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Lesson 05 · Sun and planets

5 Sun and planets

Subtract adjacent midnight rows for daily motion, scale by the UT fraction of a day, and preserve the sign of travel.

Bench G1Stage 1 of 4 · Demonstration
Demonstration

G1 · Royal Observatory, Greenwich

Follow the source and working. Advance one numbered line at a time.

0 of 9 lines checked0%
Shared table instrument · D:sun

Sun · midnight to moment

Source, scales & paper working
Dec 13, 2023 · 0h UT20° ♐︎ 42′00.00″
Dec 14, 2023 · 0h UT21° ♐︎ 43′00.00″
One UT day · time runs forward
UT 08:00:00
First midnight · 0hNext midnight · 24h

28800 s ÷ 86,400 s
≈ 0.33333333 of the day. Decimal shown approximately; use the full ratio, without rounding it to two decimals.

Signed daily arc · schematic
D1 · first midnight
20° ♐︎ 42′00.00″D2 · next midnight
21° ♐︎ 43′00.00″

Direct · add the travel →

Admitted reference

+61′ × 28800 s ÷ 86,400 s → +20′ rounded travel

D1 + signed travel → 21° ♐︎ 02′00.00″

Paper convention: round each source position to the nearest arcminute, take the shortest signed difference, then round the travel to whole arcminutes. The arc marker follows that rounded travel.

Station interval: no. Neither row has a station marker and the daily motion exceeds the teaching slow-interval threshold.

Frozen teaching plate · Moira 6.4.1 · de441.bsp. Schematic paper arithmetic; no fresh engine calculation.

Admitted reference

D1 · first midnight
20° ♐︎ 42′00.00″
D2 · next midnight
21° ♐︎ 43′00.00″
Daily motion
+61′
Travel to UT
+20′
Retrograde
No
Station interval
No
D5 · position at birth
21° ♐︎ 02′00.00″
Temporary exploration

Move the moment within these two source rows. This never changes your paper, lesson checks or saved progress.

All source cells for D:sun
Permanent reduction formParts A–F

  1. Sun: this midnight, next midnight, motion, × A6 ÷ 24, position

    active line

    Rule negative motion is retrograde, write R · a negative travel subtracts

    Shared table instrument · D:sun

    Sun · midnight to moment

    Source, scales & paper working
    Dec 13, 2023 · 0h UT20° ♐︎ 42′00.00″
    Dec 14, 2023 · 0h UT21° ♐︎ 43′00.00″
    One UT day · time runs forward
    UT 08:00:00
    First midnight · 0hNext midnight · 24h

    28800 s ÷ 86,400 s
    ≈ 0.33333333 of the day. Decimal shown approximately; use the full ratio, without rounding it to two decimals.

    Signed daily arc · schematic
    D1 · first midnight
    20° ♐︎ 42′00.00″    D2 · next midnight
    21° ♐︎ 43′00.00″

    Direct · add the travel →

    Admitted reference

    +61′ × 28800 s ÷ 86,400 s → +20′ rounded travel

    D1 + signed travel → 21° ♐︎ 02′00.00″

    Paper convention: round each source position to the nearest arcminute, take the shortest signed difference, then round the travel to whole arcminutes. The arc marker follows that rounded travel.

    Station interval: no. Neither row has a station marker and the daily motion exceeds the teaching slow-interval threshold.

    Frozen teaching plate · Moira 6.4.1 · de441.bsp. Schematic paper arithmetic; no fresh engine calculation.

    Admitted reference

    D1 · first midnight
    20° ♐︎ 42′00.00″
    D2 · next midnight
    21° ♐︎ 43′00.00″
    Daily motion
    +61′
    Travel to UT
    +20′
    Retrograde
    No
    Station interval
    No
    D5 · position at birth
    21° ♐︎ 02′00.00″
    Temporary exploration

    Move the moment within these two source rows. This never changes your paper, lesson checks or saved progress.

    All source cells for D:sun

    Why sun uses the signed short arc between adjacent midnights because motion can cross a sign boundary.

    Your paper result20° ♐︎ 42′00.00″ → 21° ♐︎ 43′00.00″ · +61′ · 21° ♐︎ 02′00.00″
    Reference answer20° ♐︎ 42′00.00″ → 21° ♐︎ 43′00.00″ · +61′ · 21° ♐︎ 02′00.00″
    Tolerance · within 1′

  2. Venus: this midnight, next midnight, motion, × A6 ÷ 24, position

    waiting

    Rule negative motion is retrograde, write R · a negative travel subtracts

  3. Mars: this midnight, next midnight, motion, × A6 ÷ 24, position

    waiting

    Rule negative motion is retrograde, write R · a negative travel subtracts

  4. Jupiter: this midnight, next midnight, motion, × A6 ÷ 24, position

    waiting

    Rule negative motion is retrograde, write R · a negative travel subtracts

  5. Saturn: this midnight, next midnight, motion, × A6 ÷ 24, position

    waiting

    Rule negative motion is retrograde, write R · a negative travel subtracts

  6. Uranus: this midnight, next midnight, motion, × A6 ÷ 24, position

    waiting

    Rule negative motion is retrograde, write R · a negative travel subtracts

  7. Neptune: this midnight, next midnight, motion, × A6 ÷ 24, position

    waiting

    Rule negative motion is retrograde, write R · a negative travel subtracts

  8. Pluto: this midnight, next midnight, motion, × A6 ÷ 24, position

    waiting

    Rule negative motion is retrograde, write R · a negative travel subtracts

  9. True Node: this midnight, next midnight, motion, × A6 ÷ 24, position

    waiting

    Rule negative motion is retrograde, write R · a negative travel subtracts

Moira Craft School

Blank permanent A–F reduction form

Part ATime

LineOperation and ruleWorkingResult
A1Birth date, civil
A2Clock time, 24-hour
A3Summer time in force?if Y subtract 1h · older war time may be 2h · stated on the bench
A4Standard time = A2 − A3
A5Zone offset from GreenwichWest add · East subtract
A6Universal Time = A4 + A5if 24h or more subtract 24h and move A7 forward a day · if below 0 add 24h and move A7 back
A7UT datemay differ from A1 · every plate row is read on this date

Part BSidereal time

LineOperation and ruleWorkingResult
B1Plate GST at midnight (0h UT) on the A7 dateread from the ephemeris row for A7
B2Interval since 0h = A6
B3Acceleration = B2 × 9.86 s per hourCheck: always under 4 minutes
B4Greenwich sidereal time at birth = B1 + B2 + B3carry at 60
B5Longitude in time = longitude × 4 min per degreeEast add · West subtract
B6Local sidereal time = B4 + B5if 24h or more subtract 24h
B7Southern hemisphere?if Y add 12h to B6 and normalise · this is the table entry

Part CAngles and cusps

LineOperation and ruleWorkingResult
C1Table rows bracketing B7: lower ST, upper STrows are 4 minutes apart
C2Fraction f = (B7 − lower) in seconds ÷ 240Check: always between 0 and 1
C3MC: lower, upper, difference, × f, + lowerthe same for every latitude
C4Latitude rows bracketing the birth: lower, upper; fraction gtable rows are 1° apart
C511 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
C10Southern? Reverse every sign on C3 and C5degrees and minutes unchanged
C11Opposites: IC = MC + 180, DSC = ASC + 180, 5 6 8 9 = 11 12 2 3 + 180same degree and minute, opposite sign

Part DBodies

LineOperation and ruleWorkingResult
D:sunSun: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts
D:moonMoon: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts
D:mercuryMercury: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts
D:venusVenus: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts
D:marsMars: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts
D:jupiterJupiter: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts
D:saturnSaturn: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts
D:uranusUranus: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts
D:neptuneNeptune: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts
D:plutoPluto: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts
D:trueNodeTrue Node: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts

Part EFigure and aspects

LineOperation and ruleWorkingResult
E1Cusps on the wheel. ASC at the left, houses counterclockwise, C11 filled
E2Bodies into houses by comparing D5 with the cuspsnote any body within 1° of a cusp
E3Aspectarian: the five Ptolemaic aspects, applying or separating from motionorbs as on the free transits surface

Part FReceipt

LineOperation and ruleWorkingResult
FReceipt: paper, Moira, Δ, cause for every computed line

Part F · continuationPaper-to-Moira discrepancy account

Retain the paper value; record Moira, the signed delta, and one cause from the fixed vocabulary.
LinePaperMoiraΔCause / 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