Solar Arc Aspect Calendar: True and Naibod Methods

A solar arc is one common rotation

Solar arc directions begin with a natal chart and add the same zodiac distance to every selected natal point. If the arc is 20°, natal Mercury at 10° Taurus is directed to 0° Gemini, natal Venus at 25° Gemini is directed to 15° Cancer, and natal Saturn at 4° Libra is directed to 24° Libra. The planets do not travel at their own astronomical speeds in this operation. Their natal spacing remains unchanged because every longitude receives the same addition.

That shared rotation distinguishes a solar arc from an ordinary secondary progressed chart. A secondary progression calculates each planet at the symbolic ephemeris date, so the progressed Moon moves much farther than the progressed Saturn. A solar arc uses the progressed Sun only to define one direction amount, then applies it to all natal planets. This calendar therefore labels rows as directed planet to natal planet, not progressed planet to natal planet.

The true progressed-Sun arc

The true method first maps life age to symbolic time. One tropical year of 365.24219 lived days advances the ephemeris by one day after birth. At age 30, the symbolic Sun is evaluated 30 days after the birth instant. The true arc is the forward tropical-longitude distance from the natal Sun to that symbolic Sun. The same arc is added to natal Sun through Pluto.

The apparent geocentric Sun advances through the tropical zodiac at a changing rate. It moves somewhat faster during one part of the year and slower during another. The true arc therefore varies around one degree per life year. Its rate depends on the part of the solar year represented by the post-birth symbolic days. Two people of the same age but born in different seasons can have slightly different true arcs.

An exact-date search needs a continuous symbolic instant. The site’s single-date chart rounds a finished symbolic chart to a UTC minute for display. This calendar evaluates the Sun at the unrounded symbolic instant while solving a root, then checks its endpoints against the verified solar-arc engine. That keeps an exact crossing from being forced onto a minute-wide symbolic step.

The mean or Naibod arc

The mean option uses a fixed key of 0.98564733° for each tropical life year. At age 20, the mean arc is 19.7129466°. At age 50, it is 49.2823665°. This is an ecliptic-longitude direction applied to natal planets. Other techniques also use a Naibod rate for right ascension, sidereal time, or directed angles; those are different coordinate operations and are outside this planet-only calendar.

Because the key is a positive constant, the mean arc is strictly increasing. Its inverse is direct: divide a required arc by 0.98564733 to obtain the exact age. The true method needs a numerical search because its solar speed varies. The two outputs should be compared as separate methods rather than averaged or merged.

How a directed-to-natal contact becomes a required arc

Let P be a natal planet that will be directed, Q a natal target, and A the common solar arc. The directed longitude is P + A, reduced around the 360° circle. An exact conjunction requires P + A = Q. A sextile requires P + A = Q + 60° or Q − 60°. Square and trine also have two branches. Opposition has one 180° branch because +180° and −180° are the same point on a circle.

Suppose natal Mercury is at 10° absolute longitude and natal Jupiter is at 85°. A directed Mercury sextile natal Jupiter occurs when directed Mercury reaches 25° or 145°. Those positions require arcs of 15° and 135°. The first lies inside an ordinary early-life interval. Under Naibod, its exact age is 15 ÷ 0.98564733, or about 15.2184 tropical years. The second branch is much later than this calendar’s age-120 limit.

The calculator enumerates both valid branches, reduces each required arc to the forward 0°–360° range, and keeps only arcs reached between the selected start and end ages. Within a 30-year interval, either supported method advances by roughly 30°. The branches of one major aspect are much farther apart than that, so one directed-planet, aspect, natal-planet key cannot produce two exact rows under these monotonic methods.

A measured true-versus-Naibod example

Use an invented working record of 15 June 1990 at 12:00 UTC. In the locally calculated natal chart, the Moon and Mercury geometry gives one required forward arc of 20.3325036° for directed Moon sextile natal Mercury. The directed Moon crosses 0° Aries on its way to the exact branch, which makes the example a useful check that zodiac wrap is not confused with backward motion.

The required exact arc is identical because the natal geometry is identical. The ages differ because each method reaches that arc on its own schedule. With a one-degree orb, applying begins at arc 19.3325036° and separating ends at arc 21.3325036°. Changing the orb moves the two boundaries but leaves the exact required arc unchanged.

Applying and separating belong to each exact hit

For an increasing solar arc, distance to a chosen aspect branch closes as the arc approaches the required value. The applying boundary is therefore the age when the arc reaches required arc minus orb. Exactness is the age at the required arc. The separating boundary is the age when the arc reaches required arc plus orb. If the selected interval starts after the true ingress or ends before the true egress, the table marks the interval boundary instead of pretending it found the missing outer edge.

This three-root method prevents a subtle repeated-hit error. A general planetary progression can reverse, cross an aspect, turn while still inside the orb, and cross it again. Treating the whole connected in-orb region as the window for both hits would falsely label some separating motion as applying. Solar arc avoids that specific geometry because both supported arcs are forward and monotonic. The calculator still verifies the true-arc samples and refuses phase labels if the required condition fails.

Why a zodiac wrap is not a reversal

A directed point can move from 359.9° to 0.1° while continuing forward. Comparing the displayed longitudes directly would look like a fall of 359.8°. The search instead works with the common arc before reducing directed points to the zodiac circle. An arc rising from 0.9° to 1.1° stays increasing even when a planet carried by that arc crosses 0° Aries.

The true arc itself is kept below the supported age limit, so it does not complete a full 360° revolution. The calendar samples 24 times per life year. One life sample step represents one symbolic hour, enough to verify the Sun’s forward motion without confusing a sign boundary with a station. Naibod needs no ephemeris sampling for monotonicity because its constant is explicitly positive.

Life dates and recorded birth time

Exact ages are measured in tropical years from the UTC birth instant. The corresponding life date is the birth instant plus age multiplied by 365.24219 days. This continuous clock can differ by hours from a civil birthday count after many years. The page prints a UTC calendar date and a fractional age so the convention remains visible.

The local birth time and historical UTC offset establish the natal longitudes and the start of both clocks. An incorrect offset shifts the natal Moon and every directed-to-natal target involving it. This planet-only calendar does not request a birthplace because geocentric planetary longitudes do not require latitude or longitude. It also omits the Ascendant, Midheaven, and house cusps; directing those points introduces additional coordinate and house-method choices.

What the result can and cannot show

The exact table reports geometry: directed planet, aspect, natal target, age, life date, and arc. The window table reports the selected angular tolerance around that geometry. A one-degree orb is an angular band, not a claim that an event lasts a fixed number of months. True and Naibod arcs reach the band at different rates, and interval clipping can shorten what is displayed.

Solar arc directions are an astrological symbolic technique. The calculation does not establish that a life event will occur, name an event, or rank one contact as beneficial or difficult. Use the natal chart and the stated direction method when interpreting a row. Switching the method, birth record, aspect family, or orb changes the calculation and should remain visible beside any interpretation.

Reading the exports

The SVG is an exact-contact map. Its horizontal axis is life age and its ten lanes identify the directed planet. Marker colors identify the five aspect classes; the embedded marker title names the natal target and directed arc. Several targets can share nearly the same age, so clustered markers may overlap visually.

The CSV carries the complete record. In addition to exact age, life date, and directed arc, it includes applying and separating ages, boundary arcs, the chosen orb, and flags for boundaries clipped by the requested interval. Use the table when two markers are close or when a date needs to be compared across the true and Naibod methods.

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