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TOPOCENTRICA

I. Introduction

Topocentrica is an implementation of the Polich & Page Topocentric Ascensional Transit System, first published in 1964. It provides precision transit analysis using equatorial coordinates, topocentric house poles, and the concept of Distance from Meridian in Oblique Ascension (DMO).

Unlike ecliptic-based transit methods that measure contacts in zodiacal longitude, this system operates in the equatorial plane, measuring how far a planet has traveled through its diurnal arc relative to the meridian. Every planet is located by its angular distance from the MC or IC, expressed as a fraction of its own semi-arc — yielding a universal 0–90° coordinate that makes mundane position directly comparable across declinations.

This application was built for practitioners already familiar with house systems, aspects, and primary directions. It assumes working knowledge of RA, declination, and the celestial sphere.

II. Core Doctrine

Distance from Meridian (DMO)

The foundational measure of the topocentric system. DMO expresses a planet's position as the ratio of its meridian distance (MD) to its semi-arc (SA), scaled to 90°:

DMO = (MD / SA) × 90°

A planet exactly on the MC or IC has DMO = 0°. A planet exactly on the ASC or DSC has DMO = 90°. The range 0–90° maps uniformly across all four quadrants regardless of a planet's declination or the observer's latitude.

Hour Angle (HA)

The angular distance of a celestial body westward from the meridian, measured along the equator:

HA = (RAMC − RA) mod 360°

HA = 0° at the MC, increasing westward. HA = 180° at the IC. The four quadrants are defined by HA ranges:

  • Q4 (Houses 7, 8, 9): Above horizon, west — HA 0–90°
  • Q3 (Houses 4, 5, 6): Below horizon, west — HA 91–180°
  • Q2 (Houses 1, 2, 3): Below horizon, east — HA 181–270°
  • Q1 (Houses 10, 11, 12): Above horizon, east — HA 271–360°

Oblique Ascension & Oblique Descension (OA / OD)

OA is the equatorial degree rising at the eastern horizon at the moment a planet crosses it, computed under the planet's own topocentric pole. OD is the corresponding degree at the western horizon. These are the fundamental values for computing equatorial aspects in the Polich & Page framework.

OA = RA − AD   |   OD = RA + AD

where AD (Ascensional Difference) is derived from the planet's declination and its topocentric pole.

Topocentric Poles

Each house cusp in the topocentric system has a unique pole — the geographic latitude at which that cusp's ecliptic degree would be exactly on the horizon. Planets inherit their pole from their house position. This is what distinguishes topocentric from Placidus: Placidus uses the observer's latitude uniformly; topocentric uses a pole specific to each planet's actual altitude in the local sphere.

Semi-Arc (SA)

The angular measure from horizon to meridian for a given declination at a given latitude. The diurnal semi-arc (DSA) runs from the eastern horizon through the MC to the western horizon. The nocturnal semi-arc (NSA) runs beneath. A planet above the horizon uses DSA; below uses NSA.

III. Chart Modes

ASC (Ascensional Chart)

The native Polich & Page view. Planets are placed on the wheel by their DMO within their quadrant. The four angles are fixed: ASC at 9 o'clock, MC at 12 o'clock, DSC at 3 o'clock, IC at 6 o'clock. House sizes reflect the equatorial semi-arc proportions at the observer's latitude.

This is the primary working chart of the application. All DMO analysis, aspect computation in OA/OD space, and directed transposition features operate in this mode.

ECL (Ecliptic Chart)

Traditional ecliptic zodiac wheel with selectable house systems:

  • Placidus (P) — time-based house division
  • Regiomontanus (R) — equatorial-based
  • Campanus (C) — prime vertical
  • Porphyry (O) — trisection of arcs
  • Equal (E) — 30° from ASC
  • Whole Sign (W) — sign-based houses

Supports Tropical (default) and Sidereal (Fagan-Allen ayanamsa) zodiac frames. Ecliptic chart always shows unequal houses with zodiacal divisions (signs, decans, bounds).

IV. Display Toggles

  • ASP — Aspect lines connecting planets on the wheel
  • TICK — DMO degree tick marks (0°, 10°, 20°, 30° markers in each house)
  • RAD — Radial spoke lines from center to each planet
  • CUSP — House cusp ring showing OA/OD values at each cusp, with ecliptic longitude labels
  • DEC — Decanic sectors: activates the fractal subdivision system (decans, dodekatemoria, dodek-decans)

V. The Decanic Fractal System

When DEC is active, the cusp ring reveals a layered subdivision system that becomes progressively visible as you zoom in:

36 Decans (visible at base zoom)

Traditional 10° divisions of the 360° wheel, numbered 1–36. Three decans per house. Each decan occupies the full width of the cusp ring and displays its DMO range at zoom ≥ 2.5×.

144 Dodekatemoria (zoom ≥ 3×)

Four subdivisions per decan, 12 per house, each spanning 2.5°. Labeled 1–12 within each house following the fractal house journey rule: the dodek number cycles through the house sequence offset by the starting house. Each dodek carries:

  • Elemental coloring — Fire (red), Earth (gold), Air (blue), Water (green) based on sign association
  • Planetary joy glyph — the traditional planetary ruler displayed outside the dodek ring
  • DMO range — shown at zoom ≥ 8×, alternating above/below the dodek number

432 Dodek-Decans (zoom ≥ 12.5×)

Three sub-decans per dodek, each ~0.833°. Numbered sequentially within each dodek. These provide the finest level of mundane subdivision, with their own DMO range labels alternating sides to prevent overlap.

Use the mouse wheel to zoom (1× to 100×, logarithmic) and click-drag to pan at zoom > 1×. Double-click resets the view.

VI. The Four RAMC Transpositions

The heart of the Polich & Page transit methodology. By shifting the natal RAMC, we transpose the entire natal chart into a new frame while overlaying live transits at their actual current positions. This reveals directed contacts in real-time.

RADIX

Baseline — no shift. The natal chart at its original RAMC. Transit planets overlay at the event's actual RAMC. This is the standard biwheel view.

TEMPORAL

The natal RAMC is shifted forward (direct) or backward (converse) by the solar arc: one degree of RAMC rotation for each year of life elapsed.

Temporal RAMC = Natal RAMC + (Event JD − Natal JD) / 365.2422

This is the primary directed DMO chart. Natal planets retain their birth RA and declination but are recalculated for DMO, house, quadrant, and pole under the new RAMC. Transit planets remain at their actual sky positions against the actual current RAMC.

The result is a living directed chart: you see where your natal significators have progressed to in mundane space, and which transiting planets are contacting those directed positions right now. Combined with the decanic fractal system, this reveals directed contacts at extraordinary precision — down to sub-degree dodek-decan sectors.

Toggle between Direct (RAMC advances) and Converse (RAMC retreats) using the D/C buttons.

LOCAL

The natal RAMC is shifted by the geographic longitude difference between the birthplace and the event location. This is a mundane relocation: the natal chart recast for a different place on Earth.

Local RAMC = Natal RAMC + (ΔLongitude in time)

FULL

The combined time + space transposition: solar arc shift plus longitude shift applied together. This is the most comprehensive transposition, showing the directed chart as it would appear at the event location.

Full RAMC = Natal RAMC + Solar Arc + ΔLongitude

VII. Speculum & Aspects

Speculum Columns

  • Planet — Planet glyph and name
  • DMO — Distance from Meridian (degrees, minutes, seconds)
  • Q — Quadrant (Q1–Q4, color-coded)
  • H — House number (1–12)
  • Pos — Above (▵) or below (▿) the horizon
  • DSA — Distance in Semi-Arc (degrees)
  • Pole — Topocentric pole of the planet
  • Ecl.Lon — Ecliptic longitude (sign + degree)
  • RA — Right Ascension
  • Decl — Declination
  • OA — Oblique Ascension
  • OD — Oblique Descension
  • AD — Ascensional Difference

Aspect Types

  • Ecliptical Transits — Traditional aspects measured in ecliptic longitude
  • Equatorial OA/OD — Harmonic aspects computed in OA space (above horizon) or OD space (below horizon). These are the primary topocentric aspects.
  • Ascensional Transits — Transit-to-Transit (T→T), Natal-to-Natal (N→N), and Transit-to-Natal (T→N) contacts in equatorial space
  • Symmetric Aspects — Antiscio / mirror aspects based on adjacent-quadrant DMO proximity. Two planets at equal DMO in adjacent quadrants form a symmetric contact.

Resonance Scoring

Each aspect row displays a resonance score (1–4 dots) indicating how many independent aspect spaces confirm the contact. A single ecliptical aspect scores 1; if the same pair also aspects in OA/OD, ascensional, and symmetric space, it scores up to 4. Higher resonance suggests greater mundane significance.

Perfection

The PERF column shows aspect lifecycle: A (applying) with percentage toward exactitude, or S (separating) with percentage of decay. This updates in real-time during LIVE mode.

VIII. Orb System

Orbs follow a soft power law based on harmonic number:

Orb(h) = 25′ × h−0.6

This produces: H1 ≈ 25′, H2 ≈ 17′, H3 ≈ 13′, H7 ≈ 8′, H10 ≈ 6′. The taper is gentler than inverse-linear but still discriminates meaningfully between low and high harmonics.

  • Master scale (0.10× to 3.00×) — scales all orbs proportionally
  • Individual sliders (H1–H12) — fine-tune each harmonic
  • Symmetric orb — separate slider for antiscio/mirror contacts

Orb snapshots are stored with each research event, enabling reproducible statistical analysis across sessions.

IX. Time Features

LIVE Mode

Real-time chart updating at 50ms intervals with millisecond UTC clock display. The chart continuously recalculates all planet positions, aspects, and directed contacts. Essential for timing elections, observing exact perfection moments, and real-time event work.

DYN (Dynamic Mode)

Animated time-lapse with full playback controls: play/pause, step forward/back, variable speed (days per frame), and a scrubbing slider. Watch aspects form and dissolve over time. Useful for identifying windows of activity and understanding temporal patterns.

CHRON (Chronoscope)

A stopwatch/lapwatch for capturing precise moments. Start the chronoscope, then mark "laps" to snapshot the current chart state with timestamp and coordinates. Each lap can be named and saved to the research database. Designed for real-time event timing — births, elections, synastry snapshots.

X. Research & Logging

The LOG button captures the current moment as a research event, storing the full chart data along with the current orb settings snapshot. Events are persisted in SQLite and designed for statistical frequency analysis.

The research system uses orb-weighted scoring: each event's aspects are weighted by proximity to exactitude (weight = 1 − actual_orb / max_orb). Tight-orb events score near 1.0; barely-in-orb events score near 0. This allows meaningful statistical comparison across different orb settings and research sessions.

XI. Chart Library & Management

The Library panel (left sidebar) stores all saved charts in a hierarchical folder structure backed by SQLite. Charts persist across sessions and can be organized, searched, and loaded into any ring slot.

Saving a Chart

  • Cmd+S (Mac) or Ctrl+S (Windows) — keyboard shortcut to save the current RADIX chart.
  • Alternatively, click the SAVE button in the header toolbar.
  • If the chart is new (unsaved), a dialog prompts for a name. If it already exists in the library, it overwrites silently.
  • Saved charts store: name, date/time (UTC), latitude, longitude, timezone, Rodden Rating, and all computed positions at the moment of save.
Tip: Save frequently when experimenting with rectification — each save creates a distinct library entry you can compare later.

Folder Organization

  • Create folder — right-click in the library panel or use the folder icon. Enter a name and press Enter.
  • Rename — double-click a folder name to edit it inline.
  • Delete — right-click a folder and choose Delete. Charts inside are moved to the root level, not destroyed.
  • Drag-and-drop — click and drag any chart entry onto a folder to move it. Drag a chart out of a folder back to root.
  • Folders can be nested one level deep.

Loading Charts into Slots

  • RADIX (natal) slot — double-click a chart in the library, or select it and click LOAD. This sets the inner wheel.
  • TRANSIT slot — with a chart loaded in RADIX, right-click a second chart and choose “Load as Transit” to populate the outer ring.
  • The header shows which chart occupies each slot, with the chart name and date.

Biwheel & Triwheel

  • Biwheel — load a natal chart in the RADIX slot and a second chart (transit, return, or another nativity) in the TRANSIT slot. The inner ring shows natal positions; the outer ring shows the second chart.
  • Triwheel — the TRIWHEEL toggle adds a third concentric ring. Load a third chart via the Triwheel slot selector. Useful for comparing natal + directed + transiting positions simultaneously.
  • Each ring is independently color-coded. Aspect lines can be drawn ring-to-ring or within a single ring, controlled by the aspect-line toggles.

ADB (Astro-Databank) Charts

  • The library ships with 4,800+ celebrity and historical nativities from the Astro-Databank public dataset.
  • These appear in a dedicated ADB folder. Browse alphabetically or use the search bar to filter by name.
  • Each ADB entry includes the published Rodden Rating (AA through DD, X, XX) indicating data reliability.
  • ADB charts can be loaded into any slot just like user-saved charts.

Rodden Rating System

  • AA — from birth certificate or official record.
  • A — from memory of the native or family member.
  • B — from biography or autobiography.
  • C — caution, original source unknown.
  • DD — conflicting data, two or more sources disagree.
  • X — no time of birth available (noon chart).
  • XX — no date of birth available.
The Rodden Rating is displayed next to the chart name in the header. Always check the rating before drawing conclusions about house cusps or angles.

XII. Atlas & Location

Accurate geographic coordinates are essential — they determine house cusps, semi-arcs, ascensional differences, and every topocentric calculation in the system.

City Search

  • Click the location field in the header to open the Atlas panel.
  • Begin typing a city name — results appear after 2+ characters, filtered by population-weighted relevance.
  • Select a result to auto-fill latitude, longitude, and timezone.

Interactive Map Picker

  • Click the map icon to open an interactive map view.
  • Click anywhere on the map to set coordinates directly — useful for rural birth locations or specific addresses.

Saving & Recent Locations

  • Favorites — click the star icon next to any location to save it for quick access.
  • Recents — the atlas remembers your recently used locations, listed at the top of search results.

How Location Affects the Chart

  • House cusps — latitude determines the oblique ascension of each cusp. At extreme latitudes, some houses become very large or very small.
  • Semi-arcs — the diurnal and nocturnal semi-arcs depend on latitude. These govern DMO values and all topocentric calculations.
  • Pole of the planet — each planet’s topocentric pole is a function of its declination and the observer’s latitude.
  • Longitude shifts the RAMC (sidereal time), rotating the entire house framework around the ecliptic.

XIII. Returns — Solar, Lunar & Planetary

Returns mark the moment a transiting body returns to its exact natal position. The app computes these to sub-arcsecond precision using bisection search over the Swiss Ephemeris.

Solar Return

  • Tropical Solar Return — Sun returns to natal tropical longitude. The standard Western return.
  • Sidereal Solar Return (SSR) — Sun returns to natal sidereal longitude.
  • Precessed (PSSR) and Reversed (RSSR) variants also available.
  • Select the return year from the year selector. The computed return chart loads into the transit slot, creating a biwheel with the natal chart.

Lunar Return

  • The Moon returns to its natal longitude approximately every 27.3 days.
  • Tropical, Sidereal (SLR), Precessed (PSLR), and Reversed (RSLR) variants.
  • Anlunar — Moon returns to the Sun’s natal position (a solar-lunar hybrid return).
  • Quotidian — daily Moon return, used as a daily timing refinement.
  • ALL YEAR view — displays all 13 lunar returns for the selected year. Click any entry to load that return chart.

Planetary Returns

  • Available for Mercury, Venus, Mars, Jupiter, and Saturn.
  • Mercury and Venus return roughly yearly; Mars every ~2 years; Jupiter every ~12 years; Saturn every ~29.5 years.

Relocation Returns

  • Cast a return chart for a different location using the coordinate input boxes on the return pane.
  • The USE HEADER button copies the current header coordinates into the relocation fields.
  • Relocated returns shift house cusps and angles while keeping planetary positions the same.
Relocated solar returns are a cornerstone of the Colucci/Volguine predictive method — moving to a location where a benefic is angular in the return chart.

XIV. Primary Directions

Primary directions are the oldest and most precise predictive technique in Western astrology, based on the apparent diurnal rotation of the celestial sphere.

Theory

  • A promissor (signifying planet) is carried by diurnal rotation toward the position of a significator (receiving planet or cusp).
  • The arc of direction is the equatorial degrees between them.
  • An arc-to-time key converts this arc into years of life.

Six Direction Systems

  • Placidus — semi-arc proportional houses. The dominant system from the 17th century onward.
  • Regiomontanus — equatorial houses. Directions measured by hour-angle distance.
  • Campanus — prime vertical houses.
  • Topocentric — Polich-Page system (1964). Each planet has its own pole. The native system of this application.
  • Alcabitius — semi-arc houses divided by equal time intervals. Medieval standard.
  • Equal — 30° from the Ascendant. Simple ecliptic longitude arcs.

Four Arc-to-Time Keys

  • Ptolemy — 1° = 1 year. The simplest and oldest.
  • Naibod — 1° = 1.0147 years (mean daily solar motion in RA: 0°59′08″).
  • True Solar Arc — actual daily solar motion on the native’s birthday.
  • Cardan — 1° = 1.0027 years (mean sidereal day).

Direct vs Converse

  • Direct — promissor carried forward (westward) by diurnal rotation.
  • Converse — significator carried backward (eastward). Both computed simultaneously.

Direction Modes

  • Natal-to-Natal — both from birth chart. The standard mode.
  • Natal-to-Event — natal significators directed to event positions.
  • Event-to-Natal — event positions directed to natal significators.
  • Event-to-Event — both from the event chart.

EVENTS Sub-tab

  • Record life events with dates and descriptions.
  • The app computes which primary directions were active at each event date across all selected systems and keys.
  • Starkman scoring — ranks directions by closeness of arc to event date, weighting by aspect type and planet significance.

RECTIFY Sub-tab

  • Enter known life events with approximate dates.
  • The rectification engine tests a range of birth times and scores each candidate by how precisely its directions align with events.
  • Results ranked by composite score — best-fitting birth time at top.
Primary directions are the gold standard for rectification — house cusps move roughly 1° every 4 minutes of clock time, making them highly sensitive to birth time.

XV. Circumambulations — Hellenistic Life Timing

Circumambulations (also called “distributions”) are the primary Hellenistic method for timing life events. A releaser is directed through the zodiacal bounds at the rate of ascensional times.

RELEASER Sub-tab

  • Seven classical Hyleg algorithms implemented: Ptolemy, Dorotheus, Valens, Hephaistio, Abu Ma’shar, Bonatti, Lilly.
  • Each uses different selection criteria for determining the planet or point that “releases” life.
  • Select an algorithm and the app highlights which planet qualifies and shows the reasoning chain.

MASTER Sub-tab — Alcochoden

  • The Alcochoden is the planet with the most dignities at the degree of the Hyleg.
  • Montulmo method — classical algorithm. Its minor/middle/major years give life expectancy.
  • Synthesis method — averages results from multiple Hyleg algorithms.

LISTING Sub-tab

  • Full circumambulation listing: the Releaser advances through bounds at the ascensional time rate.
  • Sect scoring, left/right rays, OA distortion, neutralization, and bounds overlay all displayed.

XVI. Profections

Profections advance the chart by one sign per year from a starting point, activating the ruler of the profected sign as time-lord.

TIMELINE Sub-tab

  • Annual profection — one sign per year from ASC (or any chosen point).
  • Monthly sub-profections — three systems: solar monthly, equal monthly, lunar monthly.
  • Daily sub-profections — three rates for daily granularity.
  • Nested drill-down — click a year to expand months; click a month to expand days.
  • Profect from any point — ASC, MC, Lot of Fortune, Lot of Spirit, or any planet.

TRANSMISSIONS Sub-tab

  • Valens’ whole-sign transmissions — when a planet profects into the sign of another planet, it transmits its significations.
  • MC and Lot of Fortune included alongside the seven traditional planets.

CONTINUOUS Sub-tab

  • Degree-precise profections — continuous advancement at 30°/year.
  • Exact calendar dates for sign ingresses, bound ingresses, and aspect events.
  • Biwheel click-through — click any event to load it as a biwheel.
Profections set the annual theme, circumambulations refine it, and transits trigger specific events. Layer all three for a complete Hellenistic predictive picture.

XVII. Ascensional Times

Ascensional times measure how long each sign takes to rise above the horizon. They are the foundation of all ancient timing techniques.

SIGNS

  • OA of each sign at the native’s latitude, with ruler, cumulative OA, and long/short classification.

PERIODS

  • 7 × 12 fraction table mapping planetary periods across signs.

COMBINATIONS

  • Three cross-reference tables for advanced timing analysis.

FRACTIONS

  • Climacteric convergence finder — scans for years where multiple fraction-based methods converge.

XVIII. Ingresses & Transits

Transits scored by tension and filtered through active time-lords, following the Hellenistic principle that transits only manifest what the current time-lords signify.

EVENT Sub-tab

  • Tension scoring — based on aspect type, planet nature, speed, and proximity to exact.
  • Time-lord filtering — transits by the active profection/circumambulation lord are promoted.
  • Ancient delineations — from Dorotheus, Orpheus fragments, and Pseudo-Valens.

DELINEATIONS Sub-tab

  • 7 × 7 planet-to-planet matrix (49 cells) with color-coded classical delineations.
  • Green = benefic, red = malefic, amber = mixed.

XIX. Babylonian Module

Reconstructs Mesopotamian astronomical methods spanning 1800 BCE to 100 CE. Observational phenomena rather than house-based interpretation.

DIARY

  • Digital observational diary modeled on cuneiform astronomical diaries.
  • Generates planetary phenomena for any date range: sign ingresses, stations, conjunctions, lunar phases.

GOAL-YEAR

  • Predicts planetary positions by looking back to a year when that planet was in the same configuration.
  • Venus 8yr, Mars 79yr, Jupiter 71/83yr, Saturn 59yr, Moon 18yr Saros / 19yr Metonic.

MUL.APIN

  • Star classification by path: Enlil (dec > +17°), Anu (−17° to +17°), Ea (dec < −17°).
  • ~49 stars with Babylonian names and modern identifications.

OMENS

  • 95+ Enuma Anu Enlil omen delineations with 28 phenomenon types auto-detected.
  • Omen texts include modern star identifications in parentheses.

ECLIPSES

  • FIND — search by date range, type, and location.
  • CYCLES — 16 eclipse cycles from Pentalunex (5 months) to Tetradia (7,248 months).
  • NATAL — eclipses aspecting the natal chart.
  • RESEARCH — degree search, Saros-Inex decomposition, cycle chains, Saros book.

XX. Epoch — Trutine of Hermes

The Trutine posits that at conception, the Moon occupied the degree of the birth ASC (or DSC), and the conception ASC occupied the degree of the birth Moon.

  • Four rules govern the calculation depending on lunar altitude and phase at birth.
  • Multiple candidates are generated and scored on internal consistency.
  • Higher-scoring candidates imply a specific birth-chart ASC, aiding rectification.

XXI. Astrolabe View

A fully interactive digital astrolabe with two projection modes.

  • Planispheric — standard stereographic projection. Plate shows altitude/azimuth circles; rete overlays ecliptic and star pointers.
  • Universal (Saphea) — Saphea Arzachelis, usable at any latitude without plate change.
  • 23 animations demonstrate astronomical concepts: diurnal rotation, precession, planetary motion, eclipse geometry.
  • Guided tour walks through 10 panel sections with explanatory text.

XXII. Time Controls

LIVE Mode

  • Real-time at 50ms intervals with millisecond UTC clock (HH:MM:SS.mm).
  • All transits, aspects, and house cusps recalculate continuously.

DYN Mode (Dynamic Animation)

  • Adjustable speed from 1× to thousands of times faster.
  • Step buttons: 1 minute, 1 hour, 1 day, 1 month, 1 year per click.
  • Scrubbing slider for smooth time navigation.

CALC Mode

  • Manual date/time entry. Chart computes once and remains static.

CHRON Mode (Chronoscope)

  • Lap timer for capturing precise moments. Press LAP to snapshot the chart state.

XXIII. Research & Statistics

  • LOG captures the current chart state as a research event with full aspect and orb data.
  • Orb-weighted scoring: weight = 1 − (actual_orb / max_orb)
  • Both raw count and weighted score displayed in frequency tables.
  • Orb settings and master scale stored with each event for reproducibility.

XXIV. Export & Bug Reports

  • PNG — 4× resolution for print quality.
  • JPG — compressed, suitable for web sharing.
  • SVG — scalable vector, ideal for publication.
  • Bug Report — submits chart state + diagnostic info. Use the BUG button in the header.

XXV. Keyboard Shortcuts & Navigation

  • Cmd+S / Ctrl+S — save chart.
  • Mouse wheel — zoom (1× to 100×, logarithmic, centered on cursor).
  • Click-drag — pan when zoomed in.
  • Double-click — reset zoom and pan.

XXVI. Heliocentric Mode

  • View from the Sun’s perspective. Moon, ASC, MC, and houses are hidden.
  • Heliocentric aspects reveal different geometric relationships between planets.
  • Nodes and apsides (perihelion/aphelion) displayed as fixed orbital reference points.

XXVII. Phase Tab — Heliacal Phenomena

  • Heliacal rising — first morning visibility above eastern horizon before sunrise.
  • Heliacal setting — last evening visibility above western horizon after sunset.
  • Acronychal rising — planet rises as Sun sets (opposition region).
  • Arcus visionis computed per planet, accounting for magnitude, extinction, and latitude.
In Hellenistic astrology, a planet making its heliacal rising (phasis) was at peak power — “appearing” to announce its significations. Many ancient timing techniques use phasis as triggers.

Topocentrica reconstructs the full scope of pre-modern astronomical calculation — from Babylonian observation logs through Hellenistic time-lord systems to medieval primary directions — unified in a single topocentric framework. Every algorithm is sourced from the historical literature and implemented with modern computational precision.
Built by Cameron Cassidy.

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