Constructed bench · D2

Denver, Colorado

A complete paper reduction with its frozen engine comparand and named residuals.

Open printable form
Civil inputs

The bench card

Place
Denver, Colorado
Coordinates
39.7392°N · 104.9903°W
Civil date
2021-07-19
Clock
21:30
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.

Complete answer key

Permanent form A–F

Part ACivil time to UT

LineOperationPaper result
A1Birth date, civil2021-07-19
A2Clock time, 24-hour21:30:00
A3Summer time in force?Yes · 1h
A4Standard time = A2 − A320:30:00
A5Zone offset from Greenwich+07:00:00
A6Universal Time = A4 + A503:30:00
A7UT date2021-07-20

Part BSidereal time

LineOperationPaper result
B1Plate GST at midnight (0h UT) on the A7 date19:51:59
B2Interval since 0h = A603:30:00
B3Acceleration = B2 × 9.86 s per hour00:00:35
B4Greenwich sidereal time at birth = B1 + B2 + B323:22:34
B5Longitude in time = longitude × 4 min per degree−06:59:58
B6Local sidereal time = B4 + B516:22:36
B7Southern hemisphere?No · 16:22:36

Part CAngles and cusps

LineOperationPaper result
C1Table rows bracketing B7: lower ST, upper ST16:20:00 → 16:24:00
C2Fraction f = (B7 − lower) in seconds ÷ 2400.65
C3MC: lower, upper, difference, × f, + lowerMC Sagittarius 7°27′
C4Latitude rows bracketing the birth: lower, upper; fraction g39° → 40° · g 0.74
C511 12 ASC 2 3 as columns: at the lower latitude, at the upper latitude, then by gC11 Sagittarius 28°44′ · C12 Capricorn 21°00′ · ASC Aquarius 20°47′ · C2 Aries 8°05′ · C3 Taurus 12°35′
C10Southern? Reverse every sign on C3 and C5No
C11Opposites: IC = MC + 180, DSC = ASC + 180, 5 6 8 9 = 11 12 2 3 + 180MC Gemini 7°27′ · C11 Gemini 28°44′ · C12 Cancer 21°00′ · ASC Leo 20°47′ · C2 Libra 8°05′ · C3 Scorpio 12°35′

Part DBodies

LineOperationPaper result
D:sunSun: this midnight, next midnight, motion, × A6 ÷ 24, positionCancer 27°31′ → Cancer 28°28′ · +57′ · Cancer 27°39′
D:moonMoon: this midnight, next midnight, motion, × A6 ÷ 24, positionSagittarius 1°44′ → Sagittarius 16°15′ · +871′ · Sagittarius 3°51′
D:mercuryMercury: this midnight, next midnight, motion, × A6 ÷ 24, positionCancer 13°39′ → Cancer 15°34′ · +115′ · Cancer 13°56′
D:venusVenus: this midnight, next midnight, motion, × A6 ÷ 24, positionLeo 27°34′ → Leo 28°46′ · +72′ · Leo 27°45′
D:marsMars: this midnight, next midnight, motion, × A6 ÷ 24, positionLeo 23°50′ → Leo 24°27′ · +37′ · Leo 23°55′
D:jupiterJupiter: this midnight, next midnight, motion, × A6 ÷ 24, positionPisces 0°50′ → Pisces 0°45′ · R −5′ · Pisces 0°49′
D:saturnSaturn: this midnight, next midnight, motion, × A6 ÷ 24, positionAquarius 11°09′ → Aquarius 11°05′ · R −4′ · Aquarius 11°08′
D:uranusUranus: this midnight, next midnight, motion, × A6 ÷ 24, positionTaurus 14°24′ → Taurus 14°25′ · +1′ · Taurus 14°24′
D:neptuneNeptune: this midnight, next midnight, motion, × A6 ÷ 24, positionPisces 23°03′ → Pisces 23°02′ · R −1′ · Pisces 23°03′
D:plutoPluto: this midnight, next midnight, motion, × A6 ÷ 24, positionCapricorn 25°31′ → Capricorn 25°29′ · R −2′ · Capricorn 25°31′
D:trueNodeTrue Node: this midnight, next midnight, motion, × A6 ÷ 24, positionGemini 9°48′ → Gemini 9°48′ · +0′ · Gemini 9°48′

Part EFigure and aspects

LineOperationPaper result
E1Cusps on the wheel. ASC at the left, houses counterclockwise, C11 filledCompleted on the figure · counterclockwise
E2Bodies into houses by comparing D5 with the cuspssun H6 · moon H9 · mercury H5 · venus H7 · mars H7 · jupiter H1 · saturn H12 · uranus H3 · neptune H1 · pluto H12 · trueNode H4
E3Aspectarian: the five Ptolemaic aspects, applying or separating from motionsun/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

LineOperationPaper result
FReceipt: paper, Moira, Δ, cause for every computed lineCompleted on the figure
Reduction receipt

Paper, engine, residual, cause

LinePaperMoiraΔCause
A420:30:0020:30:000 sZone or DST
A5+07:00:00+07:00:000 sZone or DST
A603:30:0003:30:000 sZone or DST
A72021-07-202021-07-20exactDate change
B119:51:5919:51:590 sSidereal-time rounding
B203:30:0003:30:000 sSidereal-time rounding
B300:00:3500:00:350 sSidereal-time rounding
B423:22:3423:22:340 sSidereal-time rounding
B5−06:59:58−06:59:580 sSidereal-time rounding
B616:22:3616:22:35+0.7 sSidereal-time rounding
B7No · 16:22:36No · 16:22:35+0.7 sSidereal-time rounding
C116:20:00 → 16:24:0016:20:00 → 16:24:00exactTable grid
C20.650.650.00Table grid
C3MC Sagittarius 7°27′MC Sagittarius 7°27′+0.14′Table grid
C439° → 40° · g 0.7439° → 40° · g 0.74exactLatitude grid
C5C11 Sagittarius 28°44′ · C12 Capricorn 21°00′ · ASC Aquarius 20°47′ · C2 Aries 8°05′ · C3 Taurus 12°35′ASC Aquarius 20°47′ · C11 Sagittarius 28°43′ · C12 Capricorn 21°00′ · C2 Aries 8°05′ · C3 Taurus 12°34′max +0.80′Latitude grid
C10NoNoexactLatitude grid
C11MC Gemini 7°27′ · C11 Gemini 28°44′ · C12 Cancer 21°00′ · ASC Leo 20°47′ · C2 Libra 8°05′ · C3 Scorpio 12°35′MC Gemini 7°27′ · ASC Leo 20°47′ · C11 Gemini 28°43′ · C12 Cancer 21°00′ · C2 Libra 8°05′ · C3 Scorpio 12°34′max +0.80′Table grid
D:sunCancer 27°31′ → Cancer 28°28′ · +57′ · Cancer 27°39′Cancer 27°31′ → Cancer 28°28′ · +57′ · Cancer 27°39′−0.38′Table grid
D:moonSagittarius 1°44′ → Sagittarius 16°15′ · +871′ · Sagittarius 3°51′Sagittarius 1°44′ → Sagittarius 16°15′ · +871′ · Sagittarius 3°50′+0.60′Linear Moon
D:mercuryCancer 13°39′ → Cancer 15°34′ · +115′ · Cancer 13°56′Cancer 13°39′ → Cancer 15°34′ · +115′ · Cancer 13°55′+0.76′Table grid
D:venusLeo 27°34′ → Leo 28°46′ · +72′ · Leo 27°45′Leo 27°34′ → Leo 28°46′ · +72′ · Leo 27°44′+0.52′Table grid
D:marsLeo 23°50′ → Leo 24°27′ · +37′ · Leo 23°55′Leo 23°50′ → Leo 24°27′ · +37′ · Leo 23°55′−0.30′Table grid
D:jupiterPisces 0°50′ → Pisces 0°45′ · R −5′ · Pisces 0°49′Pisces 0°50′ → Pisces 0°45′ · R −5′ · Pisces 0°50′−0.54′Station
D:saturnAquarius 11°09′ → Aquarius 11°05′ · R −4′ · Aquarius 11°08′Aquarius 11°09′ → Aquarius 11°05′ · R −4′ · Aquarius 11°09′−0.72′Station
D:uranusTaurus 14°24′ → Taurus 14°25′ · +1′ · Taurus 14°24′Taurus 14°24′ → Taurus 14°25′ · +1′ · Taurus 14°24′−0.15′Station
D:neptunePisces 23°03′ → Pisces 23°02′ · R −1′ · Pisces 23°03′Pisces 23°03′ → Pisces 23°02′ · R −1′ · Pisces 23°03′+0.45′Station
D:plutoCapricorn 25°31′ → Capricorn 25°29′ · R −2′ · Capricorn 25°31′Capricorn 25°31′ → Capricorn 25°29′ · R −2′ · Capricorn 25°30′+0.57′Station
D:trueNodeGemini 9°48′ → Gemini 9°48′ · +0′ · Gemini 9°48′Gemini 9°48′ → Gemini 9°48′ · +0′ · Gemini 9°48′−0.09′Mean vs true node
E2sun H6 · moon H9 · mercury H5 · venus H7 · mars H7 · jupiter H1 · saturn H12 · uranus H3 · neptune H1 · pluto H12 · trueNode H4sun H6 · moon H9 · mercury H5 · venus H7 · mars H7 · jupiter H1 · saturn H12 · uranus H3 · neptune H1 · pluto H12 · trueNode H4exactTable grid
E3sun/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′ applyingsun/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′ applyingdifferentTable grid

A residual is admitted only with a named cause. It is never silently corrected.

ΔT policy · engine default hybrid