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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, TDB) and time representations (e.g. JD, MJD, ISO 8601) that are used in astronomy and required to calculate, e.g., sidereal times and barycentric corrections. It uses Cython to wrap the C language ERFA time and calendar routines, using a fast and memory efficient vectorization scheme.

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 = ['1999-01-01T00:00:00.123456789', '2010-01-01T00:00:00']
    >>> t = Time(times, format='isot', scale='utc')
    >>> t
    <Time object: scale='utc' format='isot' value=['1999-01-01T00:00:00.123' '2010-01-01T00:00:00.000']>
    >>> t[1]
    <Time object: scale='utc' format='isot' value=2010-01-01T00:00:00.000>

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. The `scale` argument is optional and defaults to UTC except for Time from epoch formats. We could have written the above as:

    >>> t = Time(times, format='isot')

When the format of the input can be unambiguously determined then the `format` argument is not required, so we can simplify even further:

    >>> t = Time(times)

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.        ])

The default representation can be changed by setting the `format` attribute:

    >>> t.format = 'fits'
    >>> t
    <Time object: scale='utc' format='fits' value=['1999-01-01T00:00:00.123(UTC)'
                                                   '2010-01-01T00:00:00.000(UTC)']>
    >>> t.format = 'isot'

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='isot' value=['1999-01-01T00:01:04.307' '2010-01-01T00:01:06.184']>
    >>> t2.jd
    array([ 2451179.5007443 ,  2455197.50076602])

Note that both the ISO (ISOT) and JD representations of `t2` are different than for `t` because they are expressed relative to the TT time scale. Of course, from the numbers or strings one could not tell; one format in which this information is kept is the `fits` format:

    >>> t2.fits
    array(['1999-01-01T00:01:04.307(TT)', '2010-01-01T00:01:06.184(TT)'],
          dtype='|S27')

Finally, some further examples of what is possible. For details, see the API documentation below.

    >>> dt = t[1] - t[0]
    >>> dt
    <TimeDelta object: scale='tai' format='jd' value=4018.00002172>

Here, note the conversion of the timescale to TAI. Time differences can only have scales in which one day is always equal to 86400 seconds.

    >>> import numpy as np
    >>> t[0] + dt * np.linspace(0.,1.,12)
    <Time object: scale='utc' format='isot' value=['1999-01-01T00:00:00.123' '2000-01-01T06:32:43.930'
     '2000-12-31T13:05:27.737' '2001-12-31T19:38:11.544'
     '2003-01-01T02:10:55.351' '2004-01-01T08:43:39.158'
     '2004-12-31T15:16:22.965' '2005-12-31T21:49:06.772'
     '2007-01-01T04:21:49.579' '2008-01-01T10:54:33.386'
     '2008-12-31T17:27:17.193' '2010-01-01T00:00:00.000']>

    >>> t.sidereal_time('apparent', 'greenwich')
    <Longitude [ 6.68050179, 6.70281947] hourangle>

## 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 | Example argument
--- | --- | ---
byear | `TimeBesselianEpoch` | 1950.0
byear_str | `TimeBesselianEpochString` | ‘B1950.0’
cxcsec | `TimeCxcSec` | 63072064.184
datetime | `TimeDatetime` | datetime(2000, 1, 2, 12, 0, 0)
decimalyear | `TimeDecimalYear` | 2000.45
fits | `TimeFITS` | ‘2000-01-01T00:00:00.000(TAI)’
gps | `TimeGPS` | 630720013.0
iso | `TimeISO` | ‘2000-01-01 00:00:00.000’
isot | `TimeISOT` | ‘2000-01-01T00:00:00.000’
jd | `TimeJD` | 2451544.5
jyear | `TimeJulianEpoch` | 2000.0
jyear_str | `TimeJulianEpochString` | ‘J2000.0’
mjd | `TimeMJD` | 51544.0
plot_date | `TimePlotDate` | 730120.0003703703
unix | `TimeUnix` | 946684800.0
yday | `TimeYearDayTime` | 2000:001:00:00:00.000

Note

The `TimeFITS` format allows for most but not all of the the FITS standard [2]. Not implemented (yet) is support for a `LOCAL` timescale. Furthermore, FITS supports some deprecated names for timescales; these are translated to the formal names upon initialization. Furthermore, any specific realization information, such as `UT(NIST)` is stored only as long as the time scale is not changed.

[2] | Rots et al. 2015, A&A 574:A36

##### Changing format

The default representation can be changed by setting the `format` attribute in place:

    >>> t = Time('2000-01-02')
    >>> t.format = 'jd'
    >>> t
    <Time object: scale='utc' format='jd' value=2451545.5>

Be aware that when changing format, the current output subformat (see section below) may not exist in the new format. In this case the subformat will not be preserved:

    >>> t = Time('2000-01-02', format='fits', out_subfmt='longdate')
    >>> t.value
    '+02000-01-02(UTC)'
    >>> t.format = 'iso'
    >>> t.out_subfmt
    u'*'
    >>> t.format = 'fits'
    >>> t.value
    '2000-01-02T00:00:00.000(UTC)'

##### Subformat

The time format classes `TimeISO`, `TimeISOT`, `TimeFITS`, 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` for all but the `TimeFITS` format; the latter does not support `data_hm` but does support `longdate_hms` and `longdate` for years before the year 0 and after the year 10000. The table below illustrates these subformats for `iso`, `fits`, `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
`fits` | date_hms | 2001-01-02T03:04:05.678(UTC)
`fits` | longdate_hms | +02001-01-02T03:04:05.678(UTC)
`fits` | longdate | +02001-01-02(UTC)
`yday` | date_hms | 2001:032:03:04:05.678
`yday` | date_hm | 2001:032:03:04
`yday` | date | 2001:032

##### Time from epoch formats

The formats `cxcsec`, `gps`, and `unix` are a little special in that they provide a floating point representation of the elapsed time in seconds since a particular reference date. These formats have a intrinsic time scale which is used to compute the elapsed seconds since the reference date.

Format | Scale | Reference date
--- | --- | ---
`cxcsec` | TT | `1998-01-01 00:00:00`
`unix` | UTC | `1970-01-01 00:00:00`
`gps` | TAI | `1980-01-06 00:00:19`

Unlike the other formats which default to UTC, if no `scale` is provided when initializing a `Time` object then the above intrinsic scale is used. This is done for computational efficiency.

#### 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” [3]. See also [4] and [5].

    >>> 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)

[3] | Wikipedia time standard article

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

[5] | 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')
    >>> t.jd
    2400100.5
    >>> t = Time([100.0, 200.0, 300.], format='mjd')
    >>> 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>
    >>> t = Time(np.arange(50000., 50003.)[:, np.newaxis],
    ...          np.arange(0., 1., 0.5), format='mjd')
    >>> t
    <Time object: scale='utc' format='mjd' value=[[ 50000.   50000.5]
     [ 50001.   50001.5]
     [ 50002.   50002.5]]>
    >>> t[0]
    <Time object: scale='utc' format='mjd' value=[ 50000.   50000.5]>

#### Numpy method analogs

For `Time` instances holding arrays, many of the same methods and attributes that work on `ndarray` instances can be used. E.g., one can reshape `Time` instances and take specific parts using `reshape()`, `ravel()`, `flatten()`, `T`, `transpose()`, `swapaxes()`, `diagonal()`, `squeeze()`, `take()`:

    >>> t.reshape(2, 3)
    <Time object: scale='utc' format='mjd' value=[[ 50000.   50000.5  50001. ]
     [ 50001.5  50002.   50002.5]]>
    >>> t.T
    <Time object: scale='utc' format='mjd' value=[[ 50000.   50001.   50002. ]
     [ 50000.5  50001.5  50002.5]]>

Note that similarly to the `ndarray` methods, all but `flatten()` try to use new views of the data, with the data copied only if that it is impossible (as discussed, e.g., in the documentation for numpy `reshape()`).

Some arithmetic methods are supported as well: `min()`, `max()`, `ptp()`, `sort()`, `argmin()`, `argmax()`, and `argsort()`. E.g.:

    >> t.max()
    <Time object: scale='utc' format='mjd' value=50002.5>
    >> t.ptp(axis=0)
    <TimeDelta object: scale='tai' format='jd' value=[ 2.  2.]>

#### 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))
    >>> t.format
    'datetime'
    >>> t = Time('2010-01-02 01:02:03')
    >>> 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
location : `EarthLocation` or tuple, optional
  If a tuple, 3 `Quantity` items with length units for geocentric coordinates, or a longitude, latitude, and optional height for geodetic coordinates. Can be a single location, or one for each input time.

#### 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'])
    <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', in_subfmt='date_hm')
    >>> t = Time('2000:002', 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', out_subfmt='date').iso
    '2000-01-01'
    >>> Time('2000-01-01 02:03:04', out_subfmt='date_hms').iso
    '2000-01-01 02:03:04.000'
    >>> Time('2000-01-01 02:03:04', out_subfmt='date*').iso
    '2000-01-01 02:03:04.000'

#### location

This optional parameter specifies the observer location, using an `EarthLocation` object or a tuple containing any form that can initialize one: either a tuple with geocentric coordinates (X, Y, Z), or a tuple with geodetic coordinates (longitude, latitude, height; with height defaulting to zero). They are used for time scales that are sensitive to observer location (currently, only TDB, which relies on the ERFA routine `eraDtdb` to determine the time offset between TDB and TT), as well as for sidereal time if no explicit longitude is given.

    >>> t = Time('2001-03-22 00:01:44.732327132980', scale='utc',
    ...          location=('120d', '40d'))
    >>> t.sidereal_time('apparent', 'greenwich')
    <Longitude 12.00000000000001 hourangle>
    >>> t.sidereal_time('apparent')
    <Longitude 20.00000000000001 hourangle>

Note

In future versions, we hope to add the possibility to add observatory objects and/or names.

#### 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 four 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.
- Calculate the sidereal time corresponding to the time value(s).
- 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()
    733773.0
    >>> 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')
    >>> 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 `lon`, `lat`, 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
    >>> iers_a = IERS_A.open(IERS_A_URL)
    >>> 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 `lon` and `lat` 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 if `lon` and `lat` are not explicitly initialized, values of 0.0 degrees for both will be used.

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 an observer location (here, latitude and longitude).:

    >>> import astropy.units as u
    >>> t = Time('2006-01-15 21:24:37.5', format='iso', scale='utc',
    ...          location=(-155.933222*u.deg, 19.48125*u.deg), 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 21:25:42.684373'
    >>> t.tcb.iso
    '2006-01-15 21:25:56.893952'

### Sidereal Time

Apparent or mean sidereal time can be calculated using `sidereal_time()`. The method returns a `Longitude` with units of hourangle, which by default is for the longitude corresponding to the location with which the `Time` object is initialized. Like the scale transformations, ERFA C-library routines are used under the hood, which support calculations following different IAU resolutions. Sample usage:

    >>> t = Time('2006-01-15 21:24:37.5', scale='utc', location=('120d', '45d'))
    >>> t.sidereal_time('mean')
    <Longitude 13.089521870640212 hourangle>
    >>> t.sidereal_time('apparent')
    <Longitude 13.089503675087027 hourangle>
    >>> t.sidereal_time('apparent', 'greenwich')
    <Longitude 5.089503675087027 hourangle>
    >>> t.sidereal_time('apparent', '-90d')
    <Longitude 23.08950367508703 hourangle>
    >>> t.sidereal_time('apparent', '-90d', 'IAU1994')
    <Longitude 23.08950365423405 hourangle>

### 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
- Convert TimeDelta objects to and from time-like Quantities

The `TimeDelta` class is derived from the `Time` class and shares many of its properties. One difference is that the time scale has to be one for which one day is exactly 86400 seconds. Hence, the scale cannot be UTC.

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')
    >>> t2 = Time('2010-02-01 00:00:00')
    >>> 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']>

### Time Scales for Time Deltas

Above, one sees that the difference between two UTC times is a `TimeDelta` with a scale of TAI. This is because a UTC time difference cannot be uniquely defined unless one knows the two times that were differenced (because of leap seconds, a day does not always have 86400 seconds). For all other time scales, the `TimeDelta` inherits the scale of the first `Time` object:

    >>> t1 = Time('2010-01-01 00:00:00', scale='tcg')
    >>> t2 = Time('2011-01-01 00:00:00', scale='tcg')
    >>> dt = t2 - t1
    >>> dt
    <TimeDelta object: scale='tcg' format='jd' value=365.0>

When `TimeDelta` objects are added or subtracted from `Time` objects, scales are converted appropriately, with the final scale being that of the `Time` object:

    >>> t2 + dt
    <Time object: scale='tcg' format='iso' value=2012-01-01 00:00:00.000>
    >>> t2.tai
    <Time object: scale='tai' format='iso' value=2010-12-31 23:59:27.068>
    >>> t2.tai + dt
    <Time object: scale='tai' format='iso' value=2011-12-31 23:59:27.046>

`TimeDelta` objects can be converted only to objects with compatible scales, i.e., scales for which it is not necessary to know the times that were differenced:

    >>> dt.tt
    <TimeDelta object: scale='tt' format='jd' value=364.999999746>
    >>> dt.tdb
    Traceback (most recent call last):
      ...
    ScaleValueError: Cannot convert TimeDelta with scale 'tcg' to scale 'tdb'

`TimeDelta` objects can also have an undefined scale, in which case it is assumed that there scale matches that of the other `Time` or `TimeDelta` object (or is TAI in case of a UTC time):

    >>> t2.tai + TimeDelta(365., format='jd', scale=None)
    <Time object: scale='tai' format='iso' value=2011-12-31 23:59:27.068>

### Interaction with Time-like Quantities

Where possible, `Quantity` objects with units of time are treated as TimeDelta objects with undefined scale (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='None' 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='None' 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='None' format='jd' value=[ 100.  200.  300.]>

### Writing a Custom Format

Some applications may need a custom `Time` format, and this capability is available by making a new subclass of the `TimeFormat` class. When such a subclass is defined in your code then the format class and corresponding name is automatically registered in the set of available time formats.

The key elements of a new format class are illustrated by examining the code for the `jd` format (which is one of the simplest):

    class TimeJD(TimeFormat):
        """
        Julian Date time format.
        """
        name = 'jd'  # Unique format name

        def set_jds(self, val1, val2):
            """
            Set the internal jd1 and jd2 values from the input val1, val2.
            The input values are expected to conform to this format, as
            validated by self._check_val_type(val1, val2) during __init__.
            """
            self._check_scale(self._scale)  # Validate scale.
            self.jd1, self.jd2 = day_frac(val1, val2)

        @property
        def value(self):
            """
            Return format ``value`` property from internal jd1, jd2
            """
            return self.jd1 + self.jd2

As mentioned above, the `_check_val_type(self, val1, val2)` method may need to be overridden to validate the inputs as conforming to the format specification. By default this checks for valid float, float array, or `Quantity` inputs. In contrast the `iso` format class ensures the inputs meet the ISO format spec for strings.

One special case that is relatively common and easier to implement is a format that represents the time since a particular epoch. The classic example is Unix time which is the number of seconds since 1970-01-01 00:00:00 UTC, not counting leap seconds. What if we wanted that value but do want to count leap seconds. This would be done by using the TAI scale instead of the UTC scale. In this case we inherit from the `TimeFromEpoch` class and define a few class attributes:

    >>> from astropy.time.formats import erfa, TimeFromEpoch
    >>> class TimeUnixLeap(TimeFromEpoch):
    ...    """
    ...    Seconds from 1970-01-01 00:00:00 TAI.  Similar to Unix time
    ...    but this includes leap seconds.
    ...    """
    ...    name = 'unix_leap'
    ...    unit = 1.0 / erfa.DAYSEC  # in days (1 day == 86400 seconds)
    ...    epoch_val = '1970-01-01 00:00:00'
    ...    epoch_val2 = None
    ...    epoch_scale = 'tai'  # Scale for epoch_val class attribute
    ...    epoch_format = 'iso'  # Format for epoch_val class attribute

    >>> t = Time('2000-01-01')
    >>> t.unix_leap
    946684832.0
    >>> t.unix_leap - t.unix
    32.0

Going beyond this will probably require looking at the astropy code for more guidance, but if you get stuck the astropy developers are more than happy to help. If you write a format class that is widely useful then we might want to include it in the core!

### Timezones

When a `Time` object is constructed from a timezone-aware `datetime`, no timezone information is saved in the `Time` object. However, `Time` objects can be converted to timezone-aware datetime objects:

    >>> from datetime import datetime
    >>> from astropy.time import Time, TimezoneInfo
    >>> import astropy.units as u
    >>> utc_plus_one_hour = TimezoneInfo(utc_offset=1*u.hour)
    >>> dt_aware = datetime(2000, 1, 1, 0, 0, 0, tzinfo=utc_plus_one_hour)
    >>> t = Time(dt_aware)  # Loses timezone info, converts to UTC
    >>> print(t)            # will return UTC
    1999-12-31 23:00:00
    >>> print(t.to_datetime(timezone=utc_plus_one_hour)) # to timezone-aware datetime
    2000-01-01 00:00:00+01:00

Timezone database packages, like pytz for example, may be more convenient to use to create `tzinfo` objects used to specify timezones rather than the `TimezoneInfo` object.

## Reference/API

### astropy.time Package

#### Classes

`OperandTypeError`(left, right[, op]) |
`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
`TimeDecimalYear`(val1, val2, scale, ...[, ...]) | Time as a decimal year, with integer values corresponding to midnight of the first day of each year.
`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.
`TimeFITS`(val1, val2, scale, precision, ...) | FITS format: “[±Y]YYYY-MM-DD[THH:MM:SS[.sss]][(SCALE[(REALIZATION)])]”.
`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 For example, 630720013.0 is midnight on January 1, 2000.
`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:
`TimeString`(val1, val2, scale, precision, ...) | Base class for string-like time representations.
`TimeUnique`(val1, val2, scale, precision, ...) | Base class for time formats that can uniquely create a time object without requiring an explicit format specifier.
`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...”.
`TimezoneInfo`([utc_offset, dst, tzname]) | Subclass of the `tzinfo` object, used in the to_datetime method to specify timezones.

#### 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.