equinox on the twenty second or twenty third, and Scorpio does not begin until the Sun reaches thirty degrees further on, around the twenty third of October. This date sits between those, roughly nine degrees in and twenty one from the far edge.
The narrow spread in that figure across more than a century is a product of the leap year rule. Each ordinary year the Sun is caught about six hours further along when the date comes round again, and each leap day pulls it back by about eighteen, so the position circles a small area for as long as the calendar keeps working.
Resolving it for your own birth
The widget above computes the Sun's longitude from your year, hour and birthplace rather than from an average, which on this date is the difference between a decan you can state and one you can only guess at. It also reports the distance to the nearest sign boundary, and that will come back wide.
The rest of a chart remains outside the reach of a date. The Moon changes sign every couple of days and so has two candidates here, and the Ascendant covers all twelve signs during any twenty four hours. A birthday fixes the Sun and leaves the individual part of a chart to the birth record.
If the birth hour is genuinely unknown, the correct answer on this date is that the decan is undetermined for the later years in the range and settled for the earlier ones. That is a more useful thing to record than a guess, and it is the sort of distinction a fixed table has no way to express.
Questions people ask about this
Which decan is 2 October in?
Usually the first decan of Libra, but not in every case. The noon Sun runs from 8.4 to 9.7 degrees depending on the year, so in the later years a birth late in the day can pass ten degrees into the second decan.
What changes at ten degrees of Libra?
The decan sub ruler. The Chaldean order moves from the Moon to Saturn at that point, and the triplicity scheme moves from the Libra decan to the Aquarius decan. Venus rules the sign on both sides.
Is 2 October always Libra?
Yes, in every year calculated. The Sun is around nine degrees into the sign, more than a week past the equinox and about three weeks short of Scorpio.
Does the decan boundary matter as much as a sign boundary?
It carries less weight in most practice, since the sign is unchanged either side of it. It does change which planet the tradition reads as colouring the position.
Why does my birth hour matter on this date?
Because the Sun moves roughly a degree a day and the decan line is within a degree of the noon position in some years. Morning and evening births in those years can fall on different sides.
How much does the position vary between years?
By around a degree and a third across the span from 1930 to 2035. The leap year cycle keeps the calendar aligned with the orbit, so the figure oscillates instead of drifting.