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- Time and Dates (`astropy.time`)

# Time and Dates (`astropy.time`)

## Introduction

The `astropy.time` package provides functionality for manipulating times and dates. Specific emphasis is placed on supporting time scales (e.g. UTC, TAI, UT1) and time representations (e.g. JD, MJD, ISO 8601) that are used in astronomy. It uses Cython to wrap the C language ERFA time and calendar routines. All time scale conversions are done by Cython vectorized versions of the ERFA routines and are fast and memory efficient.

All time manipulations and arithmetic operations are done internally using two 64-bit floats to represent time. Floating point algorithms from [1] are used so that the `Time` object maintains sub-nanosecond precision over times spanning the age of the universe.

[1] | Shewchuk, 1997, Discrete & Computational Geometry 18(3):305-363

## Getting Started

The basic way to use `astropy.time` is to create a `Time` object by supplying one or more input time values as well as the time format and time scale of those values. The input time(s) can either be a single scalar like `"2010-01-01 00:00:00"` or a list or a `numpy` array of values as shown below. In general any output values have the same shape (scalar or array) as the input.

    >>> from astropy.time import Time

    >>> times = ['1999-01-01 00:00:00.123456789', '2010-01-01 00:00:00']
    >>> t = Time(times, format='iso', scale='utc')
    >>> t
    <Time object: scale='utc' format='iso' value=['1999-01-01 00:00:00.123' '2010-01-01 00:00:00.000']>
    >>> t[1]
    <Time object: scale='utc' format='iso' value=2010-01-01 00:00:00.000>

The `format` argument specifies how to interpret the input values, e.g. ISO or JD or Unix time. The `scale` argument specifies the time scale for the values, e.g. UTC or TT or UT1.

Now let’s get the representation of these times in the JD and MJD formats by requesting the corresponding `Time` attributes:

    >>> t.jd
    array([ 2451179.50000143,  2455197.5       ])
    >>> t.mjd
    array([ 51179.00000143,  55197.        ])

We can also convert to a different time scale, for instance from UTC to TT. This uses the same attribute mechanism as above but now returns a new `Time` object:

    >>> t2 = t.tt
    >>> t2
    <Time object: scale='tt' format='iso' value=['1999-01-01 00:01:04.307' '2010-01-01 00:01:06.184']>
    >>> t2.jd
    array([ 2451179.5007443 ,  2455197.50076602])

Note that both the ISO and JD representations of `t2` are different than for `t` because they are expressed relative to the TT time scale.

## Using `astropy.time`

### Time object basics

In `astropy.time` a “time” is a single instant of time which is independent of the way the time is represented (the “format”) and the time “scale” which specifies the offset and scaling relation of the unit of time. There is no distinction made between a “date” and a “time” since both concepts (as loosely defined in common usage) are just different representations of a moment in time.

Once a `Time` object is created it cannot be altered internally. In code lingo it is “immutable.” In particular the common operation of “converting” to a different time scale is always performed by returning a copy of the original `Time` object which has been converted to the new time scale.

#### Time Format

The time format specifies how an instant of time is represented. The currently available formats are can be found in the `Time.FORMATS` dict and are listed in the table below. Each of these formats is implemented as a class that derives from the base `TimeFormat` class. This class structure can be easily adapted and extended by users for specialized time formats not supplied in `astropy.time`.

Format | Class
--- | ---
byear | `TimeBesselianEpoch`
byear_str | `TimeBesselianEpochString`
cxcsec | `TimeCxcSec`
datetime | `TimeDatetime`
gps | `TimeGPS`
iso | `TimeISO`
isot | `TimeISOT`
jd | `TimeJD`
jyear | `TimeJulianEpoch`
jyear_str | `TimeJulianEpochString`
mjd | `TimeMJD`
plot_date | `TimePlotDate`
unix | `TimeUnix`
yday | `TimeYearDayTime`

##### Subformat

The time format classes `TimeISO`, `TimeISOT`, and `TimeYearDayTime` support the concept of subformats. This allows for variations on the basic theme of a format in both the input string parsing and the output.

The supported subformats are `date_hms`, `date_hm`, and `date`. The table below illustrates these subformats for `iso` and `yday` formats:

Format | Subformat | Input / output
--- | --- | ---
`iso` | date_hms | 2001-01-02 03:04:05.678
`iso` | date_hm | 2001-01-02 03:04
`iso` | date | 2001-01-02
`yday` | date_hms | 2001:032:03:04:05.678
`yday` | date_hm | 2001:032:03:04
`yday` | date | 2001:032

#### Time Scale

The time scale (or time standard) is “a specification for measuring time: either the rate at which time passes; or points in time; or both” [2]. See also [3] and [4].

    >>> Time.SCALES
    ('tai', 'tcb', 'tcg', 'tdb', 'tt', 'ut1', 'utc')

Scale | Description
--- | ---
tai | International Atomic Time (TAI)
tcb | Barycentric Coordinate Time (TCB)
tcg | Geocentric Coordinate Time (TCG)
tdb | Barycentric Dynamical Time (TDB)
tt | Terrestrial Time (TT)
ut1 | Universal Time (UT1)
utc | Coordinated Universal Time (UTC)

[2] | Wikipedia time standard article

[3] | SOFA Time Scale and Calendar Tools (PDF)

[4] | http://www.ucolick.org/~sla/leapsecs/timescales.html

The system of transformation between supported time scales is shown in the figure below. Further details are provided in the Convert time scale section.

#### Scalar or Array

A `Time` object can hold either a single time value or an array of time values. The distinction is made entirely by the form of the input time(s). If a `Time` object holds a single value then any format outputs will be a single scalar value, and likewise for arrays. Like other arrays and lists, `Time` objects holding arrays are subscriptable, returning scalar or array objects as appropriate:

    >>> from astropy.time import Time
    >>> t = Time(100.0, format='mjd', scale='utc')
    >>> t.jd
    2400100.5
    >>> t = Time([100.0, 200.0, 300.], format='mjd', scale='utc')
    >>> t.jd
    array([ 2400100.5,  2400200.5,  2400300.5])
    >>> t[:2]
    <Time object: scale='utc' format='mjd' value=[ 100.  200.]>
    >>> t[2]
    <Time object: scale='utc' format='mjd' value=300.0>

#### Inferring input format

The `Time` class initializer will not accept ambiguous inputs, but it will make automatic inferences in cases where the inputs are unambiguous. This can apply when the times are supplied as `datetime` objects or strings. In the latter case it is not required to specify the format because the available string formats have no overlap. However, if the format is known in advance the string parsing will be faster if the format is provided.

    >>> from datetime import datetime
    >>> t = Time(datetime(2010, 1, 2, 1, 2, 3), scale='utc')
    >>> t.format
    'datetime'
    >>> t = Time('2010-01-02 01:02:03', scale='utc')
    >>> t.format
    'iso'

#### Internal representation

The `Time` object maintains an internal representation of time as a pair of double precision numbers expressing Julian days. The sum of the two numbers is the Julian Date for that time relative to the given time scale. Users requiring no better than microsecond precision over human time scales (~100 years) can safely ignore the internal representation details and skip this section.

This representation is driven by the underlying ERFA C-library implementation. The ERFA routines take care throughout to maintain overall precision of the double pair. The user is free to choose the way in which total JD is provided, though internally one part contains integer days and the other the fraction of the day, as this ensures optimal accuracy for all conversions. The internal JD pair is available via the `jd1` and `jd2` attributes:

    >>> t = Time('2010-01-01 00:00:00', scale='utc')
    >>> t.jd1, t.jd2
    (2455197.5, 0.0)
    >>> t2 = t.tai
    >>> t2.jd1, t2.jd2
    (2455197.5, 0.0003935185185185185)

### Creating a Time object

The allowed `Time` arguments to create a time object are listed below:

val : numpy ndarray, list, str, or number
  Data to initialize table.
val2 : numpy ndarray, list, str, or number; optional
  Data to initialize table.
format : str, optional
  Format of input value(s)
scale : str, optional
  Time scale of input value(s)
precision : int between 0 and 9 inclusive
  Decimal precision when outputting seconds as floating point
in_subfmt : str
  Unix glob to select subformats for parsing string input times
out_subfmt : str
  Unix glob to select subformats for outputting string times
lat : float, optional
  Earth latitude of observer
lon : float, optional
  Earth longitude of observer

#### val

The `val` argument specifies the input time or times and can be a single string or number, or it can be a Python list or `numpy` array of strings or numbers. To initialize a `Time` object based on a specified time, it must be present. If `val` is absent (or `None`), the `Time` object will be created for the time corresponding to the instant the object is created.

In most situations one also needs to specify the time scale via the `scale` argument. The `Time` class will never guess the time scale, so a simple example would be:

    >>> t1 = Time(50100.0, scale='tt', format='mjd')
    >>> t2 = Time('2010-01-01 00:00:00', scale='utc')

It is possible to create a new `Time` object from one or more existing time objects. In this case the format and scale will be inferred from the first object unless explicitly specified.

    >>> Time([t1, t2])
    <Time object: scale='tt' format='mjd' value=[ 50100.  55197.00076602]>

#### val2

The `val2` argument is available for specialized situations where extremely high precision is required. Recall that the internal representation of time within `astropy.time` is two double-precision numbers that when summed give the Julian date. If provided the `val2` argument is used in combination with `val` to set the second the internal time values. The exact interpretation of `val2` is determined by the input format class. As of this release all string-valued formats ignore `val2` and all numeric inputs effectively add the two values in a way that maintains the highest precision. Example:

    >>> t = Time(100.0, 0.000001, format='mjd', scale='tt')
    >>> t.jd, t.jd1, t.jd2
    (2400100.500001, 2400100.5, 1e-06)

#### format

The `format` argument sets the time time format, and as mentioned it is required unless the format can be unambiguously determined from the input times.

#### scale

The `scale` argument sets the time scale and is required except for time formats such as `plot_date` (`TimePlotDate`) and `unix` (`TimeUnix`). These formats represent the duration in SI seconds since a fixed instant in time which is independent of time scale.

#### precision

The `precision` setting affects string formats when outputting a value that includes seconds. It must be an integer between 0 and 9. There is no effect when inputting time values from strings. The default precision is 3. Note that the limit of 9 digits is driven by the way that ERFA handles fractional seconds. In practice this should should not be an issue.

    >>> t = Time('B1950.0', scale='utc', precision=3)
    >>> t.byear_str
    'B1950.000'
    >>> t.precision = 0
    >>> t.byear_str
    'B1950'

#### in_subfmt

The `in_subfmt` argument provides a mechanism to select one or more subformat values from the available subformats for string input. Multiple allowed subformats can be selected using Unix-style wildcard characters, in particular `*` and `?`, as documented in the Python fnmatch module.

The default value for `in_subfmt` is `*` which matches any available subformat. This allows for convenient input of values with unknown or heterogeneous subformat:

    >>> Time(['2000:001', '2000:002:03:04', '2001:003:04:05:06.789'], scale='utc')
    <Time object: scale='utc' format='yday'
     value=['2000:001:00:00:00.000' '2000:002:03:04:00.000' '2001:003:04:05:06.789']>

One can explicitly specify `in_subfmt` in order to strictly require a certain subformat:

    >>> t = Time('2000:002:03:04', scale='utc', in_subfmt='date_hm')
    >>> t = Time('2000:002', scale='utc', in_subfmt='date_hm')
    Traceback (most recent call last):
      ...
    ValueError: Input values did not match any of the formats where the
    format keyword is optional ['astropy_time', 'datetime',
    'byear_str', 'iso', 'isot', 'jyear_str', 'yday']

#### out_subfmt

The `out_subfmt` argument is similar to `in_subfmt` except that it applies to output formatting. In the case of multiple matching subformats the first matching subformat is used.

    >>> Time('2000-01-01 02:03:04', scale='utc', out_subfmt='date').iso
    '2000-01-01'
    >>> Time('2000-01-01 02:03:04', scale='utc', out_subfmt='date_hms').iso
    '2000-01-01 02:03:04.000'
    >>> Time('2000-01-01 02:03:04', scale='utc', out_subfmt='date*').iso
    '2000-01-01 02:03:04.000'

#### lat and lon

These optional parameters specify the observer latitude and longitude in decimal degrees. They default to 0.0 and are used for time scales that are sensitive to observer position. Currently the only time scale for which this applies is TDB, which relies on the ERFA routine `eraDtdb` to determine the time offset between TDB and TT.

#### Getting the Current Time

The current time can be determined as a `Time` object using the `now` class method:

    >>> nt = Time.now()
    >>> ut = Time(datetime.utcnow(), scale='utc')

The two should be very close to each other.

### Using Time objects

There are three basic operations available with `Time` objects:

- Get the representation of the time value(s) in a particular time format.
- Get a new time object for the same time value(s) but referenced to a different time scale.
- Do time arithmetic involving `Time` and/or `TimeDelta` objects.

#### Get representation

Instants of time can be represented in different ways, for instance as an ISO-format date string (`'1999-07-23 04:31:00'`) or seconds since 1998.0 (`49091460.0`) or Modified Julian Date (`51382.187451574`).

The representation of a `Time` object in a particular format is available by getting the object attribute corresponding to the format name. The list of available format names is in the time format section.

    >>> t = Time('2010-01-01 00:00:00', format='iso', scale='utc')
    >>> t.jd        # JD representation of time in current scale (UTC)
    2455197.5
    >>> t.iso       # ISO representation of time in current scale (UTC)
    '2010-01-01 00:00:00.000'
    >>> t.unix      # seconds since 1970.0 (UTC)
    1262304000.0
    >>> t.plot_date # Date value for plotting with matplotlib plot_date()
    733773.0003935185
    >>> t.datetime  # Representation as datetime.datetime object
    datetime.datetime(2010, 1, 1, 0, 0)

Example:

    >>> import matplotlib.pyplot as plt
    >>> jyear = np.linspace(2000, 2001, 20)
    >>> t = Time(jyear, format='jyear', scale='utc')
    >>> plt.plot_date(t.plot_date, jyear)
    >>> plt.gcf().autofmt_xdate()  # orient date labels at a slant
    >>> plt.draw()

#### Convert time scale

A new `Time` object for the same time value(s) but referenced to a new time scale can be created getting the object attribute corresponding to the time scale name. The list of available time scale names is in the time scale section and in the figure below illustrating the network of time scale transformations.

Examples:

    >>> t = Time('2010-01-01 00:00:00', format='iso', scale='utc')
    >>> t.tt        # TT scale
    <Time object: scale='tt' format='iso' value=2010-01-01 00:01:06.184>
    >>> t.tai
    <Time object: scale='tai' format='iso' value=2010-01-01 00:00:34.000>

In this process the `format` and other object attributes like `lat`, `lon`, and `precision` are also propagated to the new object.

As noted in the `Time object basics` section, a `Time` object is immutable and the internal time values cannot be altered once the object is created. The process of changing the time scale therefore begins by making a copy of the original object and then converting the internal time values in the copy to the new time scale. The new `Time` object is returned by the attribute access.

##### Transformation offsets

Time scale transformations that cross one of the orange circles in the image above require an additional offset time value that is model or observation-dependent. See SOFA Time Scale and Calendar Tools for further details.

The two attributes `delta_ut1_utc` and `delta_tdb_tt` provide a way to set these offset times explicitly. These represent the time scale offsets UT1 - UTC and TDB - TT, respectively. As an example:

    >>> t = Time('2010-01-01 00:00:00', format='iso', scale='utc')
    >>> t.delta_ut1_utc = 0.334  # Explicitly set one part of the transformation
    >>> t.ut1.iso    # ISO representation of time in UT1 scale
    '2010-01-01 00:00:00.334'

For the UT1 to UTC offset, one has to interpolate in observed values provided by the International Earth Rotation and Reference Systems Service. By default, `astropy` is shipped with the final values provided in Bulletin B, which cover the period from 1962 to shortly before an astropy release, and these will be used to compute the offset if the `delta_ut1_utc` attribute is not set explicitly. For more recent times, one can download an updated version of IERS B or IERS A (which also has predictions), and set `delta_ut1_utc` as described in `get_delta_ut1_utc`:

    >>> from astropy.utils.iers import IERS_A, IERS_A_URL
    >>> from astropy.utils.data import download_file
    >>> iers_a_file = download_file(IERS_A_URL, cache=True))
    >>> iers_a = IERS_A.open(iers_a_file)
    >>> t.delta_ut1_utc = t.get_delta_ut1_utc(iers_a)

In the case of the TDB to TT offset, most users need only provide the `lat` and `lon` values when creating the `Time` object. If the `delta_tdb_tt` attribute is not explicitly set then the ERFA C-library routine `eraDtdb` will be used to compute the TDB to TT offset. Note that `lat` and `lon` are initialized to 0.0 by default, so those defaults will be used if they are not provided.

The following code replicates an example in the SOFA Time Scale and Calendar Tools document. It does the transform from UTC to all supported time scales (TAI, TCB, TCG, TDB, TT, UT1, UTC). This requires auxilliary information (latitude and longitude).

    >>> lat = 19.48125
    >>> lon = -155.933222
    >>> t = Time('2006-01-15 21:24:37.5', format='iso', scale='utc',
    ...          lat=lat, lon=lon, precision=6)
    >>> t.utc.iso
    '2006-01-15 21:24:37.500000'
    >>> t.ut1.iso
    '2006-01-15 21:24:37.834078'
    >>> t.tai.iso
    '2006-01-15 21:25:10.500000'
    >>> t.tt.iso
    '2006-01-15 21:25:42.684000'
    >>> t.tcg.iso
    '2006-01-15 21:25:43.322690'
    >>> t.tdb.iso
    '2006-01-15 21:25:42.683799'
    >>> t.tcb.iso
    '2006-01-15 21:25:56.893378'

### Time Deltas

Simple time arithmetic is supported using the `TimeDelta` class. The following operations are available:

- Create a TimeDelta explicitly by instantiating a class object
- Create a TimeDelta by subtracting two Times
- Add a TimeDelta to a Time object to get a new Time
- Subtract a TimeDelta from a Time object to get a new Time
- Add two TimeDelta objects to get a new TimeDelta
- Negate a TimeDelta or take its absolute value
- Multiply or divide a TimeDelta by a constant or array

The `TimeDelta` class is derived from the `Time` class and shares many of its properties. The key difference is that the time scale is always TAI so that all time deltas are referenced to a uniform Julian Day which is exactly 86400 standard SI seconds.

The available time formats are:

Format | Class
--- | ---
sec | `TimeDeltaSec`
jd | `TimeDeltaJD`

#### Examples

Use of the `TimeDelta` object is easily illustrated in the few examples below:

    >>> t1 = Time('2010-01-01 00:00:00', scale='utc')
    >>> t2 = Time('2010-02-01 00:00:00', scale='utc')
    >>> dt = t2 - t1  # Difference between two Times
    >>> dt
    <TimeDelta object: scale='tai' format='jd' value=31.0>
    >>> dt.sec
    2678400.0

    >>> from astropy.time import TimeDelta
    >>> dt2 = TimeDelta(50.0, format='sec')
    >>> t3 = t2 + dt2  # Add a TimeDelta to a Time
    >>> t3.iso
    '2010-02-01 00:00:50.000'

    >>> t2 - dt2  # Subtract a TimeDelta from a Time
    <Time object: scale='utc' format='iso' value=2010-01-31 23:59:10.000>

    >>> dt + dt2
    <TimeDelta object: scale='tai' format='jd' value=31.0005787037>

    >>> import numpy as np
    >>> t1 + dt * np.linspace(0, 1, 5)
    <Time object: scale='utc' format='iso' value=['2010-01-01 00:00:00.000'
    '2010-01-08 18:00:00.000' '2010-01-16 12:00:00.000' '2010-01-24 06:00:00.000'
    '2010-02-01 00:00:00.000']>

### Interaction with Time-like Quantities

Where possible, `Quantity` objects with units of time are treated as TimeDelta (though necessarily with lower precision). They can also be used as input in constructing `Time` and `TimeDelta` objects, and `TimeDelta` objects can be converted to `Quantity` objects of arbitrary units of time. Usage is most easily illustrated by examples:

    >>> import astropy.units as u
    >>> Time(10.*u.yr, format='gps')   # time-valued quantities can be used for
    ...                                # for formats requiring a time offset
    <Time object: scale='tai' format='gps' value=315576000.0>
    >>> Time(10.*u.yr, 1.*u.s, format='gps')
    <Time object: scale='tai' format='gps' value=315576001.0>
    >>> Time(2000.*u.yr, scale='utc', format='jyear')
    <Time object: scale='utc' format='jyear' value=2000.0>
    >>> Time(2000.*u.yr, scale='utc', format='byear')
    ...                                # but not for Besselian year, which implies
    ...                                # a different time scale
    ...
    Traceback (most recent call last):
      ...
    ValueError: Input values did not match the format class byear

    >>> TimeDelta(10.*u.yr)            # With a quantity, no format is required
    <TimeDelta object: scale='tai' format='jd' value=3652.5>

    >>> dt = TimeDelta([10., 20., 30.], format='jd')
    >>> dt.to(u.hr)                    # can convert TimeDelta to a quantity
    <Quantity [ 240., 480., 720.] h>
    >>> dt > 400. * u.hr               # and compare to quantities with units of time
    array([False,  True,  True], dtype=bool)
    >>> dt + 1.*u.hr                   # can also add/subtract such quantities
    <TimeDelta object: scale='tai' format='jd' value=[ 10.04166667  20.04166667  30.04166667]>
    >>> Time(50000., format='mjd', scale='utc') + 1.*u.hr
    <Time object: scale='utc' format='mjd' value=50000.0416667>
    >>> dt * 10.*u.km/u.s              # for multiplication and division with a
    ...                                # Quantity, TimeDelta is converted
    <Quantity [ 100., 200., 300.] d km / s>
    >>> dt * 10.*u.Unit(1)             # unless the Quantity is dimensionless
    <TimeDelta object: scale='tai' format='jd' value=[ 100.  200.  300.]>

## Reference/API

### astropy.time Module

#### Classes

`OperandTypeError`(left, right) |
`ScaleValueError` |
`Time`(val[, val2, format, scale, precision, ...]) | Represent and manipulate times and dates for astronomy.
`TimeBesselianEpoch`(val1, val2, scale, ...[, ...]) | Besselian Epoch year as floating point value(s) like 1950.0
`TimeBesselianEpochString`(val1, val2, scale, ...) | Besselian Epoch year as string value(s) like ‘B1950.0’
`TimeCxcSec`(val1, val2, scale, precision, ...) | Chandra X-ray Center seconds from 1998-01-01 00:00:00 TT
`TimeDatetime`(val1, val2, scale, precision, ...) | Represent date as Python standard library `datetime` object
`TimeDelta`(val[, val2, format, scale, copy]) | Represent the time difference between two times.
`TimeDeltaFormat`(val1, val2, scale, ...[, ...]) | Base class for time delta representations
`TimeDeltaJD`(val1, val2, scale, precision, ...) | Time delta in Julian days (86400 SI seconds)
`TimeDeltaSec`(val1, val2, scale, precision, ...) | Time delta in SI seconds
`TimeEpochDate`(val1, val2, scale, precision, ...) | Base class for support floating point Besselian and Julian epoch dates
`TimeEpochDateString`(val1, val2, scale, ...) | Base class to support string Besselian and Julian epoch dates such as ‘B1950.0’ or ‘J2000.0’ respectively.
`TimeFormat`(val1, val2, scale, precision, ...) | Base class for time representations.
`TimeFromEpoch`(val1, val2, scale, precision, ...) | Base class for times that represent the interval from a particular epoch as a floating point multiple of a unit time interval (e.g.
`TimeGPS`(val1, val2, scale, precision, ...[, ...]) | GPS time: seconds from 1980-01-06 00:00:00 UTC GPS time includes leap seconds.
`TimeISO`(val1, val2, scale, precision, ...[, ...]) | ISO 8601 compliant date-time format “YYYY-MM-DD HH:MM:SS.sss...”.
`TimeISOT`(val1, val2, scale, precision, ...) | ISO 8601 compliant date-time format “YYYY-MM-DDTHH:MM:SS.sss...”.
`TimeJD`(val1, val2, scale, precision, ...[, ...]) | Julian Date time format
`TimeJulianEpoch`(val1, val2, scale, ...[, ...]) | Julian Epoch year as floating point value(s) like 2000.0
`TimeJulianEpochString`(val1, val2, scale, ...) | Julian Epoch year as string value(s) like ‘J2000.0’
`TimeMJD`(val1, val2, scale, precision, ...[, ...]) | Modified Julian Date time format
`TimePlotDate`(val1, val2, scale, precision, ...) | Matplotlib `plot_date` input: 1 + number of days from 0001-01-01 00:00:00 UTC
`TimeString`(val1, val2, scale, precision, ...) | Base class for string-like time represetations.
`TimeUnix`(val1, val2, scale, precision, ...) | Unix time: seconds from 1970-01-01 00:00:00 UTC.
`TimeYearDayTime`(val1, val2, scale, ...[, ...]) | Year, day-of-year and time as “YYYY:DOY:HH:MM:SS.sss...”.

#### Class Inheritance Diagram

## Acknowledgments and Licenses

This package makes use of the ERFA Software ANSI C library. The copyright of the ERFA software belongs to the NumFOCUS Foundation. The library is made available under the terms of the “BSD-three clauses” license.

The ERFA library is derived, with permission, from the International Astronomical Union’s “Standards of Fundamental Astronomy” library, available from http://www.iausofa.org.