Constructed bench · G1
Open printable formRoyal Observatory, Greenwich
A complete paper reduction with its frozen engine comparand and named residuals.
The bench card
- Place
- Royal Observatory, Greenwich
- Coordinates
- 51.4778°N · 0.0015°W
- Civil date
- Dec 13, 2023
- Clock
- 8:00 AM
- Time zone
- Europe/London
- Zone note
- GMT, not BST
Time-zone and summer-time status are stated from the IANA tzdb record frozen with this constructed bench.
Permanent form A–F
Part ACivil time to UT
| Line | Operation | Paper result |
|---|---|---|
| A1 | Birth date, civil | Dec 13, 2023 |
| A2 | Clock time, 24-hour | 08:00:00 |
| A3 | Summer time in force? | No · 0h |
| A4 | Standard time = A2 − A3 | 08:00:00 |
| A5 | Zone offset from Greenwich | +00:00:00 |
| A6 | Universal Time = A4 + A5 | 08:00:00 |
| A7 | UT date | Dec 13, 2023 |
Part BSidereal time
| Line | Operation | Paper result |
|---|---|---|
| B1 | Plate GST at midnight (0h UT) on the A7 date | 05:25:42 |
| B2 | Interval since 0h = A6 | 08:00:00 |
| B3 | Acceleration = B2 × 9.86 s per hour | 00:01:19 |
| B4 | Greenwich sidereal time at birth = B1 + B2 + B3 | 13:27:01 |
| B5 | Longitude in time = longitude × 4 min per degree | −00:00:00 |
| B6 | Local sidereal time = B4 + B5 | 13:27:01 |
| B7 | Southern hemisphere? | No · 13:27:01 |
Part CAngles and cusps
| Line | Operation | Paper result |
|---|---|---|
| C1 | Table rows bracketing B7: lower ST, upper ST | 13:24:00 → 13:28:00 |
| C2 | Fraction f = (B7 − lower) in seconds ÷ 240 | 0.75 |
| C3 | MC: lower, upper, difference, × f, + lower | MC 23° ♎︎ 30′00.00″ |
| C4 | Latitude rows bracketing the birth: lower, upper; fraction g | 51° → 52° · g 0.48 |
| C5 | 11 12 ASC 2 3 as columns: at the lower latitude, at the upper latitude, then by g | 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 C5 | No |
| C11 | Opposites: IC = MC + 180, DSC = ASC + 180, 5 6 8 9 = 11 12 2 3 + 180 | 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 | Paper result |
|---|---|---|
| D:sun | Sun: this midnight, next midnight, motion, × A6 ÷ 24, position | 20° ♐︎ 42′00.00″ → 21° ♐︎ 43′00.00″ · +61′ · 21° ♐︎ 02′00.00″ |
| D:moon | Moon: this midnight, next midnight, motion, × A6 ÷ 24, position | 20° ♐︎ 57′00.00″ → 4° ♑︎ 59′00.00″ · +842′ · 25° ♐︎ 38′00.00″ |
| D:mercury | Mercury: this midnight, next midnight, motion, × A6 ÷ 24, position | 8° ♑︎ 29′00.00″ → 8° ♑︎ 27′00.00″ · R −2′ · 8° ♑︎ 28′00.00″ |
| D:venus | Venus: this midnight, next midnight, motion, × A6 ÷ 24, position | 9° ♏︎ 43′00.00″ → 10° ♏︎ 55′00.00″ · +72′ · 10° ♏︎ 07′00.00″ |
| D:mars | Mars: this midnight, next midnight, motion, × A6 ÷ 24, position | 13° ♐︎ 21′00.00″ → 14° ♐︎ 05′00.00″ · +44′ · 13° ♐︎ 36′00.00″ |
| D:jupiter | Jupiter: this midnight, next midnight, motion, × A6 ÷ 24, position | 6° ♉︎ 09′00.00″ → 6° ♉︎ 05′00.00″ · R −4′ · 6° ♉︎ 08′00.00″ |
| D:saturn | Saturn: this midnight, next midnight, motion, × A6 ÷ 24, position | 1° ♓︎ 47′00.00″ → 1° ♓︎ 51′00.00″ · +4′ · 1° ♓︎ 48′00.00″ |
| D:uranus | Uranus: this midnight, next midnight, motion, × A6 ÷ 24, position | 19° ♉︎ 55′00.00″ → 19° ♉︎ 53′00.00″ · R −2′ · 19° ♉︎ 54′00.00″ |
| D:neptune | Neptune: this midnight, next midnight, motion, × A6 ÷ 24, position | 24° ♓︎ 54′00.00″ → 24° ♓︎ 54′00.00″ · +0′ · 24° ♓︎ 54′00.00″ |
| D:pluto | Pluto: this midnight, next midnight, motion, × A6 ÷ 24, position | 28° ♑︎ 48′00.00″ → 28° ♑︎ 50′00.00″ · +2′ · 28° ♑︎ 49′00.00″ |
| D:trueNode | True Node: this midnight, next midnight, motion, × A6 ÷ 24, position | 23° ♈︎ 20′00.00″ → 23° ♈︎ 10′00.00″ · R −10′ · 23° ♈︎ 17′00.00″ |
Part EFigure and aspects
| Line | Operation | Paper 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 cusps | 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 motion | 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 | Paper result |
|---|---|---|
| F | Receipt: paper, Moira, Δ, cause for every computed line | Completed on the figure |
Paper, engine, residual, cause
| Line | Paper | Moira | Δ | Cause |
|---|---|---|---|---|
| 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 |
A residual is admitted only with a named cause. It is never silently corrected.
ΔT policy · engine default hybrid