Constructed bench · D2
Open printable formDenver, Colorado
A complete paper reduction with its frozen engine comparand and named residuals.
The bench card
- Place
- Denver, Colorado
- Coordinates
- 39.7392°N · 104.9903°W
- Civil date
- Jul 19, 2021
- Clock
- 9:30 PM
- Time zone
- America/Denver
- Zone note
- MDT, summer time in force; standard zone MST UTC−7
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 | Jul 19, 2021 |
| A2 | Clock time, 24-hour | 21:30:00 |
| A3 | Summer time in force? | Yes · 1h |
| A4 | Standard time = A2 − A3 | 20:30:00 |
| A5 | Zone offset from Greenwich | +07:00:00 |
| A6 | Universal Time = A4 + A5 | 03:30:00 |
| A7 | UT date | Jul 20, 2021 |
Part BSidereal time
| Line | Operation | Paper result |
|---|---|---|
| B1 | Plate GST at midnight (0h UT) on the A7 date | 19:51:59 |
| B2 | Interval since 0h = A6 | 03:30:00 |
| B3 | Acceleration = B2 × 9.86 s per hour | 00:00:35 |
| B4 | Greenwich sidereal time at birth = B1 + B2 + B3 | 23:22:34 |
| B5 | Longitude in time = longitude × 4 min per degree | −06:59:58 |
| B6 | Local sidereal time = B4 + B5 | 16:22:36 |
| B7 | Southern hemisphere? | No · 16:22:36 |
Part CAngles and cusps
| Line | Operation | Paper result |
|---|---|---|
| C1 | Table rows bracketing B7: lower ST, upper ST | 16:20:00 → 16:24:00 |
| C2 | Fraction f = (B7 − lower) in seconds ÷ 240 | 0.65 |
| C3 | MC: lower, upper, difference, × f, + lower | MC 7° ♐︎ 27′00.00″ |
| C4 | Latitude rows bracketing the birth: lower, upper; fraction g | 39° → 40° · g 0.74 |
| C5 | 11 12 ASC 2 3 as columns: at the lower latitude, at the upper latitude, then by g | 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 C5 | No |
| C11 | Opposites: IC = MC + 180, DSC = ASC + 180, 5 6 8 9 = 11 12 2 3 + 180 | 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 | Paper result |
|---|---|---|
| D:sun | Sun: this midnight, next midnight, motion, × A6 ÷ 24, position | 27° ♋︎ 31′00.00″ → 28° ♋︎ 28′00.00″ · +57′ · 27° ♋︎ 39′00.00″ |
| D:moon | Moon: this midnight, next midnight, motion, × A6 ÷ 24, position | 1° ♐︎ 44′00.00″ → 16° ♐︎ 15′00.00″ · +871′ · 3° ♐︎ 51′00.00″ |
| D:mercury | Mercury: this midnight, next midnight, motion, × A6 ÷ 24, position | 13° ♋︎ 39′00.00″ → 15° ♋︎ 34′00.00″ · +115′ · 13° ♋︎ 56′00.00″ |
| D:venus | Venus: this midnight, next midnight, motion, × A6 ÷ 24, position | 27° ♌︎ 34′00.00″ → 28° ♌︎ 46′00.00″ · +72′ · 27° ♌︎ 45′00.00″ |
| D:mars | Mars: this midnight, next midnight, motion, × A6 ÷ 24, position | 23° ♌︎ 50′00.00″ → 24° ♌︎ 27′00.00″ · +37′ · 23° ♌︎ 55′00.00″ |
| D:jupiter | Jupiter: this midnight, next midnight, motion, × A6 ÷ 24, position | 0° ♓︎ 50′00.00″ → 0° ♓︎ 45′00.00″ · R −5′ · 0° ♓︎ 49′00.00″ |
| D:saturn | Saturn: this midnight, next midnight, motion, × A6 ÷ 24, position | 11° ♒︎ 09′00.00″ → 11° ♒︎ 05′00.00″ · R −4′ · 11° ♒︎ 08′00.00″ |
| D:uranus | Uranus: this midnight, next midnight, motion, × A6 ÷ 24, position | 14° ♉︎ 24′00.00″ → 14° ♉︎ 25′00.00″ · +1′ · 14° ♉︎ 24′00.00″ |
| D:neptune | Neptune: this midnight, next midnight, motion, × A6 ÷ 24, position | 23° ♓︎ 03′00.00″ → 23° ♓︎ 02′00.00″ · R −1′ · 23° ♓︎ 03′00.00″ |
| D:pluto | Pluto: this midnight, next midnight, motion, × A6 ÷ 24, position | 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, position | 9° ♊︎ 48′00.00″ → 9° ♊︎ 48′00.00″ · +0′ · 9° ♊︎ 48′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 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 motion | 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 | 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 | 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 |
A residual is admitted only with a named cause. It is never silently corrected.
ΔT policy · engine default hybrid