The astronomical conversion rate or ephemeris equation that translates a primary direction's equatorial arc (ΔRAMC, in degrees) into years, months, and days of the native's life.
Meaning
Once spherical trigonometry has determined the arc of direction (ΔRAMC, in degrees of equatorial rotation), a time-key (or measure of time, Latin mensura temporis) translates that angular arc into an exact age in years and a calendar date.
All primary direction keys rest on the symbolic and astronomical equivalence between one diurnal rotation of the Earth (or one day's solar motion after birth) and one tropical year of life. Because the Earth's orbital speed around the Sun varies slightly between perihelion (early January, when the Sun moves fastest) and aphelion (early July, when the Sun moves slowest), and because the ecliptic is tilted to the equator by the obliquity ε, historical astronomers debated whether the conversion rate should be a fixed constant or a dynamic function of the Sun's true post-natal motion.
The Six Canonical Time-Keys
Moira's Primary Directions Observatory computes and compares all six major historical and ephemeris time-keys side by side:
| Time-Key | Rate / Equation | Historical Origin & Behaviour |
|---|---|---|
| 1. SPK Dynamic Solar RA (Placidus) | RA(Sun at t_0 + Δt days) − RA(Sun at t_0) = ΔRAMC | Placidus de Titis (1657) [3]. Equates the equatorial arc ΔRAMC to the true post-natal advance of the Sun's Right Ascension in the ephemeris (1 ephemeris day = 1 tropical year). Solved in Moira by exact JPL DE440 bisection. |
| 2. SPK Dynamic Solar Longitude | λ(Sun at t_0 + Δt days) − λ(Sun at t_0) = ΔRAMC | Equates ΔRAMC to the true post-natal advance of the Sun's ecliptic longitude λ in the JPL DE440 ephemeris. Captures the eccentricity of Earth's orbit without the obliquity projection of RA. |
| 3. Naibod Mean Solar Key | 0°59′08.33″ / yr (0.98564736°/yr) | Valentine Naibod (1560) [2]. Uses the Sun's mean daily motion (360° / 365.24219 days). Because 0.9856° < 1.0000°, Naibod dates every direction ~1.46% later than Ptolemy (about +0.52 years at age 36, or +0.87 years at age 60). |
| 4. Ptolemy Symbolic Key | 1°00′00.00″ / yr (1.00000000°/yr) | Claudius Ptolemy (2nd c. CE) [1]. The classic symbolic degree-for-a-year rate (Age = ΔRAMC). Simple, invariant across seasons, and mandatory in Hellenistic Circumambulation through the Bounds. |
| 5. Cardan Key | 0°59′12.00″ / yr (0.98666667°/yr) | Girolamo Cardano (1554) [4]. Renaissance approximation to mean solar motion, yielding timings slightly faster than Naibod. |
| 6. Natal Solar Daily Rate | v_α(Sun at birth) ° / yr | Uses the instantaneous derivative of the Sun's Right Ascension (or longitude) on the exact birthday. Very fast for Capricorn/Cancer births where RA changes rapidly (~1.08°/yr), and slower near the equinoxes (~0.91°/yr). |
Why Time-Keys Diverge by Up to Several Years
At age 10, the difference between Ptolemy (1.0000°/yr) and Naibod (0.9856°/yr) is only about
52 days. By age 50, that cumulative divergence grows to 8.7 months, and between Ptolemy and
the Dynamic Solar RA key (for a native born near the summer or winter solstice, where dα/dλ ≈ cos(ε)⁻¹ ≈ 1.09)
the divergence can reach 2 to 3 years. Inspecting the 6-Key Ephemeris Comparator in Section 04
of the Primary Directions Observatory reveals immediately which time-key aligns most tightly with
known biographical events.
Related terms
Sources
- Claudius Ptolemy, Tetrabiblos III.10 (trans. F. E. Robbins, Loeb Classical Library, 1940)
- Valentine Naibod (Valentinus Nabod), Enarratio elementorum astrologiae (Cologne, 1560)
- Placidus de Titis, Primum Mobile (Padua, 1657)
- Girolamo Cardano, Commentaria in Quadripartitum Ptolemaei (Basel, 1554)
- Jean-Baptiste Morin, Astrologia Gallica, Book XXII, sec. IV 'De mensura temporis directionum' (The Hague, 1661)