Paper instrument
Paper instrument / A–FThe permanent reduction form
One numbered A–F form for every lesson and every constructed bench.
A clean copy of the permanent form. Carry the same numbered lines through every lesson. Each print action chooses its own paper; native browser printing includes all available papers.
Reduce a chart by hand
Part ATime
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| A1 | Birth date, civil | ||
| A2 | Clock time, 24-hour | ||
| A3 | Summer time in force?if Y subtract 1h · older war time may be 2h · stated on the bench | ||
| A4 | Standard time = A2 − A3 | ||
| A5 | Zone offset from GreenwichWest add · East subtract | ||
| A6 | Universal Time = A4 + A5if 24h or more subtract 24h and move A7 forward a day · if below 0 add 24h and move A7 back | ||
| A7 | UT datemay differ from A1 · every plate row is read on this date |
Part BSidereal time
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| B1 | Plate GST at midnight (0h UT) on the A7 dateread from the ephemeris row for A7 | ||
| B2 | Interval since 0h = A6 | ||
| B3 | Acceleration = B2 × 9.86 s per hourCheck: always under 4 minutes | ||
| B4 | Greenwich sidereal time at birth = B1 + B2 + B3carry at 60 | ||
| B5 | Longitude in time = longitude × 4 min per degreeEast add · West subtract | ||
| B6 | Local sidereal time = B4 + B5if 24h or more subtract 24h | ||
| B7 | Southern hemisphere?if Y add 12h to B6 and normalise · this is the table entry |
Part CAngles and cusps
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| C1 | Table rows bracketing B7: lower ST, upper STrows are 4 minutes apart | ||
| C2 | Fraction f = (B7 − lower) in seconds ÷ 240Check: always between 0 and 1 | ||
| C3 | MC: lower, upper, difference, × f, + lowerthe same for every latitude | ||
| C4 | Latitude rows bracketing the birth: lower, upper; fraction gtable rows are 1° apart | ||
| C5 | 11 12 ASC 2 3 as columns: at the lower latitude, at the upper latitude, then by ga column that looks unlike its neighbours is the column with the mistake | ||
| C10 | Southern? Reverse every sign on C3 and C5degrees and minutes unchanged | ||
| C11 | Opposites: IC = MC + 180, DSC = ASC + 180, 5 6 8 9 = 11 12 2 3 + 180same degree and minute, opposite sign |
Part DBodies
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| D:sun | Sun: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | ||
| D:moon | Moon: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | ||
| D:mercury | Mercury: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | ||
| D:venus | Venus: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | ||
| D:mars | Mars: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | ||
| D:jupiter | Jupiter: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | ||
| D:saturn | Saturn: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | ||
| D:uranus | Uranus: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | ||
| D:neptune | Neptune: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | ||
| D:pluto | Pluto: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | ||
| D:trueNode | True Node: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts |
Part EFigure and aspects
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| E1 | Cusps on the wheel. ASC at the left, houses counterclockwise, C11 filled | ||
| E2 | Bodies into houses by comparing D5 with the cuspsnote any body within 1° of a cusp | ||
| E3 | Aspectarian: the five Ptolemaic aspects, applying or separating from motionorbs as on the free transits surface |
Part FReceipt
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| F | Receipt: paper, Moira, Δ, cause for every computed line |
Part F · continuationPaper-to-Moira discrepancy account
| Line | Paper | Moira | Δ | Cause / notes |
|---|---|---|---|---|
| A4 | ||||
| A5 | ||||
| A6 | ||||
| A7 | ||||
| B1 | ||||
| B2 | ||||
| B3 | ||||
| B4 | ||||
| B5 | ||||
| B6 | ||||
| B7 | ||||
| C1 | ||||
| C2 | ||||
| C3 | ||||
| C4 | ||||
| C5 | ||||
| C10 | ||||
| C11 | ||||
| D:sun | ||||
| D:moon | ||||
| D:mercury | ||||
| D:venus | ||||
| D:mars | ||||
| D:jupiter | ||||
| D:saturn | ||||
| D:uranus | ||||
| D:neptune | ||||
| D:pluto | ||||
| D:trueNode | ||||
| E2 | ||||
| E3 |
Blank permanent A–F reduction form · tropical zodiac · Placidus houses
Royal Observatory, Greenwich
Part ATime
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| A1 | Birth date, civil | Dec 13, 2023 | |
| A2 | Clock time, 24-hour | 08:00:00 | |
| A3 | Summer time in force?if Y subtract 1h · older war time may be 2h · stated on the bench | No · 0h | |
| A4 | Standard time = A2 − A3 | 08:00:00 | |
| A5 | Zone offset from GreenwichWest add · East subtract | +00:00:00 | |
| A6 | Universal Time = A4 + A5if 24h or more subtract 24h and move A7 forward a day · if below 0 add 24h and move A7 back | 08:00:00 | |
| A7 | UT datemay differ from A1 · every plate row is read on this date | Dec 13, 2023 |
Part BSidereal time
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| B1 | Plate GST at midnight (0h UT) on the A7 dateread from the ephemeris row for A7 | 05:25:42 | |
| B2 | Interval since 0h = A6 | 08:00:00 | |
| B3 | Acceleration = B2 × 9.86 s per hourCheck: always under 4 minutes | 00:01:19 | |
| B4 | Greenwich sidereal time at birth = B1 + B2 + B3carry at 60 | 13:27:01 | |
| B5 | Longitude in time = longitude × 4 min per degreeEast add · West subtract | −00:00:00 | |
| B6 | Local sidereal time = B4 + B5if 24h or more subtract 24h | 13:27:01 | |
| B7 | Southern hemisphere?if Y add 12h to B6 and normalise · this is the table entry | No · 13:27:01 |
Part CAngles and cusps
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| C1 | Table rows bracketing B7: lower ST, upper STrows are 4 minutes apart | 13:24:00 → 13:28:00 | |
| C2 | Fraction f = (B7 − lower) in seconds ÷ 240Check: always between 0 and 1 | 0.75 | |
| C3 | MC: lower, upper, difference, × f, + lowerthe same for every latitude | MC 23° ♎︎ 30′00.00″ | |
| C4 | Latitude rows bracketing the birth: lower, upper; fraction gtable rows are 1° apart | 51° → 52° · g 0.48 | |
| C5 | 11 12 ASC 2 3 as columns: at the lower latitude, at the upper latitude, then by ga column that looks unlike its neighbours is the column with the mistake | C11 16° ♏︎ 46′00.00″ · C12 4° ♐︎ 28′00.00″ · ASC 20° ♐︎ 15′00.00″ · C2 1° ♒︎ 34′00.00″ · C3 19° ♓︎ 03′00.00″ | |
| C10 | Southern? Reverse every sign on C3 and C5degrees and minutes unchanged | No | |
| C11 | Opposites: IC = MC + 180, DSC = ASC + 180, 5 6 8 9 = 11 12 2 3 + 180same degree and minute, opposite sign | IC 23° ♈︎ 30′00.00″ · 5 16° ♉︎ 46′00.00″ · 6 4° ♊︎ 28′00.00″ · DSC 20° ♊︎ 15′00.00″ · 8 1° ♌︎ 34′00.00″ · 9 19° ♍︎ 03′00.00″ |
Part DBodies
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| D:sun | Sun: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 20° ♐︎ 42′00.00″ → 21° ♐︎ 43′00.00″ · +61′ · 21° ♐︎ 02′00.00″ | |
| D:moon | Moon: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 20° ♐︎ 57′00.00″ → 4° ♑︎ 59′00.00″ · +842′ · 25° ♐︎ 38′00.00″ | |
| D:mercury | Mercury: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 8° ♑︎ 29′00.00″ → 8° ♑︎ 27′00.00″ · R −2′ · 8° ♑︎ 28′00.00″ | |
| D:venus | Venus: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 9° ♏︎ 43′00.00″ → 10° ♏︎ 55′00.00″ · +72′ · 10° ♏︎ 07′00.00″ | |
| D:mars | Mars: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 13° ♐︎ 21′00.00″ → 14° ♐︎ 05′00.00″ · +44′ · 13° ♐︎ 36′00.00″ | |
| D:jupiter | Jupiter: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 6° ♉︎ 09′00.00″ → 6° ♉︎ 05′00.00″ · R −4′ · 6° ♉︎ 08′00.00″ | |
| D:saturn | Saturn: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 1° ♓︎ 47′00.00″ → 1° ♓︎ 51′00.00″ · +4′ · 1° ♓︎ 48′00.00″ | |
| D:uranus | Uranus: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 19° ♉︎ 55′00.00″ → 19° ♉︎ 53′00.00″ · R −2′ · 19° ♉︎ 54′00.00″ | |
| D:neptune | Neptune: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 24° ♓︎ 54′00.00″ → 24° ♓︎ 54′00.00″ · +0′ · 24° ♓︎ 54′00.00″ | |
| D:pluto | Pluto: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 28° ♑︎ 48′00.00″ → 28° ♑︎ 50′00.00″ · +2′ · 28° ♑︎ 49′00.00″ | |
| D:trueNode | True Node: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 23° ♈︎ 20′00.00″ → 23° ♈︎ 10′00.00″ · R −10′ · 23° ♈︎ 17′00.00″ |
Part EFigure and aspects
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| E1 | Cusps on the wheel. ASC at the left, houses counterclockwise, C11 filled | Completed on the figure · counterclockwise | |
| E2 | Bodies into houses by comparing D5 with the cuspsnote any body within 1° of a cusp | sun H1 · moon H1 · mercury H1 · venus H10 · mars H12 · jupiter H4 · saturn H2 · uranus H5 · neptune H3 · pluto H1 · trueNode H3 | |
| E3 | Aspectarian: the five Ptolemaic aspects, applying or separating from motionorbs as on the free transits surface | sun/moon Conjunction 276′ separating · sun/mars Conjunction 446′ separating · sun/neptune Square 232′ applying · sun/trueNode Trine 135′ applying · moon/neptune Square 44′ separating · moon/trueNode Trine 141′ separating · mercury/venus Sextile 99′ separating · mercury/jupiter Trine 140′ separating · venus/jupiter Opposition 239′ separating · jupiter/saturn Sextile 260′ applying · uranus/neptune Sextile 300′ separating · neptune/pluto Sextile 235′ separating · pluto/trueNode Square 332′ separating |
Part FReceipt
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| F | Receipt: paper, Moira, Δ, cause for every computed line | Completed on the figure |
Part F · continuationPaper-to-Moira discrepancy account
| Line | Paper | Moira | Δ | Cause / notes |
|---|---|---|---|---|
| A4 | 08:00:00 | 08:00:00 | 0 s | Zone or DST |
| A5 | +00:00:00 | +00:00:00 | 0 s | Zone or DST |
| A6 | 08:00:00 | 08:00:00 | 0 s | Zone or DST |
| A7 | Dec 13, 2023 | Dec 13, 2023 | exact | Date change |
| B1 | 05:25:42 | 05:25:42 | 0 s | Sidereal-time rounding |
| B2 | 08:00:00 | 08:00:00 | 0 s | Sidereal-time rounding |
| B3 | 00:01:19 | 00:01:19 | 0 s | Sidereal-time rounding |
| B4 | 13:27:01 | 13:27:01 | 0 s | Sidereal-time rounding |
| B5 | −00:00:00 | −00:00:00 | 0 s | Sidereal-time rounding |
| B6 | 13:27:01 | 13:27:00 | +0.8 s | Sidereal-time rounding |
| B7 | No · 13:27:01 | No · 13:27:00 | +0.8 s | Sidereal-time rounding |
| C1 | 13:24:00 → 13:28:00 | 13:24:00 → 13:28:00 | exact | Table grid |
| C2 | 0.75 | 0.75 | 0.00 | Table grid |
| C3 | MC 23° ♎︎ 30′00.00″ | MC 23° ♎︎ 30′00.00″ | −0.12′ | Table grid |
| C4 | 51° → 52° · g 0.48 | 51° → 52° · g 0.48 | exact | Latitude grid |
| C5 | C11 16° ♏︎ 46′00.00″ · C12 4° ♐︎ 28′00.00″ · ASC 20° ♐︎ 15′00.00″ · C2 1° ♒︎ 34′00.00″ · C3 19° ♓︎ 03′00.00″ | ASC 20° ♐︎ 15′00.00″ · C11 16° ♏︎ 46′00.00″ · C12 4° ♐︎ 28′00.00″ · C2 1° ♒︎ 34′00.00″ · C3 19° ♓︎ 03′00.00″ | max −0.44′ | Latitude grid |
| C10 | No | No | exact | Latitude grid |
| C11 | IC 23° ♈︎ 30′00.00″ · 5 16° ♉︎ 46′00.00″ · 6 4° ♊︎ 28′00.00″ · DSC 20° ♊︎ 15′00.00″ · 8 1° ♌︎ 34′00.00″ · 9 19° ♍︎ 03′00.00″ | IC 23° ♈︎ 30′00.00″ · DSC 20° ♊︎ 15′00.00″ · 5 16° ♉︎ 46′00.00″ · 6 4° ♊︎ 28′00.00″ · 8 1° ♌︎ 34′00.00″ · 9 19° ♍︎ 03′00.00″ | max −0.44′ | Table grid |
| D:sun | 20° ♐︎ 42′00.00″ → 21° ♐︎ 43′00.00″ · +61′ · 21° ♐︎ 02′00.00″ | 20° ♐︎ 42′00.00″ → 21° ♐︎ 43′00.00″ · +61′ · 21° ♐︎ 02′00.00″ | +0.05′ | Table grid |
| D:moon | 20° ♐︎ 57′00.00″ → 4° ♑︎ 59′00.00″ · +842′ · 25° ♐︎ 38′00.00″ | 20° ♐︎ 57′00.00″ → 4° ♑︎ 59′00.00″ · +842′ · 25° ♐︎ 36′00.00″ | +2.22′ | Linear Moon |
| D:mercury | 8° ♑︎ 29′00.00″ → 8° ♑︎ 27′00.00″ · R −2′ · 8° ♑︎ 28′00.00″ | 8° ♑︎ 29′00.00″ → 8° ♑︎ 27′00.00″ · R −2′ · 8° ♑︎ 29′00.00″ | −1.33′ | Station |
| D:venus | 9° ♏︎ 43′00.00″ → 10° ♏︎ 55′00.00″ · +72′ · 10° ♏︎ 07′00.00″ | 9° ♏︎ 43′00.00″ → 10° ♏︎ 55′00.00″ · +72′ · 10° ♏︎ 07′00.00″ | −0.26′ | Table grid |
| D:mars | 13° ♐︎ 21′00.00″ → 14° ♐︎ 05′00.00″ · +44′ · 13° ♐︎ 36′00.00″ | 13° ♐︎ 21′00.00″ → 14° ♐︎ 05′00.00″ · +44′ · 13° ♐︎ 36′00.00″ | −0.04′ | Table grid |
| D:jupiter | 6° ♉︎ 09′00.00″ → 6° ♉︎ 05′00.00″ · R −4′ · 6° ♉︎ 08′00.00″ | 6° ♉︎ 09′00.00″ → 6° ♉︎ 05′00.00″ · R −4′ · 6° ♉︎ 08′00.00″ | +0.49′ | Station |
| D:saturn | 1° ♓︎ 47′00.00″ → 1° ♓︎ 51′00.00″ · +4′ · 1° ♓︎ 48′00.00″ | 1° ♓︎ 47′00.00″ → 1° ♓︎ 51′00.00″ · +4′ · 1° ♓︎ 48′00.00″ | −0.45′ | Station |
| D:uranus | 19° ♉︎ 55′00.00″ → 19° ♉︎ 53′00.00″ · R −2′ · 19° ♉︎ 54′00.00″ | 19° ♉︎ 55′00.00″ → 19° ♉︎ 53′00.00″ · R −2′ · 19° ♉︎ 55′00.00″ | −0.57′ | Station |
| D:neptune | 24° ♓︎ 54′00.00″ → 24° ♓︎ 54′00.00″ · +0′ · 24° ♓︎ 54′00.00″ | 24° ♓︎ 54′00.00″ → 24° ♓︎ 54′00.00″ · +0′ · 24° ♓︎ 54′00.00″ | −0.10′ | Station |
| D:pluto | 28° ♑︎ 48′00.00″ → 28° ♑︎ 50′00.00″ · +2′ · 28° ♑︎ 49′00.00″ | 28° ♑︎ 48′00.00″ → 28° ♑︎ 50′00.00″ · +2′ · 28° ♑︎ 49′00.00″ | +0.24′ | Station |
| D:trueNode | 23° ♈︎ 20′00.00″ → 23° ♈︎ 10′00.00″ · R −10′ · 23° ♈︎ 17′00.00″ | 23° ♈︎ 20′00.00″ → 23° ♈︎ 10′00.00″ · R −10′ · 23° ♈︎ 17′00.00″ | −0.06′ | Mean vs true node |
| E2 | sun H1 · moon H1 · mercury H1 · venus H10 · mars H12 · jupiter H4 · saturn H2 · uranus H5 · neptune H3 · pluto H1 · trueNode H3 | sun H1 · moon H1 · mercury H1 · venus H10 · mars H12 · jupiter H4 · saturn H2 · uranus H5 · neptune H3 · pluto H1 · trueNode H3 | exact | Table grid |
| E3 | sun/moon Conjunction 276′ separating · sun/mars Conjunction 446′ separating · sun/neptune Square 232′ applying · sun/trueNode Trine 135′ applying · moon/neptune Square 44′ separating · moon/trueNode Trine 141′ separating · mercury/venus Sextile 99′ separating · mercury/jupiter Trine 140′ separating · venus/jupiter Opposition 239′ separating · jupiter/saturn Sextile 260′ applying · uranus/neptune Sextile 300′ separating · neptune/pluto Sextile 235′ separating · pluto/trueNode Square 332′ separating | sun/moon Conjunction 274′ separating · sun/mars Conjunction 446′ separating · sun/neptune Square 232′ applying · sun/trueNode Trine 135′ applying · moon/neptune Square 42′ separating · moon/trueNode Trine 139′ separating · mercury/venus Sextile 98′ separating · mercury/jupiter Trine 141′ separating · venus/jupiter Opposition 239′ separating · jupiter/saturn Sextile 260′ applying · uranus/neptune Sextile 299′ separating · neptune/pluto Sextile 235′ separating · pluto/trueNode Square 332′ separating | different | Table grid |
G1ΔT policy · engine default hybrid
Denver, Colorado
Part ATime
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| A1 | Birth date, civil | Jul 19, 2021 | |
| A2 | Clock time, 24-hour | 21:30:00 | |
| A3 | Summer time in force?if Y subtract 1h · older war time may be 2h · stated on the bench | Yes · 1h | |
| A4 | Standard time = A2 − A3 | 20:30:00 | |
| A5 | Zone offset from GreenwichWest add · East subtract | +07:00:00 | |
| A6 | Universal Time = A4 + A5if 24h or more subtract 24h and move A7 forward a day · if below 0 add 24h and move A7 back | 03:30:00 | |
| A7 | UT datemay differ from A1 · every plate row is read on this date | Jul 20, 2021 |
Part BSidereal time
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| B1 | Plate GST at midnight (0h UT) on the A7 dateread from the ephemeris row for A7 | 19:51:59 | |
| B2 | Interval since 0h = A6 | 03:30:00 | |
| B3 | Acceleration = B2 × 9.86 s per hourCheck: always under 4 minutes | 00:00:35 | |
| B4 | Greenwich sidereal time at birth = B1 + B2 + B3carry at 60 | 23:22:34 | |
| B5 | Longitude in time = longitude × 4 min per degreeEast add · West subtract | −06:59:58 | |
| B6 | Local sidereal time = B4 + B5if 24h or more subtract 24h | 16:22:36 | |
| B7 | Southern hemisphere?if Y add 12h to B6 and normalise · this is the table entry | No · 16:22:36 |
Part CAngles and cusps
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| C1 | Table rows bracketing B7: lower ST, upper STrows are 4 minutes apart | 16:20:00 → 16:24:00 | |
| C2 | Fraction f = (B7 − lower) in seconds ÷ 240Check: always between 0 and 1 | 0.65 | |
| C3 | MC: lower, upper, difference, × f, + lowerthe same for every latitude | MC 7° ♐︎ 27′00.00″ | |
| C4 | Latitude rows bracketing the birth: lower, upper; fraction gtable rows are 1° apart | 39° → 40° · g 0.74 | |
| C5 | 11 12 ASC 2 3 as columns: at the lower latitude, at the upper latitude, then by ga column that looks unlike its neighbours is the column with the mistake | C11 28° ♐︎ 44′00.00″ · C12 21° ♑︎ 00′00.00″ · ASC 20° ♒︎ 47′00.00″ · C2 8° ♈︎ 05′00.00″ · C3 12° ♉︎ 35′00.00″ | |
| C10 | Southern? Reverse every sign on C3 and C5degrees and minutes unchanged | No | |
| C11 | Opposites: IC = MC + 180, DSC = ASC + 180, 5 6 8 9 = 11 12 2 3 + 180same degree and minute, opposite sign | IC 7° ♊︎ 27′00.00″ · 5 28° ♊︎ 44′00.00″ · 6 21° ♋︎ 00′00.00″ · DSC 20° ♌︎ 47′00.00″ · 8 8° ♎︎ 05′00.00″ · 9 12° ♏︎ 35′00.00″ |
Part DBodies
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| D:sun | Sun: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 27° ♋︎ 31′00.00″ → 28° ♋︎ 28′00.00″ · +57′ · 27° ♋︎ 39′00.00″ | |
| D:moon | Moon: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 1° ♐︎ 44′00.00″ → 16° ♐︎ 15′00.00″ · +871′ · 3° ♐︎ 51′00.00″ | |
| D:mercury | Mercury: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 13° ♋︎ 39′00.00″ → 15° ♋︎ 34′00.00″ · +115′ · 13° ♋︎ 56′00.00″ | |
| D:venus | Venus: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 27° ♌︎ 34′00.00″ → 28° ♌︎ 46′00.00″ · +72′ · 27° ♌︎ 45′00.00″ | |
| D:mars | Mars: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 23° ♌︎ 50′00.00″ → 24° ♌︎ 27′00.00″ · +37′ · 23° ♌︎ 55′00.00″ | |
| D:jupiter | Jupiter: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 0° ♓︎ 50′00.00″ → 0° ♓︎ 45′00.00″ · R −5′ · 0° ♓︎ 49′00.00″ | |
| D:saturn | Saturn: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 11° ♒︎ 09′00.00″ → 11° ♒︎ 05′00.00″ · R −4′ · 11° ♒︎ 08′00.00″ | |
| D:uranus | Uranus: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 14° ♉︎ 24′00.00″ → 14° ♉︎ 25′00.00″ · +1′ · 14° ♉︎ 24′00.00″ | |
| D:neptune | Neptune: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 23° ♓︎ 03′00.00″ → 23° ♓︎ 02′00.00″ · R −1′ · 23° ♓︎ 03′00.00″ | |
| D:pluto | Pluto: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 25° ♑︎ 31′00.00″ → 25° ♑︎ 29′00.00″ · R −2′ · 25° ♑︎ 31′00.00″ | |
| D:trueNode | True Node: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 9° ♊︎ 48′00.00″ → 9° ♊︎ 48′00.00″ · +0′ · 9° ♊︎ 48′00.00″ |
Part EFigure and aspects
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| E1 | Cusps on the wheel. ASC at the left, houses counterclockwise, C11 filled | Completed on the figure · counterclockwise | |
| E2 | Bodies into houses by comparing D5 with the cuspsnote any body within 1° of a cusp | sun H6 · moon H9 · mercury H5 · venus H7 · mars H7 · jupiter H1 · saturn H12 · uranus H3 · neptune H1 · pluto H12 · trueNode H4 | |
| E3 | Aspectarian: the five Ptolemaic aspects, applying or separating from motionorbs as on the free transits surface | sun/moon Trine 372′ separating · sun/neptune Trine 276′ separating · sun/pluto Opposition 128′ separating · moon/venus Square 366′ separating · moon/jupiter Square 182′ separating · moon/trueNode Opposition 357′ separating · mercury/uranus Sextile 28′ separating · venus/mars Conjunction 230′ separating · venus/jupiter Opposition 184′ applying · mars/jupiter Opposition 414′ applying · saturn/uranus Square 196′ separating · saturn/trueNode Trine 80′ applying · neptune/pluto Sextile 148′ applying |
Part FReceipt
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| F | Receipt: paper, Moira, Δ, cause for every computed line | Completed on the figure |
Part F · continuationPaper-to-Moira discrepancy account
| Line | Paper | Moira | Δ | Cause / notes |
|---|---|---|---|---|
| A4 | 20:30:00 | 20:30:00 | 0 s | Zone or DST |
| A5 | +07:00:00 | +07:00:00 | 0 s | Zone or DST |
| A6 | 03:30:00 | 03:30:00 | 0 s | Zone or DST |
| A7 | Jul 20, 2021 | Jul 20, 2021 | exact | Date change |
| B1 | 19:51:59 | 19:51:59 | 0 s | Sidereal-time rounding |
| B2 | 03:30:00 | 03:30:00 | 0 s | Sidereal-time rounding |
| B3 | 00:00:35 | 00:00:35 | 0 s | Sidereal-time rounding |
| B4 | 23:22:34 | 23:22:34 | 0 s | Sidereal-time rounding |
| B5 | −06:59:58 | −06:59:58 | 0 s | Sidereal-time rounding |
| B6 | 16:22:36 | 16:22:35 | +0.7 s | Sidereal-time rounding |
| B7 | No · 16:22:36 | No · 16:22:35 | +0.7 s | Sidereal-time rounding |
| C1 | 16:20:00 → 16:24:00 | 16:20:00 → 16:24:00 | exact | Table grid |
| C2 | 0.65 | 0.65 | 0.00 | Table grid |
| C3 | MC 7° ♐︎ 27′00.00″ | MC 7° ♐︎ 27′00.00″ | +0.14′ | Table grid |
| C4 | 39° → 40° · g 0.74 | 39° → 40° · g 0.74 | exact | Latitude grid |
| C5 | C11 28° ♐︎ 44′00.00″ · C12 21° ♑︎ 00′00.00″ · ASC 20° ♒︎ 47′00.00″ · C2 8° ♈︎ 05′00.00″ · C3 12° ♉︎ 35′00.00″ | ASC 20° ♒︎ 47′00.00″ · C11 28° ♐︎ 43′00.00″ · C12 21° ♑︎ 00′00.00″ · C2 8° ♈︎ 05′00.00″ · C3 12° ♉︎ 34′00.00″ | max +0.80′ | Latitude grid |
| C10 | No | No | exact | Latitude grid |
| C11 | IC 7° ♊︎ 27′00.00″ · 5 28° ♊︎ 44′00.00″ · 6 21° ♋︎ 00′00.00″ · DSC 20° ♌︎ 47′00.00″ · 8 8° ♎︎ 05′00.00″ · 9 12° ♏︎ 35′00.00″ | IC 7° ♊︎ 27′00.00″ · DSC 20° ♌︎ 47′00.00″ · 5 28° ♊︎ 43′00.00″ · 6 21° ♋︎ 00′00.00″ · 8 8° ♎︎ 05′00.00″ · 9 12° ♏︎ 34′00.00″ | max +0.80′ | Table grid |
| D:sun | 27° ♋︎ 31′00.00″ → 28° ♋︎ 28′00.00″ · +57′ · 27° ♋︎ 39′00.00″ | 27° ♋︎ 31′00.00″ → 28° ♋︎ 28′00.00″ · +57′ · 27° ♋︎ 39′00.00″ | −0.38′ | Table grid |
| D:moon | 1° ♐︎ 44′00.00″ → 16° ♐︎ 15′00.00″ · +871′ · 3° ♐︎ 51′00.00″ | 1° ♐︎ 44′00.00″ → 16° ♐︎ 15′00.00″ · +871′ · 3° ♐︎ 50′00.00″ | +0.60′ | Linear Moon |
| D:mercury | 13° ♋︎ 39′00.00″ → 15° ♋︎ 34′00.00″ · +115′ · 13° ♋︎ 56′00.00″ | 13° ♋︎ 39′00.00″ → 15° ♋︎ 34′00.00″ · +115′ · 13° ♋︎ 55′00.00″ | +0.76′ | Table grid |
| D:venus | 27° ♌︎ 34′00.00″ → 28° ♌︎ 46′00.00″ · +72′ · 27° ♌︎ 45′00.00″ | 27° ♌︎ 34′00.00″ → 28° ♌︎ 46′00.00″ · +72′ · 27° ♌︎ 44′00.00″ | +0.52′ | Table grid |
| D:mars | 23° ♌︎ 50′00.00″ → 24° ♌︎ 27′00.00″ · +37′ · 23° ♌︎ 55′00.00″ | 23° ♌︎ 50′00.00″ → 24° ♌︎ 27′00.00″ · +37′ · 23° ♌︎ 55′00.00″ | −0.30′ | Table grid |
| D:jupiter | 0° ♓︎ 50′00.00″ → 0° ♓︎ 45′00.00″ · R −5′ · 0° ♓︎ 49′00.00″ | 0° ♓︎ 50′00.00″ → 0° ♓︎ 45′00.00″ · R −5′ · 0° ♓︎ 50′00.00″ | −0.54′ | Station |
| D:saturn | 11° ♒︎ 09′00.00″ → 11° ♒︎ 05′00.00″ · R −4′ · 11° ♒︎ 08′00.00″ | 11° ♒︎ 09′00.00″ → 11° ♒︎ 05′00.00″ · R −4′ · 11° ♒︎ 09′00.00″ | −0.72′ | Station |
| D:uranus | 14° ♉︎ 24′00.00″ → 14° ♉︎ 25′00.00″ · +1′ · 14° ♉︎ 24′00.00″ | 14° ♉︎ 24′00.00″ → 14° ♉︎ 25′00.00″ · +1′ · 14° ♉︎ 24′00.00″ | −0.15′ | Station |
| D:neptune | 23° ♓︎ 03′00.00″ → 23° ♓︎ 02′00.00″ · R −1′ · 23° ♓︎ 03′00.00″ | 23° ♓︎ 03′00.00″ → 23° ♓︎ 02′00.00″ · R −1′ · 23° ♓︎ 03′00.00″ | +0.45′ | Station |
| D:pluto | 25° ♑︎ 31′00.00″ → 25° ♑︎ 29′00.00″ · R −2′ · 25° ♑︎ 31′00.00″ | 25° ♑︎ 31′00.00″ → 25° ♑︎ 29′00.00″ · R −2′ · 25° ♑︎ 30′00.00″ | +0.57′ | Station |
| D:trueNode | 9° ♊︎ 48′00.00″ → 9° ♊︎ 48′00.00″ · +0′ · 9° ♊︎ 48′00.00″ | 9° ♊︎ 48′00.00″ → 9° ♊︎ 48′00.00″ · +0′ · 9° ♊︎ 48′00.00″ | −0.09′ | Mean vs true node |
| E2 | sun H6 · moon H9 · mercury H5 · venus H7 · mars H7 · jupiter H1 · saturn H12 · uranus H3 · neptune H1 · pluto H12 · trueNode H4 | sun H6 · moon H9 · mercury H5 · venus H7 · mars H7 · jupiter H1 · saturn H12 · uranus H3 · neptune H1 · pluto H12 · trueNode H4 | exact | Table grid |
| E3 | sun/moon Trine 372′ separating · sun/neptune Trine 276′ separating · sun/pluto Opposition 128′ separating · moon/venus Square 366′ separating · moon/jupiter Square 182′ separating · moon/trueNode Opposition 357′ separating · mercury/uranus Sextile 28′ separating · venus/mars Conjunction 230′ separating · venus/jupiter Opposition 184′ applying · mars/jupiter Opposition 414′ applying · saturn/uranus Square 196′ separating · saturn/trueNode Trine 80′ applying · neptune/pluto Sextile 148′ applying | sun/moon Trine 371′ separating · sun/neptune Trine 276′ separating · sun/pluto Opposition 129′ separating · moon/venus Square 366′ separating · moon/jupiter Square 180′ separating · moon/trueNode Opposition 358′ separating · mercury/uranus Sextile 29′ separating · venus/mars Conjunction 229′ separating · venus/jupiter Opposition 186′ applying · mars/jupiter Opposition 415′ applying · saturn/uranus Square 195′ separating · saturn/trueNode Trine 81′ applying · neptune/pluto Sextile 147′ applying | different | Table grid |
D2ΔT policy · engine default hybrid
Buenos Aires
Part ATime
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| A1 | Birth date, civil | Mar 5, 2018 | |
| A2 | Clock time, 24-hour | 14:20:00 | |
| A3 | Summer time in force?if Y subtract 1h · older war time may be 2h · stated on the bench | No · 0h | |
| A4 | Standard time = A2 − A3 | 14:20:00 | |
| A5 | Zone offset from GreenwichWest add · East subtract | +03:00:00 | |
| A6 | Universal Time = A4 + A5if 24h or more subtract 24h and move A7 forward a day · if below 0 add 24h and move A7 back | 17:20:00 | |
| A7 | UT datemay differ from A1 · every plate row is read on this date | Mar 5, 2018 |
Part BSidereal time
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| B1 | Plate GST at midnight (0h UT) on the A7 dateread from the ephemeris row for A7 | 10:50:46 | |
| B2 | Interval since 0h = A6 | 17:20:00 | |
| B3 | Acceleration = B2 × 9.86 s per hourCheck: always under 4 minutes | 00:02:51 | |
| B4 | Greenwich sidereal time at birth = B1 + B2 + B3carry at 60 | 28:13:37 | |
| B5 | Longitude in time = longitude × 4 min per degreeEast add · West subtract | −03:53:32 | |
| B6 | Local sidereal time = B4 + B5if 24h or more subtract 24h | 00:20:05 | |
| B7 | Southern hemisphere?if Y add 12h to B6 and normalise · this is the table entry | Yes · 12:20:05 |
Part CAngles and cusps
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| C1 | Table rows bracketing B7: lower ST, upper STrows are 4 minutes apart | 12:20:00 → 12:24:00 | |
| C2 | Fraction f = (B7 − lower) in seconds ÷ 240Check: always between 0 and 1 | 0.02 | |
| C3 | MC: lower, upper, difference, × f, + lowerthe same for every latitude | MC 5° ♈︎ 28′00.00″ | |
| C4 | Latitude rows bracketing the birth: lower, upper; fraction gtable rows are 1° apart | 34° → 35° · g 0.60 | |
| C5 | 11 12 ASC 2 3 as columns: at the lower latitude, at the upper latitude, then by ga column that looks unlike its neighbours is the column with the mistake | C11 4° ♉︎ 14′00.00″ · C12 27° ♉︎ 47′00.00″ · ASC 18° ♊︎ 59′00.00″ · C2 22° ♋︎ 41′00.00″ · C3 0° ♍︎ 17′00.00″ | |
| C10 | Southern? Reverse every sign on C3 and C5degrees and minutes unchanged | Yes | |
| C11 | Opposites: IC = MC + 180, DSC = ASC + 180, 5 6 8 9 = 11 12 2 3 + 180same degree and minute, opposite sign | IC 5° ♎︎ 28′00.00″ · 5 4° ♏︎ 14′00.00″ · 6 27° ♏︎ 47′00.00″ · DSC 18° ♐︎ 59′00.00″ · 8 22° ♑︎ 41′00.00″ · 9 0° ♓︎ 17′00.00″ |
Part DBodies
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| D:sun | Sun: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 14° ♓︎ 21′00.00″ → 15° ♓︎ 21′00.00″ · +60′ · 15° ♓︎ 04′00.00″ | |
| D:moon | Moon: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 22° ♎︎ 37′00.00″ → 5° ♏︎ 47′00.00″ · +790′ · 2° ♏︎ 08′00.00″ | |
| D:mercury | Mercury: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 27° ♓︎ 40′00.00″ → 29° ♓︎ 27′00.00″ · +107′ · 28° ♓︎ 57′00.00″ | |
| D:venus | Venus: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 27° ♓︎ 31′00.00″ → 28° ♓︎ 46′00.00″ · +75′ · 28° ♓︎ 25′00.00″ | |
| D:mars | Mars: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 22° ♐︎ 37′00.00″ → 23° ♐︎ 12′00.00″ · +35′ · 23° ♐︎ 02′00.00″ | |
| D:jupiter | Jupiter: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 23° ♏︎ 12′00.00″ → 23° ♏︎ 12′00.00″ · +0′ · 23° ♏︎ 12′00.00″ | |
| D:saturn | Saturn: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 7° ♑︎ 36′00.00″ → 7° ♑︎ 40′00.00″ · +4′ · 7° ♑︎ 39′00.00″ | |
| D:uranus | Uranus: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 26° ♈︎ 06′00.00″ → 26° ♈︎ 09′00.00″ · +3′ · 26° ♈︎ 08′00.00″ | |
| D:neptune | Neptune: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 13° ♓︎ 57′00.00″ → 13° ♓︎ 59′00.00″ · +2′ · 13° ♓︎ 58′00.00″ | |
| D:pluto | Pluto: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 20° ♑︎ 43′00.00″ → 20° ♑︎ 44′00.00″ · +1′ · 20° ♑︎ 44′00.00″ | |
| D:trueNode | True Node: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | 14° ♌︎ 38′00.00″ → 14° ♌︎ 33′00.00″ · R −5′ · 14° ♌︎ 34′00.00″ |
Part EFigure and aspects
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| E1 | Cusps on the wheel. ASC at the left, houses counterclockwise, C11 filled | Completed on the figure · counterclockwise | |
| E2 | Bodies into houses by comparing D5 with the cuspsnote any body within 1° of a cusp | sun H9 · moon H4 · mercury H9 · venus H9 · mars H7 · jupiter H5 · saturn H7 · uranus H10 · neptune H9 · pluto H7 · trueNode H2 | |
| E3 | Aspectarian: the five Ptolemaic aspects, applying or separating from motionorbs as on the free transits surface | sun/neptune Conjunction 66′ separating · moon/uranus Opposition 360′ separating · mercury/venus Conjunction 32′ separating · mercury/mars Square 355′ separating · mercury/jupiter Trine 345′ separating · venus/mars Square 323′ separating · venus/jupiter Trine 313′ separating · mars/uranus Trine 186′ applying · jupiter/pluto Sextile 148′ applying · uranus/pluto Square 324′ separating |
Part FReceipt
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| F | Receipt: paper, Moira, Δ, cause for every computed line | Completed on the figure |
Part F · continuationPaper-to-Moira discrepancy account
| Line | Paper | Moira | Δ | Cause / notes |
|---|---|---|---|---|
| A4 | 14:20:00 | 14:20:00 | 0 s | Zone or DST |
| A5 | +03:00:00 | +03:00:00 | 0 s | Zone or DST |
| A6 | 17:20:00 | 17:20:00 | 0 s | Zone or DST |
| A7 | Mar 5, 2018 | Mar 5, 2018 | exact | Date change |
| B1 | 10:50:46 | 10:50:46 | 0 s | Sidereal-time rounding |
| B2 | 17:20:00 | 17:20:00 | 0 s | Sidereal-time rounding |
| B3 | 00:02:51 | 00:02:51 | 0 s | Sidereal-time rounding |
| B4 | 28:13:37 | 28:13:37 | 0 s | Sidereal-time rounding |
| B5 | −03:53:32 | −03:53:32 | 0 s | Sidereal-time rounding |
| B6 | 00:20:05 | 00:20:05 | −0.5 s | Sidereal-time rounding |
| B7 | Yes · 12:20:05 | Yes · 12:20:05 | −0.5 s | Sidereal-time rounding |
| C1 | 12:20:00 → 12:24:00 | 12:20:00 → 12:24:00 | exact | Table grid |
| C2 | 0.02 | 0.02 | 0.00 | Table grid |
| C3 | MC 5° ♈︎ 28′00.00″ | MC 5° ♈︎ 28′00.00″ | −0.31′ | Table grid |
| C4 | 34° → 35° · g 0.60 | 34° → 35° · g 0.60 | exact | Latitude grid |
| C5 | C11 4° ♉︎ 14′00.00″ · C12 27° ♉︎ 47′00.00″ · ASC 18° ♊︎ 59′00.00″ · C2 22° ♋︎ 41′00.00″ · C3 0° ♍︎ 17′00.00″ | ASC 18° ♊︎ 59′00.00″ · C11 4° ♉︎ 14′00.00″ · C12 27° ♉︎ 46′00.00″ · C2 22° ♋︎ 41′00.00″ · C3 0° ♍︎ 17′00.00″ | max +0.57′ | Latitude grid |
| C10 | Yes | Yes | exact | Latitude grid |
| C11 | IC 5° ♎︎ 28′00.00″ · 5 4° ♏︎ 14′00.00″ · 6 27° ♏︎ 47′00.00″ · DSC 18° ♐︎ 59′00.00″ · 8 22° ♑︎ 41′00.00″ · 9 0° ♓︎ 17′00.00″ | IC 5° ♎︎ 28′00.00″ · DSC 18° ♐︎ 59′00.00″ · 5 4° ♏︎ 14′00.00″ · 6 27° ♏︎ 46′00.00″ · 8 22° ♑︎ 41′00.00″ · 9 0° ♓︎ 17′00.00″ | max +0.57′ | Table grid |
| D:sun | 14° ♓︎ 21′00.00″ → 15° ♓︎ 21′00.00″ · +60′ · 15° ♓︎ 04′00.00″ | 14° ♓︎ 21′00.00″ → 15° ♓︎ 21′00.00″ · +60′ · 15° ♓︎ 05′00.00″ | −0.67′ | Table grid |
| D:moon | 22° ♎︎ 37′00.00″ → 5° ♏︎ 47′00.00″ · +790′ · 2° ♏︎ 08′00.00″ | 22° ♎︎ 37′00.00″ → 5° ♏︎ 47′00.00″ · +790′ · 2° ♏︎ 10′00.00″ | −1.51′ | Linear Moon |
| D:mercury | 27° ♓︎ 40′00.00″ → 29° ♓︎ 27′00.00″ · +107′ · 28° ♓︎ 57′00.00″ | 27° ♓︎ 40′00.00″ → 29° ♓︎ 27′00.00″ · +107′ · 28° ♓︎ 57′00.00″ | −0.21′ | Table grid |
| D:venus | 27° ♓︎ 31′00.00″ → 28° ♓︎ 46′00.00″ · +75′ · 28° ♓︎ 25′00.00″ | 27° ♓︎ 31′00.00″ → 28° ♓︎ 46′00.00″ · +75′ · 28° ♓︎ 25′00.00″ | −0.33′ | Table grid |
| D:mars | 22° ♐︎ 37′00.00″ → 23° ♐︎ 12′00.00″ · +35′ · 23° ♐︎ 02′00.00″ | 22° ♐︎ 37′00.00″ → 23° ♐︎ 12′00.00″ · +35′ · 23° ♐︎ 02′00.00″ | −0.42′ | Table grid |
| D:jupiter | 23° ♏︎ 12′00.00″ → 23° ♏︎ 12′00.00″ · +0′ · 23° ♏︎ 12′00.00″ | 23° ♏︎ 12′00.00″ → 23° ♏︎ 12′00.00″ · +0′ · 23° ♏︎ 12′00.00″ | −0.22′ | Station |
| D:saturn | 7° ♑︎ 36′00.00″ → 7° ♑︎ 40′00.00″ · +4′ · 7° ♑︎ 39′00.00″ | 7° ♑︎ 36′00.00″ → 7° ♑︎ 40′00.00″ · +4′ · 7° ♑︎ 39′00.00″ | +0.26′ | Station |
| D:uranus | 26° ♈︎ 06′00.00″ → 26° ♈︎ 09′00.00″ · +3′ · 26° ♈︎ 08′00.00″ | 26° ♈︎ 06′00.00″ → 26° ♈︎ 09′00.00″ · +3′ · 26° ♈︎ 08′00.00″ | +0.10′ | Station |
| D:neptune | 13° ♓︎ 57′00.00″ → 13° ♓︎ 59′00.00″ · +2′ · 13° ♓︎ 58′00.00″ | 13° ♓︎ 57′00.00″ → 13° ♓︎ 59′00.00″ · +2′ · 13° ♓︎ 59′00.00″ | −0.57′ | Station |
| D:pluto | 20° ♑︎ 43′00.00″ → 20° ♑︎ 44′00.00″ · +1′ · 20° ♑︎ 44′00.00″ | 20° ♑︎ 43′00.00″ → 20° ♑︎ 44′00.00″ · +1′ · 20° ♑︎ 44′00.00″ | +0.19′ | Station |
| D:trueNode | 14° ♌︎ 38′00.00″ → 14° ♌︎ 33′00.00″ · R −5′ · 14° ♌︎ 34′00.00″ | 14° ♌︎ 38′00.00″ → 14° ♌︎ 33′00.00″ · R −5′ · 14° ♌︎ 35′00.00″ | −0.57′ | Mean vs true node |
| E2 | sun H9 · moon H4 · mercury H9 · venus H9 · mars H7 · jupiter H5 · saturn H7 · uranus H10 · neptune H9 · pluto H7 · trueNode H2 | sun H9 · moon H4 · mercury H9 · venus H9 · mars H7 · jupiter H5 · saturn H7 · uranus H10 · neptune H9 · pluto H7 · trueNode H2 | exact | Table grid |
| E3 | sun/neptune Conjunction 66′ separating · moon/uranus Opposition 360′ separating · mercury/venus Conjunction 32′ separating · mercury/mars Square 355′ separating · mercury/jupiter Trine 345′ separating · venus/mars Square 323′ separating · venus/jupiter Trine 313′ separating · mars/uranus Trine 186′ applying · jupiter/pluto Sextile 148′ applying · uranus/pluto Square 324′ separating | sun/neptune Conjunction 66′ separating · moon/uranus Opposition 362′ separating · mercury/venus Conjunction 32′ separating · mercury/mars Square 355′ separating · mercury/jupiter Trine 345′ separating · venus/mars Square 323′ separating · venus/jupiter Trine 313′ separating · mars/uranus Trine 186′ applying · jupiter/pluto Sextile 148′ applying · uranus/pluto Square 324′ separating | different | Table grid |
B3ΔT policy · engine default hybrid