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Sun sign
From 1900 to 2030 the Sun’s position comes from NASA JPL’s DE440 ephemeris, so the sign is right to within seconds of an ingress; around one we also print the exact crossing time.
Methodology
The formulas, the stated accuracy, the date ranges and the sources. Everything needed to reproduce any figure on this site — or to prove one of them wrong.
Why this page exists
An astrology site can be trusted on exactly one axis: whether its arithmetic is right. Everything else is interpretation, and interpretation is not something anyone can be an authority on. So instead of a paragraph about our credentials, here is the arithmetic — with its error bars.
If you find a discrepancy between a figure here and one from software you trust, we want the report. Calculation bugs are the one kind of mistake on a site like this that is genuinely fixable.
How close are the event times to an independent check?
Within seconds for the Sun and Moon, within minutes for the slowest planets. Every station, sign change and phase from 1900 to 2050 comes from NASA JPL’s DE440 ephemeris, and all 27,607 of those moments were recomputed with a second program, Swiss Ephemeris. The largest gap for a new or full moon is 7 s; for Pluto changing sign it is 17 min, because a tiny difference in position is a long time for a planet that barely moves.
The number in parentheses is how many moments of that kind were compared; Moon sign changes cover 1990–2050. Logarithmic scale: the axis runs from one second to half an hour.
Solar longitude
The position of the Sun along the ecliptic, from which the Sun sign and degree in a chart follow. d is days elapsed since J2000.0 (January 1, 2000, 12:00 UTC).
Mean longitude
L = 280.460° + 0.9856474° × d
Mean anomaly
g = 357.528° + 0.9856003° × d
Ecliptic longitude
λ = L + 1.915° × sin(g) + 0.020° × sin(2g)
The two sine terms are the equation of center — the correction for Earth’s orbit being an ellipse rather than a circle. They are also the reason the signs are unequal in length, which most sites do not mention.
Sign ingress: the minute the Sun changes sign
How we get sign dates to the minute instead of publishing a fixed range.
A sign begins the moment the Sun’s longitude crosses a multiple of 30°. For 1900 to 2050 we take that moment from a table solved against NASA JPL’s DE440 ephemeris.
Outside those years we use bisection on λ: bracket the crossing to a day, then halve the interval — evaluating λ each time — until the bracket is under a minute wide. That takes about a dozen halvings.
Why our dates can differ from other sites
This is why our sign boundaries are given for a specific year and printed with a time. It is also why they sometimes disagree with the dates on other sites by a day: those dates are an average, and the average is wrong in many individual years.
Running it across all twelve boundaries gives the sign lengths — Cancer around 31.45 days, Capricorn around 29.44 — and from there the share of births falling under each sign, which is not one twelfth.
Moon position and phase
Lunar longitude
λ☾ = L′ + 6.289° sin M′ + 1.274° sin(2D − M′) + 0.658° sin 2D + 0.214° sin 2M′ − 0.186° sin M − 0.114° sin 2F
L′ = mean longitude of the Moon, D = mean elongation, M = Sun’s mean anomaly, M′ = Moon’s mean anomaly, F = argument of latitude — each a linear function of time from J2000.0.
Elongation, age and illuminated fraction
E = λ☾ − λ☉ (mod 360°) · age = E ⁄ 360° × 29.530588853 d · k = (1 − cos E) ⁄ 2
What changed in 2026
Until September 2026 the phase came from the mean synodic month and the sign from the Moon’s mean motion alone. That ignored the Moon’s uneven speed and put the sign up to fifteen degrees — more than a day — out, while this page claimed a few hours. The series above replaced it in every calculator, and since October 2026 the times of phases (1900–2050) and of Moon sign changes (1990–2050) come from DE440 instead.
The age in days is the elongation scaled to an average month, so it can differ by a few hours from the time elapsed since the new moon; the phase name and illumination do not depend on it.
Ascendant
Local sidereal time
LST = 280.46061837° + 360.98564736629° × d + longitude
Rising degree
Asc = atan2( cos(RAMC), −(sin(RAMC)·cos(ε) + tan(φ)·sin(ε)) )
RAMC = LST in radians, ε = obliquity of the ecliptic, φ = geographic latitude.
The ascendant cannot be computed without a birth time and a latitude — not approximated, not defaulted to noon. Where we do not have them, we say the ascendant is unavailable instead of printing one. The check that matters: at the moment of sunrise the ascendant must equal the Sun’s longitude. Until September 2026 the signs inside the formula were transposed, which returned the descendant — the opposite sign — on every page that showed a rising sign; the sunrise test is how it was caught.
Retrograde periods
Stations and shadows from 1900 to 2050 come from the DE440 tables. The planetary model below places the planets in the chart calculators and covers the years outside that range.
For each planet we take the Keplerian elements — semi-major axis, eccentricity, inclination, mean longitude, longitude of perihelion and of the ascending node — and advance them linearly from J2000.0. Kepler’s equation is then solved by Newton iteration for the eccentric anomaly, which gives heliocentric coordinates.
Do that for both the planet and Earth, subtract, and the geocentric ecliptic
longitude is atan2(yp − ye, xp −
xe). A planet is retrograde exactly when that longitude is
decreasing, so a station is a change of sign in its daily motion — found by
bisection, the same technique as the sign ingress above.
The shadow periods are root-finds on a known target in the same function:
- the pre-retrograde shadow opens when the planet first reaches the longitude where the retrograde will end;
- the post-retrograde shadow closes when it returns to the longitude where the retrograde began.
Verification. The DE440 Mercury stations for 2025 match published almanacs to the minute. The Keplerian model they replaced in October 2026 was off by about an hour for Jupiter, three hours for Uranus and six to eight for Pluto, which is why event times no longer use it. See the Mercury retrograde page for the output.
Stated accuracy
What we will defend, figure by figure.
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Sun degree
The degree within the sign is good to the arcsecond from 1900 to 2030 and to about 0.01° outside those years: enough for decan and critical-degree work.
±10 seconds
Moon phase
Since October 2026 every phase from 1900 to 2050 comes from NASA JPL’s DE440 ephemeris; an independent recomputation with Swiss Ephemeris agrees to within 8 seconds. Eclipses reproduce NASA’s list for 2024–2030 exactly, lunar types included.
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Moon sign
From 1900 to 2030 the Moon comes from NASA JPL’s DE440 ephemeris, every 6 hours and interpolated: about two seconds of clock time, so the sign can be wrong only in the seconds around a change. Outside those years the lunar series gives about 0.3°, roughly half an hour.
≈0.5°
Ascendant
Dominated by your birth time, not our formula: the ascendant moves about 1° every 4 minutes, so a 15-minute uncertainty in your records is 4° of chart.
±5 seconds
Sign ingress (Sun)
Sun and planet ingresses 1900–2050 and Moon ingresses 1990–2050 are taken from JPL DE440 and printed to the minute. The Sun’s agree with Swiss Ephemeris to within 5 seconds; slow planets less closely (Pluto to about 17 minutes), because a tiny difference in position is a long time for a planet that barely moves.
±1 minute
Retrograde stations
Stations 1900–2050 come from JPL DE440. Mercury and Venus agree with Swiss Ephemeris to within 20 seconds, Mars to Uranus within about a minute, Neptune within 2 minutes; Pluto’s median difference is 1 minute and its largest 16, because near a station it hardly moves. The 2025 Mercury stations match published almanacs to the minute.
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Planet positions in calculators
Since October 18, 2026 the birth chart, kundli, synastry and the other calculators place the Sun, the Moon and Mercury through Pluto from NASA JPL’s DE440 ephemeris for 1900 to 2030, checked against Swiss Ephemeris. Outside those years they use Keplerian elements corrected for precession, about 0.2°.
Statistical figures
Where a page says a result is rare, the number behind it was produced by enumeration, not by quoting someone. The standard range is January 1, 1930 to December 31, 2029 — 36,525 dates, printed next to the figure so you can check it.
Two findings from that process are worth naming here because they contradict what is published elsewhere:
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Six of the 22 Destiny Matrix arcana never appear as a central arcana.
Arcana 1, 2, 15, 17, 19 and 21 occur zero times across all 36,525 dates from
1930 to 2029, and four more land under half a percent each, while seven take
between 10.7% and 11.1% each. See the arcana reference.
Note: this depends on the reduction method. We reduce by summing digits, which is the canonical construction; schools that reduce by subtracting 22 produce a different set of gaps. We previously used the latter and published a parity argument that does not survive the change — it is withdrawn. - Life path 2 and 4 are rarer than they look. Not because of anything mystical: before they reduce, the master-number rule diverts 58% of the sums that would give 2 to 11, and 28% of those that would give 4 to 22. The distribution is on the life path page.
Both are reproducible in a few lines of code in any language. That is the point.
Sources
Named, including for the traditional material — so you can see where a meaning actually comes from and how old it really is.
Event times
Retrograde stations and shadows, Sun, Moon and planet ingresses, Moon phases and eclipses, 1900–2050: apparent geocentric longitudes (true equinox of date) from NASA JPL’s DE440 ephemeris (Park et al. 2021), every moment recomputed with Swiss Ephemeris (version 2.10.03, Moshier analytical theory) as an independent check. Moon sign changes are tabulated for 1990–2050. Local times use the IANA time-zone database.
Astronomical formulas
Outside 1900–2030 only: standard low-precision solar and lunar series as published in the Astronomical Almanac and in Meeus, Astronomical Algorithms (2nd ed., 1998).
Planetary positions
Calculator positions 1900–2030: apparent geocentric longitudes from NASA JPL’s DE440 ephemeris, daily for the planets and every 6 hours for the Moon, interpolated. Outside those years, Keplerian elements and their century rates from the JPL Solar System Dynamics table “Keplerian Elements for Approximate Positions of the Major Planets”, valid 1800–2050, corrected for precession to the date. Pluto, since removed from that table, uses the elements of its earlier edition.
Lunar theory
Outside 1900–2030 only: the six largest periodic terms of the Moon’s longitude — the two terms of the equation of center, evection, variation, the annual equation and the reduction to the ecliptic — with coefficients as tabulated in Meeus, Astronomical Algorithms, chapter 47.
Obliquity
IAU 1976 value of 23.4393° at J2000.0, with linear secular decrease applied.
Tarot correspondences
Golden Dawn attributions as recorded in Book T (1888) and carried into Waite’s Pictorial Key to the Tarot (1911).
Numerology tables
Pythagorean A=1…I=9 cycle, and the Chaldean table as given in Cheiro, Book of Numbers (1926) — which assigns by sound and never uses 9.
Dream prevalence
Nielsen et al., “The typical dreams of Canadian university students”, Dreaming 13(4), 2003 — the source of the chased/teeth/falling percentages.
Runes
Elder Futhark order and names from the Anglo-Saxon and Icelandic rune poems; meanings labeled as reconstructed where they are.
Gem data
Chemical formulas, crystal systems and Mohs values from standard mineralogical reference; origins from current commercial production.
Chinese calendar
Lunisolar New Year dates tabulated 1924–2033 from the traditional calendar, not approximated from a fixed date.
Destiny Matrix
Method as taught in the Russian-language schools that assembled it during the 2010s; the arithmetic is uncontested, the diagonals are not.
What we deliberately do not do
- No full ephemeris inside the chart calculators. Charts are cast from the formulas on this page, which anyone can check with a pocket calculator. DE440 is used where timing to the minute matters — stations, sign changes, phases — and the trade is stated here rather than hidden behind a claim of astronomical accuracy.
- No quadrant houses. Western charts use equal houses — 30° each from the exact ascendant degree — rather than a system such as Placidus: equal houses need nothing but the ascendant, while the quadrant schools disagree with one another and there is no basis for choosing between them. The kundli follows the Vedic whole-sign convention.
- No progressions or solar arcs.
- No tradition dressed up as a finding. If the only support for a claim is that someone wrote it down in 1888, the page says 1888.
Common questions
How accurate are the planetary positions on AstroHot?
In a birth chart born 1900 to 2030, the Sun, the Moon and the planets come from NASA JPL’s DE440 ephemeris, accurate to about an arcsecond, so a sign is wrong only in the seconds around a change. Dates and times of events from 1900 to 2050 come from NASA JPL’s DE440 ephemeris, and an independent Swiss Ephemeris recomputation agrees with them to within seconds for the Sun and Moon.
Why do your zodiac dates differ from other sites?
Because most sites publish one fixed calendar range, and it is wrong in some years. We use the exact moment the Sun crosses each 30° boundary in the year you are looking at, printed to the minute. Sign lengths genuinely vary: Cancer runs about 31.45 days and Capricorn about 29.44, because Earth moves faster near perihelion.
Where do the statistical figures come from?
They are computed by enumerating every date in the stated range, usually 1930 to 2029, which is 36,525 dates. Nothing is quoted from another site. The range is printed next to every figure so you can reproduce it.
Do you use Swiss Ephemeris or NASA data?
Both, for different jobs. Event times from 1900 to 2050 — stations, sign changes, phases and eclipses — come from NASA JPL’s DE440 ephemeris. Every station, sign change and phase was recomputed with Swiss Ephemeris as a check, and the eclipses were matched against NASA’s list for 2024–2030. The chart calculators use the published formulas on this page, which anyone can reproduce with a calculator.
Report an error
Send the input you used, the figure we returned and the figure you expected to [email protected]. See also about the site and the disclaimer.
Cite this page
AstroHot. “Methodology — How Every Figure on AstroHot Is Calculated.” Accessed October 30, 2026. https://astrohot.com/methodology/
For Wikipedia
{{cite web |title=Methodology — How Every Figure on AstroHot Is Calculated |url=https://astrohot.com/methodology/ |website=AstroHot |access-date=2026-10-30}}
