An arc of direction is just degrees.
You need a key to convert degrees into years of life.
The API supports five.
Ptolemy: exactly 1° per year, the original key used by Lilly.
Naibod: 0.9856473° per year, the mean tropical Sun's daily motion (360° divided by 365.2422 days), Gansten's preferred key.
True solar arc: the actual right ascension travel of the natal Sun between the birth date and birth date plus N days, the modern precision-school choice.
Lunar arc: progressed Moon's daily motion as a yearly rate, scaled (Moon's daily motion ÷ 13.36 ≈ 0.99°/year) so it tracks Sun-equivalent velocity.
Chart-ruler arc: the daily motion of the Ascendant lord, normalized against its mean motion and multiplied by Naibod, producing a personalized rate (Mars ruler runs fast, Saturn ruler runs slow).
Pass key=naibod (default), key=ptolemy, key=true_solar, key=lunar, or key=chart_ruler.
The response includes arc_degrees and age_years for every hit, so you can compare keys side by side.
Default Naibod; Ptolemy, true solar, lunar, and chart-ruler arc all selectable