Library of date/time manipulation routines for practical astronomy. It is named in honor of the prominent classical scholar Joseph Scaliger (1540-1609), who proposed the Julian Period1.
$ go get github.com/skrushinsky/scaliger
Most of the astronomical calculations are based on so called Julian date (JD), which is the number of days elapsed since mean UT noon of January 1st 4713 BC.
CivilToJulian(date CivilDate) float64 converts calendar date into Julian days.
date := CivilDate{Year: 837, Month: 4, Day: 10.3}
jd := CivilToJulian(date) // 2026871.8The calendar date is represented by CivilDate structure.
type CivilDate struct {
Year int // year, astronomical, negative for BC dates
Month int // month number, 1-12
Day float64 // day, fractional part represents hours
}JulianToCivil(jd float64) CivilDate converts Julian days into the calendar date.
date := JulianToCivil(2455197.5) // CivilDate{Year: 2010, Month: 1, Day: 1.0}Both the conversion functions have their conterparts accepting and receiving dates as strings in RFC-3339 format:
jd, error := DateStringToJulian("2023-04-13T06:00:00Z") // 2460047.86458333date_string := JulianToDateString(2460047.86458333) // 2023-04-13T06:00:00ZThis may be usefull for consiole applications (see the examples) and dynamic libraries called from applications written in other programming languages.
Other utilitity functions from the package are mostly used internally.
JulianMidnight(jd float64) float64calculates JD at Greenwich midnightJulianDateZero(year int) float64calculates JD corresponding to the Zero dayExtractUTC(jd float64) float64converts fractional part of a JD to decimal hours (UTC)EqualDates(a, b CivilDate) boolcompares two datesIsLeapYear(year int) boolreturnstrueif given year is a leap yearDayOfYear(date CivilDate) intreturns number of days in the year up to a particular date.
Sidereal Time is reckoned by the daily transit of a fixed point in space (fixed with respect to the distant stars), 24 hours of sidereal time elapsing between a successive transits.
JulianToSidereal(jd float64, options SiderealOptions) float64 converts Julian date to
Sidereal Time.
opts := SiderealOptions{Dpsi: -0.0043, Eps: 23.4443, Lng: 37.5833}
lst := JulianToSidereal(jd, opts) // 23.0370...SiderealOptions structure controls type of the result.
type SiderealOptions struct {
Lng float64 // geographical longitude, degrees, negative westwards
Eps float64 // obliquity of the ecliptic, degrees
Dpsi float64 // nutation in longitude, degrees
}- Geographical longitude,
Lng. If initialized, the function calculates Local Sidereal Time. Without it Greenwich Sidereal Time2 - Obliquity of the ecliptic,
Epsand and nutation in longitude,Dpsi. If provided, then the result is apparent Sidereal Time, or the Greenwich hour angle of the true vernal equinox. For Mean Sidereal Time, referred to the mean vernal point 3, leave these fields empty:
opts := SiderealOptions{Lng: 37.5833}
...To calculate obliquity of the ecliptic and nutation, use nutequ package.
By default, all the options are zeroes which means that a call with empty options:
JulianToSidereal(jd, SiderealOptions{}) will return Greenwich Mean Sidereal Time.
DeltaT indicates the difference between UTC (Universal Coordinated Time) and TDT (Terrestrial Dynamic Time), which used to be called 'Ephemeris time' in the last century. While UTC is not a uniform time scale (it is occasionally adjusted, due to irregularities in the Earth's rotation), TDT is a uniform time scale which is needed as an argument for mathematical theories of celestial movements.
The exact value of the difference DeltaT = TDT - UTC can be deduced only from observations.
Approximate value in seconds for a given Julian Date may be obtained by DeltaT(jd float64) float64
function. To correct a JD for TDT, add DeltaT seconds divided by 86400 (seconds per day).
jd := 2459040.5 // Julian date for 2020-07-10
dt := DeltaT(jd) // 93.81 seconds
jde := jd + dt / 86400 // Dynamic time.Obliquity of the ecliptic is the angle between the celestial equator and the ecliptic.
To calculate Mean Obliquity, angle which the ecliptic makes with the mean equator,
use MeanObliquity(jd float64) float64 function. For better accuracy correct JD for TDT
(see Dynamic Time).
The formula used should give an accurate results (less than 1 srcsecond) within 2000 years around the epoch J2000.0 (see J.Meeus, Astronomical Algorithms, 2d edition, p.147).
TrueObliquity(jd, deps float64) float64 function calculates True Obliquity, where deps
is the nutation in obliquity.
TrueObliquity(jd, 0) (with zero deps) gives the same result as MeanObliquity(jd).
Nutation(jd float64) (dpsi float64, deps float64) calculates
dpsi, nutation in longitude, arc-degreesdeps, nutation in obliquity, arc-degrees
AlmostEqual(a, b, threshold float64)compares two floating point numbers with a given precision.Frac(x float64) float64fractional part of a number.ReduceHours(hours float64) float64reduces hours to range0 >= x < 24.ReduceDeg(deg float64) float64reduces arc-degrees to range0 >= x < 360.ReduceRad(rad float64) float64reduces radians to range0 >= x < PI * 2.Polynome(t float64, terms ...float64) float64calculates polynome:a1 + a2*t + a3*t*t + a4*t*t*t....Radians(deg float64) float64converts arc-degrees to radians.Degrees(rad float64) float64converts radians to arc-degrees.Frac360(x float64) float64reduces arc-degrees, much likeReduceHours, used with polinomial function for better accuracy.
Please, see the API docs for details.
examples/ directory contains examples of the library usage. They will be extended over time.
There is disagreement between astronomers and historians about how to count the years preceding the year 1. Astronomers generally use zero-based system. The year before the year +1, is the year zero, and the year preceding the latter is the year -1. The year which the historians call 585 B.C. is actually the year -584.
Zero day is a special case of date: it indicates 12h UT of previous calendar date. For instance, 1900 January 0.5 is often used instead of 1899 December 31.5 to designate start of the astronomical epoch.
Civil calendar in most cases means proleptic Gregorian calendar. it is assumed that Gregorian calendar started at Oct. 4, 1582, when it was first adopted in several European countries. Many other countries still used the older Julian calendar. In Soviet Russia, for instance, Gregorian system was accepted on Jan 26, 1918. See Wiki article.
You may contribute to the project by many different ways, starting from refining and correcting its documentation, especially if you are a native English speaker, and ending with improving the code base. Any kind of testing and suggestions are welcome.
You may follow the standard Github procedures or, in case you are not comfortable with them, just send your suggestions to the author by other means.
The formulae were adopted from the following sources:
- Peter Duffett-Smith, "Astronomy With Your Personal Computer", Cambridge University Press, 1997
- Jean Meeus, "Astronomical Algorithms", 2d edition, Willmann-Bell, 1998
- J.L.Lawrence, "Celestial Calculations", The MIT Press, 2018
Footnotes
-
Julian Period 7980 years of numbered days to be used in determining time elapsed between various historical events. It is the product of three calendar cycles:
28 (solar cycle) × 19 (lunar cycle) × 15 (indiction cycle) = 7980 years↩ -
Greenwich Sidereal Time — Sidereal time at the Greenwich meridian, irrelevant to the observer's position. ↩
-
Mean vernal point — intersection of the ecliptic of the date with the mean equator of the date. ↩