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Craft · lessons, benches & plates
Lesson 08 · Aspects

8 Aspects

Measure the shortest arc, admit only a Ptolemaic angle inside the published orb, and use daily motion for applying or separating.

Bench G1Stage 1 of 3 · Demonstration
Demonstration

G1 · Royal Observatory, Greenwich

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

0 of 1 lines checked0%
Shared paper instrument · E3

Two positions, one measured arc

Source, figure & paper working
D5 positions & signed daily motions

Given results from the earlier paper reduction. These are rounded D5 longitudes, with the signed midnight-to-midnight motion from Part D.

Sun
21° ♐︎ 02′00.00″+61′ / day
Moon
25° ♐︎ 38′00.00″+842′ / day
Mercury
8° ♑︎ 28′00.00″−2′ / day
Venus
10° ♏︎ 07′00.00″+72′ / day
Mars
13° ♐︎ 36′00.00″+44′ / day
Jupiter
6° ♉︎ 08′00.00″−4′ / day
Saturn
1° ♓︎ 48′00.00″+4′ / day
Uranus
19° ♉︎ 54′00.00″−2′ / day
Neptune
24° ♓︎ 54′00.00″+0′ / day
Pluto
28° ♑︎ 49′00.00″+2′ / day
True Node
23° ♈︎ 17′00.00″−10′ / day
The five published angle & orb limits
Conjunction · 0°
≤ 8° orb
Opposition · 180°
≤ 8° orb
Trine · 120°
≤ 7° orb
Square · 90°
≤ 7° orb
Sextile · 60°
≤ 5° orb

Shared standard planetary orbs, including the True Node. Five Ptolemaic aspects only; no minor aspects or tighter asteroid orbs.

A · Sun21° ♐︎ 02′00.00″+61′ / day

B · Moon25° ♐︎ 38′00.00″+842′ / day

0°90°180°270°SHORTEST ARC4° 36′
Full zodiac circle · Aries 0° at the left · increasing longitude counterclockwise. The brass arc is the shorter path, up to 180°.
Temporary pair inspection · rounded paper sources

Conjunction

Inside the published limit, including its boundary.

Shortest separation
4° 36′
Exact conjunction
0°
Distance from exact
4° 36′
Published orb limit
8°
Orb window · distance from the exact angle

Shaded window: −8° to +8°. Exact at the center.

Daily-motion comparison · separating

The paper rule adds each signed daily motion to its D5 position, then measures the shortest separation again. It is a one-day estimate, not instantaneous velocity or a freshly calculated future chart.

Current distance from exact
4° 36′
One-day estimated separation
17° 37′
Estimated distance from exact
17° 37′

The estimated distance from exact is larger: separating under the paper rule.

Pair selection is temporary. It does not change your retained rows, lesson checks or saved progress.

Admitted reference · 13 major aspects
  1. Sun / MoonConjunction · 276′ orb · separating
  2. Sun / MarsConjunction · 446′ orb · separating
  3. Sun / NeptuneSquare · 232′ orb · applying
  4. Sun / True NodeTrine · 135′ orb · applying
  5. Moon / NeptuneSquare · 44′ orb · separating
  6. Moon / True NodeTrine · 141′ orb · separating
  7. Mercury / VenusSextile · 99′ orb · separating
  8. Mercury / JupiterTrine · 140′ orb · separating
  9. Venus / JupiterOpposition · 239′ orb · separating
  10. Jupiter / SaturnSextile · 260′ orb · applying
  11. Uranus / NeptuneSextile · 300′ orb · separating
  12. Neptune / PlutoSextile · 235′ orb · separating
  13. Pluto / True NodeSquare · 332′ orb · separating

Paper geometry from the declared D5 positions and Part D motions. No fresh engine calculation; no chart interpretation.

All source cells for E3
Permanent reduction formParts A–F

  1. Aspectarian: the five Ptolemaic aspects, applying or separating from motion

    active line

    Rule orbs as on the free transits surface

    Shared paper instrument · E3

    Two positions, one measured arc

    Source, figure & paper working
    D5 positions & signed daily motions

    Given results from the earlier paper reduction. These are rounded D5 longitudes, with the signed midnight-to-midnight motion from Part D.

    Sun
    21° ♐︎ 02′00.00″+61′ / day
    Moon
    25° ♐︎ 38′00.00″+842′ / day
    Mercury
    8° ♑︎ 28′00.00″−2′ / day
    Venus
    10° ♏︎ 07′00.00″+72′ / day
    Mars
    13° ♐︎ 36′00.00″+44′ / day
    Jupiter
    6° ♉︎ 08′00.00″−4′ / day
    Saturn
    1° ♓︎ 48′00.00″+4′ / day
    Uranus
    19° ♉︎ 54′00.00″−2′ / day
    Neptune
    24° ♓︎ 54′00.00″+0′ / day
    Pluto
    28° ♑︎ 49′00.00″+2′ / day
    True Node
    23° ♈︎ 17′00.00″−10′ / day
    The five published angle & orb limits
    Conjunction · 0°
    ≤ 8° orb
    Opposition · 180°
    ≤ 8° orb
    Trine · 120°
    ≤ 7° orb
    Square · 90°
    ≤ 7° orb
    Sextile · 60°
    ≤ 5° orb

    Shared standard planetary orbs, including the True Node. Five Ptolemaic aspects only; no minor aspects or tighter asteroid orbs.

    A · Sun21° ♐︎ 02′00.00″+61′ / day

    B · Moon25° ♐︎ 38′00.00″+842′ / day

    0°90°180°270°SHORTEST ARC4° 36′
    Full zodiac circle · Aries 0° at the left · increasing longitude counterclockwise. The brass arc is the shorter path, up to 180°.
    Temporary pair inspection · rounded paper sources

    Conjunction

    Inside the published limit, including its boundary.

    Shortest separation
    4° 36′
    Exact conjunction
    0°
    Distance from exact
    4° 36′
    Published orb limit
    8°
    Orb window · distance from the exact angle

    Shaded window: −8° to +8°. Exact at the center.

    Daily-motion comparison · separating

    The paper rule adds each signed daily motion to its D5 position, then measures the shortest separation again. It is a one-day estimate, not instantaneous velocity or a freshly calculated future chart.

    Current distance from exact
    4° 36′
    One-day estimated separation
    17° 37′
    Estimated distance from exact
    17° 37′

    The estimated distance from exact is larger: separating under the paper rule.

    Pair selection is temporary. It does not change your retained rows, lesson checks or saved progress.

    Admitted reference · 13 major aspects
    1. Sun / MoonConjunction · 276′ orb · separating
    2. Sun / MarsConjunction · 446′ orb · separating
    3. Sun / NeptuneSquare · 232′ orb · applying
    4. Sun / True NodeTrine · 135′ orb · applying
    5. Moon / NeptuneSquare · 44′ orb · separating
    6. Moon / True NodeTrine · 141′ orb · separating
    7. Mercury / VenusSextile · 99′ orb · separating
    8. Mercury / JupiterTrine · 140′ orb · separating
    9. Venus / JupiterOpposition · 239′ orb · separating
    10. Jupiter / SaturnSextile · 260′ orb · applying
    11. Uranus / NeptuneSextile · 300′ orb · separating
    12. Neptune / PlutoSextile · 235′ orb · separating
    13. Pluto / True NodeSquare · 332′ orb · separating

    Paper geometry from the declared D5 positions and Part D motions. No fresh engine calculation; no chart interpretation.

    All source cells for E3

    Why Degree separation and the shared orb contract distinguish a measured aspect from a mere sign relationship.

    Your paper resultsun/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
    Reference answersun/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
    Tolerance · exact
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