This boundary is the December solstice
Capricorn begins at two hundred and seventy degrees of ecliptic longitude, which is the December solstice: the Sun at its furthest south, the shortest day of the northern year and the longest of the southern. The instant is published in every almanac, usually without any reference to astrology at all.
It falls on 21 or 22 December. The alternation follows the leap cycle, since the Sun needs about six hours more than a calendar year to return to the same longitude, and the surplus is cleared by the extra day in February.
Why the Tropic of Capricorn is named after a sign
The line of latitude the Sun stands over at this moment was named when this solstice point lay against the stars of Capricornus. Precession has since moved the Sun's solstitial position into Sagittarius as the constellations are drawn today, so the name has outlived the alignment.
The tropical zodiac, though, is defined by the solstices and equinoxes themselves rather than by the stars behind them, so the boundary has not moved by so much as a degree relative to the year. What drifted is the backdrop.
Jupiter to Saturn, mutable fire to cardinal earth
The greater benefic hands the season to the greater malefic here, and an ending sign gives way to one that opens a quarter of the year. Cardinal signs begin at the solstices and equinoxes, which is what makes Capricorn's first degree a structural marker and not merely the day after Sagittarius.
None of that produces a blend. Solar longitude is a single value, so the placement is Sagittarius or it is Capricorn, and no technique in the tradition returns both.
Late Sagittarius and early Capricorn
Sagittarius closes under Saturn in the Chaldean decans, the gravest third of the most expansive sign, and Capricorn opens under Jupiter, the most generous third of the most austere one. The pair are almost a mirror image of what the sign names would suggest, and they explain far more about births in this window than any story about a boundary.
Mars is exalted at twenty eight degrees of Capricorn, which is at the far end of the season rather than near its start.
Resolving a birth on 21 or 22 December
Look up the solstice for the year in question, convert it into the local time of the birthplace, and see which side of it the birth falls on. The comparison is exact and leaves nothing over.
A birth two or three days clear of the solstice does not need the check at all; the published ranges all agree that far out. It is only the last day or so on either side where they cease to be reliable.
Questions people ask about this
Am I a Sagittarius Capricorn cusp?
No, because that placement does not exist. The Sun was either short of two hundred and seventy degrees at your birth or past it, which makes you Sagittarius or Capricorn.
What date does the Sun move from Sagittarius to Capricorn?
21 or 22 December, depending on the year and on the time zone the birth is dated in. The instant is the same worldwide; only the local calendar date differs.
Do I have traits of both signs?
Popular astrology says so and sells the blend as a type. The chart does not show it: one Sun, one longitude, one sign. Other placements can of course sit in either sign.
What is a cusp in real astrology?
A house boundary. Houses are divided using the horizon and the meridian of the birthplace, and their cusps are genuine dividing lines within a chart.
How close to the boundary do I need to be to bother checking?
About forty eight hours either side. Inside that window the year and the birth time decide the answer; outside it, any date range gives the same result.