Solar Arc
Directions

A solar arc is the distance your progressed Sun has moved since you were born. Solar arc directions add that one distance to every point in your birth chart, so the whole chart turns forward together, about a degree a year.

The progressed Sun is the Sun's position as many days after your birth as you are years old, the day-for-a-year rule of secondary progressions. At 30 it is the Sun of the 30th day after birth, which has moved between 28°37′ and 30°32′ depending on the time of year. Solar arc directions take that arc and apply it to the Moon, the planets, the Ascendant and the Midheaven alike. The planets keep their birth-chart spacing; only the frame moves.

What astrologers read is the moment a directed point reaches an aspect to a natal one: directed Saturn squaring the natal Sun, the directed Midheaven reaching natal Venus. Because every point moves at the same slow pace, each contact has a single exact date, and there are only a handful in a given year. Solar arc work leans on the conjunction, square and opposition and on the semi-square and sesquiquadrate, the 45° series used in the Hamburg School and in Reinhold Ebertin's cosmobiology.

The API first casts your birth chart from what you enter, using the Swiss Ephemeris (the methodology page has the details). From there:

1. Age. The calculator counts the days from your birth to midnight at the start of the chosen date, by the clock of your birth time zone, and divides by 365.2422 to get years.
2. The arc. Your age in years, taken as a number of days, is added to your birth moment; the Sun's longitude at that later moment minus its longitude at birth is the arc. This is the true solar arc. The calculator also reports Naibod's arc, your age times 0°59′08″, for comparison, but does not use it.
3. Directed points. The arc is added to the ten planets and to the true natal Ascendant and Midheaven, the exact degrees rising and culminating at your birth. It is not added to house cusps: the calculator uses Whole Sign houses, whose cusps sit at 0° of each sign, and moving those would give the wrong angles (the section below shows how far wrong).
4. Contacts. The twelve directed points are compared with the same twelve natal points for the conjunction, opposition, square, semi-square, sesquiquadrate, quincunx, trine and sextile, within 1°. A point is never compared with its own natal place, since that separation is always the arc itself.
5. Exact dates. For each contact the calculator works out the arc that makes it exact and finds, from the ephemeris, the day the progressed Sun completes that arc. A contact whose exact arc is still ahead is applying; one already passed is separating.
6. Coming contacts. The same search runs over the next 5° of arc, about five years, and lists every contact that becomes exact in that span, in date order.

Degrees are cut, not rounded, to the arc-minute, as everywhere on the site.

The official birth announcement gives 9:03 PM (UTC+1:00) for Prince William's birth in London on June 21, 1982. On his 40th birthday, June 21, 2022, read as 00:00 London time, he was 39.9985 years old. His progressed Sun had moved from 0°06′ Cancer to 8°16′ Leo, so his solar arc was 38°10′. Naibod's rate gives 39°25′, 1°15′ more: he was born on the day of the June solstice, with the Sun at 0°06′ Cancer, near the time of year when it moves slowest, so his true arc runs behind the average. Each number below was recomputed from the Swiss Ephemeris without going through the API, and each date with the ephemeris's own Sun-crossing search.

On the birthday the calculator finds 12 contacts within 1°. The tightest was directed Jupiter opposite natal Mercury, 0°18′ short of exact, which it reached on October 18, 2022. The oldest still in orb was directed Pluto conjunct natal Uranus, exact on August 6, 2021 and fading. Of these, 2 involve an angle; the calculator could not find those while it directed house cusps.

The next five degrees

Over the next 5° of arc, to his mid-forties, the calculator finds 21 more contacts: 12 hard ones, listed below, and 9 trines, sextiles and quincunxes. Directed Venus reaches his natal Moon on August 28, 2023, the only conjunction in the span. The calculator gives the same list, under Coming Contacts, for any chart.

The directed Ascendant and Midheaven are among the most-read solar arc points, so where they start matters. Whole Sign houses give each house one full sign, counted from the sign that was rising, so all twelve cusps fall on 0°. The Ascendant degree can be anywhere in its sign, and at London's latitude the Midheaven can land well away from the tenth sign.

William's Ascendant is 27°28′ Sagittarius, so his first-house cusp is 0°00′ Sagittarius and his tenth-house cusp 0°00′ Virgo. His Midheaven, 2°27′ Scorpio, falls in his twelfth sign from the Ascendant. Moving the cusps by 38°10′ would put a “directed Ascendant” at 8°10′ Capricorn and a “directed Midheaven” at 8°10′ Libra. The true directed angles are 5°38′ Aquarius and 10°37′ Sagittarius: 27°28′ and 62°27′ away. An earlier version of this calculator directed the cusps; it now directs the angles and checks them for aspects like any planet.

Because the arc is the same for every point, the age at which a directed angle reaches a natal planet can be read off the birth chart: it is the distance between them in degrees, converted to years by the progressed Sun's pace. The table lists every conjunction, square and opposition of William's directed Ascendant and Midheaven to his natal planets from birth to 90, computed from the Swiss Ephemeris. His directed Ascendant aspects the Sun first, at 2.8; his directed Midheaven first meets Venus, at 24.3. With nothing in the signs just ahead of his Ascendant, it makes no conjunction before 90.

The arc itself hardly depends on the birth time: the Sun was moving about 2.4′ an hour when William was born, so a birth an hour later changes his arc by that much. The angles are different. The Midheaven turns about a degree every four minutes, and the directed Midheaven carries any error with it into every contact it makes. The table recomputes two of William's angle contacts for clock times a few minutes either side of 9:03 PM: his directed Midheaven conjunct his natal Uranus, and his directed Ascendant opposite his natal Sun.

Every two minutes of clock time moves the Midheaven contact by about 7 months. Astrologers also run this in reverse: when a birth time is only known roughly, they compare dated events in a person's life with the directed-angle contacts of nearby times and keep the time that fits best, a process called rectification. Planet-to-planet contacts cannot help there, since they do not depend on the time.

Three arcs are in use. The true solar arc, which this calculator uses, is the progressed Sun's actual movement. Naibod's arc, named after the sixteenth-century astronomer Valentin Naboth (Naibod), assumes the Sun's average speed of 0°59′08″ a day; Astrodienst's help pages say its solar arc chart uses this mean motion. The one-degree arc simply equals your age in degrees, a shortcut that echoes Ptolemy's key of one degree per year, which he applied to primary directions.

The Earth is closest to the Sun in early January and farthest in early July, so the Sun moves faster than average around January and slower around July. For a June birth like William's, the true arc falls behind Naibod's from the start and the gap keeps growing:

At 40 a Naibod arc runs 1°15′ ahead of William's true one, so it would date every contact about 16 months early; the one-degree arc, at 1°49′ ahead, would date them 1.9 years early. In other months the gap can run the other way. The table gives the true arc minus Naibod's at 30 and 60 for a birth at noon UT on the first of each month (2000), from the Swiss Ephemeris. Births from October to February run ahead of Naibod and births from April to August behind; a December birth is 1°55′ ahead at 60 and a June birth 1°51′ behind.

A solar arc contact is read as the meeting of two parts of the chart: what the directed point stands for, brought to what the natal point stands for, in the manner of the aspect between them. Directed Jupiter opposite natal Mercury, the tightest contact in William's chart at 40, is read with Jupiter's themes of growth and travel acting on Mercury's communication and paperwork, through the culminating, other-person quality of the opposition. The usual keywords for each point:

• Claudius Ptolemy, Tetrabiblos, Book III, on the length of life: primary directions with one degree of the equator for each year of life.
• Valentin Naboth (Naibod, 1523–1593), whose name is attached to the key of 0°59′08″ a year, the Sun's mean daily motion.
• Reinhold Ebertin, Directions: Co-Determinants of Fate (English edition, American Federation of Astrologers, 1976), on solar arc directions in cosmobiology, alongside his The Combination of Stellar Influences on midpoints and the 45° series.
• Noel Tyl, Solar Arcs: Astrology's Most Successful Predictive System (Llewellyn, 2001), a book-length treatment of the method in English.
• Astrodienst's chart help pages, for its use of the Sun's mean motion (0.98564733° a day) in solar arc charts.
• Every position and date comes from the Swiss Ephemeris (Astrodienst), including the day the progressed Sun completes each required arc.

The method needs an accurate birth time for the angles: a four-minute error moves the natal Ascendant and Midheaven, and so their directions, by about a degree, which shifts every angle contact by about a year. Among the planets only the Moon moves fast enough for a small time error to matter. The calculator gives the astronomy and the dates; it makes no claim about what will happen on them.