Astrological Concepts

Coordinate System

Ecliptic Longitude

Ecliptic longitude is the position of a celestial body measured along the ecliptic (the Earth’s orbital plane around the Sun), expressed in degrees from 0° to 360°.

  • 0° = Vernal point (0° Aries)

  • 90° = Summer solstice (0° Cancer)

  • 180° = Autumn equinox (0° Libra)

  • 270° = Winter solstice (0° Capricorn)

Ecliptic Latitude

Ecliptic latitude measures the angular distance of a body above (+) or below (-) the ecliptic plane.

Distance in AU

The Astronomical Unit (AU) is the average Earth-Sun distance, approximately 149.6 million km.

Astronomical Time

Coordinated Universal Time (UTC)

UTC is the reference time standard, based on international atomic time.

Julian Day

The Julian Day (JD) is a continuous dating system used in astronomy. JD begins at noon UTC on January 1, 4713 BCE in the proleptic Julian calendar.

# Conversion in Ketu
from ketu.ephemeris.time import utc_to_julian
jday = utc_to_julian(datetime_utc)

Celestial Bodies

Ketu calculates the positions of 14 celestial bodies (body IDs 0–13):

Classical Planets

  • Sun ☉ (body_id=0)

  • Moon ☽ (body_id=1)

  • Mercury ☿ (body_id=2)

  • Venus ♀ (body_id=3)

  • Mars ♂ (body_id=4)

  • Jupiter ♃ (body_id=5)

  • Saturn ♄ (body_id=6)

Modern Planets

  • Uranus ♅ (body_id=7)

  • Neptune ♆ (body_id=8)

  • Pluto ♇ (body_id=9)

Fictitious Points

  • Rahu ☊ (body_id=10): Mean North Node

  • Ketu ☋ (body_id=11): Mean South Node

  • Lilith ⚸ (body_id=12): Black Moon (Mean Apogee)

Centaur Body (New in v1.3)

  • Chiron ⚷ (body_id=13): Centaur body between Saturn and Uranus. Computed via embedded Chebyshev polynomial coefficients; valid range 1900–2100 (expanded in v1.4). Out-of-range input is silently clamped to the nearest segment boundary. See Chiron for details.

Aspects

Harmonic Theory

Aspects lean on the geometry of the zodiac circle. A harmonic divides a base angle into n equal parts, and the resulting fractions act as landmarks for the main kinds of planetary encounters.

The default framing uses the half-circle base (180°, the distance between conjunction and opposition): harmonics 1, 2, 3, 6 yield the 7 classical-to-Ptolemaic aspects (Conjunction, Semi-sextile, Sextile, Square, Trine, Quincunx, Opposition). This is the TRADITIONAL preset, the library default.

Full-circle harmonics (5, 9, 10 — quintiles, noviles, deciles) use a 360° base and are available as opt-in presets; they are not part of the default set.

Harmonic 1 (180°/1 = 180°)

  • Conjunction (0°): same point

  • Opposition (180°): opposite point

Harmonic 2 (180°/2 = 90°)

  • Square (90°): quarter circle

Harmonic 3 (180°/3 = 60°)

  • Sextile (60°): 1/3 of semi-circle

  • Trine (120°): 2/3 of semi-circle

Harmonic 6 (180°/6 = 30°)

  • Semi-sextile (30°): 1/6 of semi-circle

  • Quincunx (150°): 5/6 of semi-circle

The full-circle minor harmonics — H5 (quintiles), H9 (noviles), H10 (deciles) — are available in code but are not part of the default framing. They are opt-in via the EXTENDED preset or aspects_for_harmonics([5, 9, 10]) (see Configurable Aspect Sets below).

Summary Table

Harmonic

Division

Aspects

1

180°/1

Conjunction (0°), Opposition (180°)

2

180°/2

Square (90°)

3

180°/3

Sextile (60°), Trine (120°)

6

180°/6

Semi-sextile (30°), Quincunx (150°)

The table above lists the 7 default half-circle aspects (the TRADITIONAL preset). The full-circle minor aspects (H5/H9/H10) are available in code; see the note above and Configurable Aspect Sets.

Default aspect set (v1.3+): the library default is the 7 half-circle aspects (harmonics 1, 2, 3, 6 — TRADITIONAL preset): Conjunction, Semi-sextile, Sextile, Square, Trine, Quincunx, Opposition. The full-circle minor harmonics (H5/H9/H10) are opt-in and not included in the default.

Configurable Aspect Sets (New in v1.1, updated in v1.3)

Rather than always computing all 14 aspects, you can select a preset or pass a custom mask:

  • TRADITIONAL (library default): the 7 half-circle aspects — Conjunction, Semi-sextile, Sextile, Square, Trine, Quincunx, Opposition (harmonics 1, 2, 3, 6)

  • CLASSICAL: Conjunction, Sextile, Square, Trine, Opposition (5 major aspects; the old v1.2 default — still available as the opt-in “5 majors” preset)

  • EXTENDED: all 14 aspects

from ketu.aspects import calculate_aspects, CLASSICAL, TRADITIONAL, EXTENDED

# New library default (7 half-circle aspects):
aspects = calculate_aspects(jday)                        # uses TRADITIONAL

# Old 5-major default (restore v1.2 behavior):
aspects = calculate_aspects(jday, aspects=CLASSICAL)     # 5 aspects

# All 14 aspects:
aspects = calculate_aspects(jday, aspects=EXTENDED)      # 14 aspects

Harmonic composition with aspects_for_harmonics (New in v1.3): build a custom aspect set from any combination of the supported harmonics. This is the harmonic-selection sister function to the named presets:

from ketu.aspects import aspects_for_harmonics

# Compose the library default explicitly (7 half-circle):
mask = aspects_for_harmonics([1, 2, 3, 6])

# Opt into the full-circle minor aspects:
minors = aspects_for_harmonics([5, 9, 10])

# Just the Sextile and Trine (harmonic 3):
h3_only = aspects_for_harmonics([3])

# All 14:
all14 = aspects_for_harmonics([1, 2, 3, 5, 6, 9, 10])

aspects_for_harmonics returns a frozen numpy.bool_ mask of length 14, which can be passed directly as the aspects= argument to any Ketu function. Valid harmonics: {1, 2, 3, 5, 6, 9, 10}.

Dynamic Harmonic Generator (generate_harmonic_aspects)

generate_harmonic_aspects(h) builds aspect specs on the fly for any integer harmonic h (2 ≤ h ≤ 64), not just the named-preset harmonics. It uses the full-circle 360° convention folded to 0–180°, and the returned array has the same dtype as core.aspects, making it a drop-in for every consumer.

from ketu.aspects import generate_harmonic_aspects

# Harmonic 7: 3 unique folded angles (septile family)
specs = generate_harmonic_aspects(7)
print(len(specs))          # 3
print(specs['name'])       # [b'H7-1', b'H7-2', b'H7-3']
print(specs['angle'])      # [51.43, 102.86, 154.29]
print(specs['coef'])       # [0.1429, 0.2857, 0.4286]

# Pass to calculate_aspects via dynamic_specs:
from ketu.aspects import calculate_aspects
jd = 2451545.0  # J2000
result = calculate_aspects(jd, dynamic_specs=generate_harmonic_aspects(7))

The returned array is a drop-in for core.aspects (same dtype) and is passed as the dynamic_specs= argument to calculate_aspects, find_aspects_between_dates, and calculate_synastry.

Note on orbs: Dynamic harmonic orbs use coef = k / h (full-circle convention). For high harmonics this yields orbs roughly half the size of the equivalent half-circle aspect — e.g. a septile (H7-1, coef ≈ 0.143) gives a smaller orb than a sextile (coef ≈ 0.333) for the same body pair. This is accepted behaviour: the two conventions coexist without unification (see the v1.4 release notes).

Synthetic harmonic naming (H{h}-{k})

Ketu uses two distinct channels for harmonic aspects, and they follow different naming rules.

GENERATOR channel — generate_harmonic_aspects(h) always emits H{h}-{k} names (k = 1…h//2), uniform and mechanical, with no traditional-name substitution. The emitted name bytes are always b'H{h}-{k}' (S16 dtype), frozen across v1.5+ minor and patch releases.

DETECTION channel — when calculate_aspects or find_aspects_between_dates detects an angle that collides with a canonical table aspect, they report the canonical table name with static-first priority. For example, a 120° hit is reported as Trine (i_asp=9), not H3-1 (i_asp=-2). The H{h}-{k} label only appears in result rows for genuinely off-table angles (i_asp=-2 sentinel).

Traditional-name reference table (documentation only — never emitted by the generator):

Synthetic name

Traditional name

H5-1

Quintile

H5-2

Biquintile

H7-1

Septile

H9-1

Novile

H9-2

Binovile

H9-4

Quadnovile

These traditional names are provided here as a human reference only. They never appear in the structured-array name bytes emitted by generate_harmonic_aspects.

--harmonics h7 — arbitrary harmonics on the CLI (New in v1.5)

The CLI accepts the h<N> token form for --harmonics to select an arbitrary harmonic family on the command line, without writing any Python code.

Syntax: --harmonics h<N> (h-prefix, case-insensitive; e.g. h7, H7). N must be an integer in [2, 64]. The token selects only the chosen harmonic family via the dynamic_specs= channel (see Synthetic harmonic naming (H{h}-{k}) for the two-channel explanation). The static aspect table mask is empty — only H{N}-{k} dynamic aspects are detected.

Semantics: the resolved-config header on stderr reads # Aspect set: h7 (...). The stdout positions block and “Aspect Timing Example” trailing block are always emitted unchanged (the timing example uses the classical Sun-Moon aspects regardless of the --harmonics selection).

Tight-grammar boundary — what is supported vs. deferred:

Form

Status

Example

h<N> alone

Supported (v1.5+)

--harmonics h7

Comma-separated index list

Supported (pre-existing)

--harmonics 0,4,9

Named preset

Supported (pre-existing)

--harmonics classical

Multi-harmonic mixing (h7,h11)

NOT YET SUPPORTED (HARMF-01)

rejected with error

Mixed preset+harmonic (traditional,h7)

NOT YET SUPPORTED (HARMF-01)

rejected with error

Mixing forms (h7,h11, traditional,h7) are deferred to HARMF-01 and currently rejected with an argparse error. Do not attempt them in v1.5.

Worked example (J2000, septile family):

python -m ketu --harmonics h7 aspects --date 2000-01-01T12:00:00Z

This emits septile-family aspects (H7-1 ≈51.43°, H7-2 ≈102.86°, H7-3 ≈154.29°) for all body pairs in orb at J2000, followed by the classical “Aspect Timing Example” block. The stderr header confirms the resolved selection: # Aspect set: h7 (3 aspects: H7-1 51°, H7-2 103°, H7-3 154°).

Orbs

Orb Principle

In the Arabic tradition, each planet has an orb (zone of influence) that is specific to it. The orb of an aspect between two planets is calculated as the half-sum of the orbs of the two planets, multiplied by the harmonic coefficient.

# Orb calculation in Ketu
orb = [(orb_planet1 + orb_planet2) / 2] * harmonic_coefficient

Default Orbs of Planets

Body

Orb

Sun, Moon

12°

Venus, Jupiter, Saturn

10°

Mercury, Mars

8°

Uranus, Neptune

6°

Pluto, Chiron

4°

Rahu, Lilith

0°

Aspect Types and Harmonic Coefficients

The 7 default half-circle aspects (TRADITIONAL preset, harmonics 1, 2, 3, 6):

Aspect

Angle

Symbol

Harmonic

Coefficient

Conjunction

0°

☌

1

1

Semi-sextile

30°

⚺

6

1/6

Sextile

60°

⚹

3

1/3

Square

90°

□

2

1/2

Trine

120°

△

3

2/3

Quincunx

150°

⚻

6

5/6

Opposition

180°

☍

1

1

The 7 full-circle minor aspects (H5/H9/H10) remain available via EXTENDED / aspects_for_harmonics([5, 9, 10]) and are listed in the full 14-aspect table in the API reference.

Calculation Examples

Sun-Moon Aspect (Conjunction)

  • Sun Orb: 12°

  • Moon Orb: 12°

  • Coefficient: 1 (conjunction)

  • Final Orb: (12 + 12) / 2 × 1 = 12°

Mercury-Mars Aspect (Square)

  • Mercury Orb: 8°

  • Mars Orb: 8°

  • Coefficient: 1/2 (square)

  • Final Orb: (8 + 8) / 2 × 0.5 = 4°

Venus-Jupiter Aspect (Sextile)

  • Venus Orb: 10°

  • Jupiter Orb: 10°

  • Coefficient: 1/3 (sextile)

  • Final Orb: (10 + 10) / 2 × 0.333 = 3.33°

House Systems

What Are Houses?

The astrological houses divide the local sky into twelve sectors based on the observer’s geographic location and the time of birth. Unlike the zodiac signs (which are fixed along the ecliptic), houses rotate with the Earth’s daily rotation and depend on the local horizon and meridian.

Ketu supports six house systems (New in v1.1/v1.2):

  • Placidus ("placidus"): The most widely used system in Western astrology. Divides each quadrant by time rather than space.

  • Koch ("koch"): Similar to Placidus but using a different time-division formula; sensitive to high latitudes.

  • Porphyry ("porphyry"): Divides each quadrant into three equal parts by longitude. Simpler and works at all latitudes.

  • Whole Sign ("whole_sign"): Each house corresponds to an entire zodiac sign, starting from the rising sign.

  • Equal ("equal"): Houses are 30° each, starting from the Ascendant degree.

  • Regiomontanus ("regiomontanus"): Divides the celestial equator into equal parts; popular in medieval astrology.

High Latitude Behavior

Placidus and Koch may fail to compute cusps at very high latitudes (above approximately 66°). Use polar_fallback="porphyry" to fall back gracefully, or polar_fallback="raise" (default) to receive a HighLatitudeError.

from ketu.houses import calculate_houses, HighLatitudeError

jd = 2451545.0  # J2000
try:
    h = calculate_houses(jd, lat=70.0, lon=25.0, system="placidus")
except HighLatitudeError:
    h = calculate_houses(jd, lat=70.0, lon=25.0, system="porphyry")

See Houses for the full API reference and examples.

Sect (Day vs. Night Chart)

What Is Sect?

Sect is a classical doctrine distinguishing day charts (Sun above the horizon at birth) from night charts (Sun below the horizon). This distinction affects the calculation of certain Arabic Parts such as the Part of Fortune and the Part of Spirit, which invert their formulas between day and night charts.

In Ketu, is_day_chart(jd, lat, lon) returns True when the Sun is above the horizon at the given time and location. This helper is used internally by calculate_part for sect-sensitive lots.

from ketu.charts import is_day_chart

jd = 2451545.0       # J2000
lat, lon = 48.8566, 2.3522  # Paris
print(is_day_chart(jd, lat, lon))

See Arabic Parts for how sect influences Fortune and Spirit formulas.

Equatorial Declination — New in v1.5

Declination δ vs. Ecliptic Latitude β

Ketu tracks two distinct north/south quantities for each body:

  • Ecliptic latitude β — angular distance above/below the ecliptic plane. Returned by lat(jd, body). The function is_ascending tracks whether β is rising.

  • Equatorial declination δ — angular distance north/south of the celestial equator. Returned by declination(jd, body). The function is_ascending_declination tracks whether δ is rising (montante/descendante).

These are different quantities and disagree on different days. “Ascending Moon” is ambiguous without specifying which coordinate system:

Function

Tracks

Concept

is_ascending(jd, 1)

β rising (ecliptic latitude)

Traditional latitude motion

is_ascending_declination(jd, 1)

δ rising (declination)

Biodynamic montant/descendant

Proof of β-vs-δ independence: at 2025-03-07 (JD=2460742.0), Moon near a major standstill peak (δ≈+28.66°), is_ascending_declination=True (dδ/dt=+0.30°/day) while is_ascending=False (β descending). They flip on different days.

Montant / Descendant (Biodynamic Framing)

In biodynamics, the montant/descendant cycle refers to the trajectory of the Moon’s own equatorial declination δ — not to zodiacal sign conventions or ecliptic latitude.

  • Montante (ascending in δ): dδ/dt > 0, Moon moving northward. is_ascending_declination returns True.

  • Descendante (descending in δ): dδ/dt < 0, Moon moving southward. is_ascending_declination returns False.

The Moon’s δ cycle period is approximately 27.21 days (draconic/nodal month) — the time between two successive northward crossings of the celestial equator. This is close to, but distinct from, the 27.32-day tropical month.

from ketu.calculations import (
    declination,
    declination_velocity,
    is_ascending_declination,
)

jd = 2451545.0  # J2000

delta = declination(jd, 1)
vel   = declination_velocity(jd, 1)

print(f"Moon δ: {delta:.4f}°")
print(f"Moon dδ/dt: {vel:.4f}°/day")
print("Montante" if is_ascending_declination(jd, 1) else "Descendante")

Out-of-Bounds (OOB)

A body is out-of-bounds (hors limites) when its declination exceeds the instantaneous obliquity of the ecliptic: |δ| > ε(jd).

Under normal conditions no planet can exceed the obliquity — the Sun’s declination defines the obliquity bounds (±ε ≈ ±23.4°). The Moon is the exception: because the lunar orbital plane is tilted ~5° relative to the ecliptic, the Moon can exceed the Sun’s extreme declinations during the major lunar standstill (~18.6-year nodal cycle). During 2024–2025, the Moon reaches |δ| ≈ 28.7°.

The OOB threshold uses the instantaneous true obliquity ε(jd) — not mean obliquity — because nutation shifts ε by up to ±17 arcseconds.

from ketu.calculations import is_out_of_bounds

jd_standstill = 2460742.0   # 2025-03-07, near major standstill peak

print(f"Moon OOB: {is_out_of_bounds(jd_standstill, 1)}")   # True

CHART_DTYPE — body_decl field (New in v1.5)

CHART_DTYPE gains an additive field body_decl (float64[14]) holding the equatorial declination δ for each of the 14 bodies. This is an additive dtype change: the body count (14) is unchanged, but downstream code using positional access or .view() on CHART_DTYPE must adapt (Kala impact documented, not auto-migrated).

from ketu.charts import compute_chart

chart = compute_chart(jd, 48.8566, 2.3522)
moon_decl = chart["body_decl"][1]   # Moon δ in degrees

Declination Aspects — New in v1.6

Declination aspects compare two bodies on the equatorial declination axis (δ), independent of ecliptic longitude. The detector lives in the additive ketu.declination subpackage — CHART_DTYPE is unchanged. It consumes chart["body_decl"] (the (14,) field shipped in v1.5).

Parallel and Contra-Parallel

  • Parallel (P): two bodies share the same declination δ AND are on the same side of the celestial equator (both north OR both south). Signed-δ rule: sign(δ₁) == sign(δ₂) ≠ 0  AND  |δ₁ − δ₂| ≤ orb. The same-hemisphere rule is strict — the dominant convention across Sepharial, Carter, Cafe Astrology, Lunarium, McAfee, Kerykeion, and astro.com.

  • Contra-parallel (CP): equal magnitude of δ but on opposite sides of the celestial equator. Signed-δ rule: sign(δ₁) ≠ sign(δ₂)  AND  both ≠ 0  AND  |δ₁ + δ₂| ≤ orb.

  • Zero-sign trap: a body exactly on the celestial equator (δ = 0, np.sign → 0) forms neither a parallel nor a contra-parallel. Two bodies exactly at δ = 0 have 0° separation but are not flagged.

import numpy as np
from ketu.declination import find_declination_aspects

decl = np.zeros(14)
decl[0] = 20.0   # Sun  δ = +20.0°
decl[1] = 20.5   # Moon δ = +20.5°  → same hemisphere, gap 0.5° ≤ 1.0° orb

aspects = find_declination_aspects(decl)
print(aspects)   # [(0, 1, 'P', 0.5, 1.0)] — Sun/Moon parallel

The Orb Formula (Body-Derived)

The per-pair orb on the declination axis is:

δ_orb(b1, b2) = max((bodies['orb'][b1] + bodies['orb'][b2]) / 2 × DECLA_COEF, MIN_DECL_ORB)

with DECLA_COEF = 1/12 ≈ 0.0833 and MIN_DECL_ORB = 0.5°.

Worked Sun/Moon example: Sun orb 12° + Moon orb 12° → mean 12° → × 1/12 → exactly 1.0°. The coefficient 1/12 is the reciprocal of the maximum body orb (Sun/Moon both at 12°) — a justified exact fraction, not a magic number — chosen so Sun/Moon lands on the published 1° natal consensus (Carter, Cafe Astrology, astro.com).

Floor example: zero-orb bodies (Rahu, Ketu, Lilith — orb 0) → formula yields 0° → floored to 0.5° so they remain detectable.

Pair

δ orb

Sun / Moon

1.0°

Sun / Mars

0.833°

Jupiter / Saturn

0.833°

Uranus / Neptune

0.5°

Rahu / Lilith

0.5° (floor)

Biodynamic Framing

Parallel ≈ conjunction by declination; contra-parallel ≈ opposition by declination (Sepharial: “they act as if in conjunction”; Carter couples parallel with conjunction). These are ANGLES/relationships between bodies on the δ axis — the same aspect-centric biodynamic framing as the rest of Ketu, not zodiacal-sign conventions.

Parallel ≠ Longitude Conjunction (the Key Distinction)

Two bodies can be parallel in declination without being conjunct in ecliptic longitude, and vice-versa. Declination δ (equatorial) and longitude (ecliptic) are independent measurements. A “double whammy” (both conjunct AND parallel) is notably stronger, but the detection paths are entirely separate — find_declination_aspects consumes only body_decl, never longitudes.

Symbols and Abbreviations

Aspect

Symbol

Text abbrev

Notes

Parallel

// (proposed U+2BDD)

P

‖ / ⫽ as text fallbacks

Contra-parallel

# (proposed U+2BDE)

CP

Dominant in printed tables

The // and # glyphs are proposals from David Faulks (Unicode L2/16-174, 2016) — not yet in the Unicode standard. Text abbreviations P / CP match Solar Fire and Astrodienst conventions and are used as the kind field values in DECLA_ASPECT_DTYPE.

Out-of-Bounds Interaction

OOB bodies (|δ| > ε, tracked via is_out_of_bounds from v1.5) participate in P/CP detection mechanically identically — the formula does not change. “Both OOB” is an interpretive annotation the caller composes (e.g. by combining is_out_of_bounds results with the aspect output), not a detection flag. Some authors (Boehrer, McAfee) consider two-OOB parallels especially intense — a delineation note only.

Planetary Movements

Retrogradation

Retrogradation is the apparent movement of a planet that seems to move backward in the zodiac. It’s an optical illusion due to differences in orbital speed between Earth and the observed planet.

from ketu.calculations import is_retrograde

if is_retrograde(jday, planet_id):
    print("Planet retrograde")

Average Speeds

Planet

Average Speed

Complete Cycle

Moon

13.18°/day

27.3 days

Mercury

1.38°/day

88 days

Venus

1.20°/day

225 days

Sun

0.99°/day

365.25 days

Mars

0.52°/day

687 days

Jupiter

0.08°/day

11.9 years

Saturn

0.03°/day

29.5 years

Uranus

0.01°/day

84 years

Neptune

0.01°/day

165 years

Pluto

0.00°/day

248 years

Zodiac Signs

No

Sign

Symbol

Start Degree

End Degree

1

Aries

♈

0°

30°

2

Taurus

♉

30°

60°

3

Gemini

♊

60°

90°

4

Cancer

♋

90°

120°

5

Leo

♌

120°

150°

6

Virgo

♍

150°

180°

7

Libra

♎

180°

210°

8

Scorpio

♏

210°

240°

9

Sagittarius

♐

240°

270°

10

Capricorn

♑

270°

300°

11

Aquarius

♒

300°

330°

12

Pisces

♓

330°

360°

 
from ketu.calculations import body_sign
import ketu

# Get a planet's sign
sign_data = body_sign(longitude)
sign_index = sign_data[0]  # 0-11
degrees = sign_data[1]      # 0-29
minutes = sign_data[2]      # 0-59
seconds = sign_data[3]      # 0-59

sign_name = ketu.signs[sign_index]

Planetary Configurations

Grand Trine

Three planets forming trines with each other (equilateral triangle of 120°).

T-Square

Two planets in opposition (180°), both square (90°) to a third planet (apex).

Yod (Finger of God)

Two planets in sextile (60°), both quincunx (150°) to a third planet (apex).

Grand Square

Four planets forming four squares (90°) and two oppositions (180°), creating a square in the chart.

Cycles and Returns

Planetary Returns

A planetary return occurs when a planet returns to its natal position (same ecliptic longitude).

Main returns:

  • Solar return: Astrological birthday (365.25 days)

  • Lunar return: Approximately every 27.3 days

  • Jupiter return: Approximately every 12 years

  • Saturn return: Approximately at 29-30 years and 58-60 years

Ketu provides dedicated functions for solar and lunar returns in ketu.returns. See Predictive Charts for details.

Next Steps