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.
>>> import numpy as np
>>> 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'
'2010-01-01T00:00:00.000']>
>>> 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:
>>> print(t2.fits)
['1999-01-01T00:01:04.307' '2010-01-01T00:01:06.184']
One can set the time values in-place using the usual numpy array setting item syntax:
>>> t2 = t.tt.copy() # Copy required if transformed Time will be modified
>>> t2[1] = '2014-12-25'
>>> print(t2)
['1999-01-01T00:01:04.307' '2014-12-25T00:00:00.000']
The Time
object also has support for missing values, which is particularly
useful for Table operations such as joining and stacking:
>>> t2[0] = np.ma.masked # Declare that first time is missing or invalid
>>> print(t2)
[-- '2014-12-25T00:00:00.000']
Finally, some further examples of what is possible. For details, see the API documentation below.
>>> dt = t[1] - t[0]
>>> dt # doctest: +FLOAT_CMP
<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') # doctest: +FLOAT_CMP
<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.
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’ |
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 |
datetime64 | TimeDatetime64 |
np.datetime64(‘2000-01-01T01:01:01’) |
Note
The TimeFITS
format implements most
of the FITS standard [2], including support for the LOCAL
timescale.
Note, though, that 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'
>>> t.format = 'iso'
>>> t.out_subfmt
u'*'
>>> t.format = 'fits'
>>> t.value
'2000-01-02T00:00:00.000'
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 date_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 |
fits |
longdate_hms | +02001-01-02T03:04:05.678 |
fits |
longdate | +02001-01-02 |
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', 'local')
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) |
local | Local Time Scale (LOCAL) |
[3] | Wikipedia time standard article |
[4] | SOFA Time Scale and Calendar Tools (PDF) |
[5] | http://www.ucolick.org/~sla/leapsecs/timescales.html |
Note
The local
time scale is meant for free-running clocks or simulation times,
i.e., to represent a time without properly defined scale. This means it cannot be converted
to any other time scale, and arithmetic is possible only with Time
instances with scale
local
and with TimeDelta
instances with scale local
or None
.
The system of transformation between supported time scales (i.e., all but local
)
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) # doctest: +FLOAT_CMP
<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
(2455198.0, -0.5)
>>> t2 = t.tai
>>> t2.jd1, t2.jd2
(2455198., -0.49960648148148146)
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, 2400101.0, -0.499999)
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') # doctest: +FLOAT_CMP
<Longitude 12. hourangle>
>>> t.sidereal_time('apparent') # doctest: +FLOAT_CMP
<Longitude 20. hourangle>
Note
In future versions, we hope to add the possibility to add observatory objects and/or names.
Using Time objects¶
The operations available with Time
objects include:
- Get and set time values(s) for an array-valued
Time
object: - Set missing (masked) values.
- 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/orTimeDelta
objects.
Get and set values¶
For an existing Time
object which is array-valued, one can use the
usual numpy array item syntax to get either a single item or a subset
of items. The returned value is a Time
object with all the same
attributes:
>>> t = Time(['2001:020', '2001:040', '2001:060', '2001:080'],
... out_subfmt='date')
>>> print(t[1])
2001:040
>>> print(t[1:])
['2001:040' '2001:060' '2001:080']
>>> print(t[[2, 0]])
['2001:060' '2001:020']
As of astropy version 3.1, one can also set values in-place for an
array-valued Time
object:
>>> t = Time(['2001:020', '2001:040', '2001:060', '2001:080'],
... out_subfmt='date')
>>> t[1] = '2010:001'
>>> print(t)
['2001:020' '2010:001' '2001:060' '2001:080']
>>> t[[2, 0]] = '1990:123'
>>> print(t)
['1990:123' '2010:001' '1990:123' '2001:080']
The new value (on the right hand side) when setting can be one of three possibilities:
- Scalar string value or array of string values where each value
is in a valid time format that can be automatically parsed and
used to create a
Time
object. - Value or array of values where each value has the same
format
as theTime
object being set. For instance, a float or numpy array of floats for an object withformat='unix'
. Time
object with identicallocation
(butscale
andformat
need not be the same). The right side value will be transformed so the timescale
matches.
Whenever any item is set then the internal cache (see Caching) is cleared
along with the delta_tdb_tt
and/or delta_ut1_utc
transformation
offsets, if they have been set.
If it is required that the Time
object be immutable then set the
writeable
attribute to False
. In this case attempting to set a value will
raise a ValueError: Time object is read-only
. See the section on
Caching for an example.
Missing values¶
The Time
and TimeDelta
objects support functionality for marking values as
missing or invalid (added in astropy 3.1). This is also known as masking,
and is especially useful for Table operations such as joining and
stacking. To set one or more items as missing, assign the special value
numpy.ma.masked
, for example:
>>> t = Time(['2001:020', '2001:040', '2001:060', '2001:080'],
... out_subfmt='date')
>>> t[2] = np.ma.masked
>>> print(t)
['2001:020' '2001:040' -- '2001:080']
Note
The operation of setting an array element to numpy.ma.masked
(missing) overwrites the actual time data and therefore there is no way to
recover the original value. In this sense the numpy.ma.masked
value
behaves just like any other valid Time
value when setting. This is
similar to how Pandas missing data works,
but somewhat different from NumPy masked arrays which
maintain a separate mask array and retain the underlying data. In the
Time
object the mask
attribute is read-only and cannot be directly set.
Once one or more values in the object are masked, any operations will
propagate those values as masked, and access to format attributes such
as unix
or value
will return a MaskedArray
object:
>>> t.unix
masked_array(data = [979948800.0 981676800.0 -- 985132800.0],
mask = [False False True False],
fill_value = 1e+20)
One can view the mask
, but note that it is read-only and
setting the mask is always done by setting the item to masked
.
>>> t.mask
array([False, False, True, False]...)
>>> t[:2] = np.ma.masked
Warning
The internal implementation of missing value support is
provisional and may change in a subsequent release. This would impact
information in the next section. However, the documented API for using missing
values with Time
and TimeDelta
objects is stable.
Custom format classes and missing values¶
For advanced users who have written a custom time format via a
TimeFormat
subclass, it may be necessary to modify your
class if you wish to support missing values. For applications that
do not take advantage of missing values then no changes are required.
Missing values in a TimeFormat
subclass object are marked by
setting the corresponding entries of the jd2
attribute to be numpy.nan
(but this is never done directly by the user). For most array operations and
numpy functions the numpy.nan
entries are propagated as expected and all is
well. However, this is not always the case, and in particular the ERFA routines do not generally support
numpy.nan
values gracefully.
In cases where numpy.nan
is not acceptable, format class methods should use the
jd2_filled
property instead of jd2
. This replaces numpy.nan
with
0.0
. Since jd2
is always in the range -1 to +1, substituting 0.0
will allow functions to return “reasonable” values which will then be masked in
any subsequent outputs. See the value
property of the
TimeDecimalYear
format for any example.
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.
Caching¶
The computations for transforming to different time scales or formats can be
time-consuming for large arrays. In order to avoid repeated computations, each
Time
or TimeDelta
instance caches such transformations internally:
>>> t = Time(np.arange(1e6), format='unix', scale='utc')
>>> time x = t.tt
CPU times: user 263 ms, sys: 4.02 ms, total: 267 ms
Wall time: 267 ms
>>> time x = t.tt
CPU times: user 28 µs, sys: 9 µs, total: 37 µs
Wall time: 32.9 µs
Actions such as changing the output precision or sub-format will clear the cache. In order to explicitly clear the internal cache do:
>>> del t.cache
>>> time x = t.tt
CPU times: user 263 ms, sys: 4.02 ms, total: 267 ms
Wall time: 267 ms
Since astropy 3.1 these objects can be changed internally. In order to ensure consistency between the transformed (and cached) version and the original, the transformed object is set to be not writeable. For example:
>>> x = t.tt
>>> x[1] = '2000:001'
Traceback (most recent call last):
...
ValueError: Time object is read-only. Make a copy() or set "writeable" attribute to True.
If you require modifying the object then make a copy first, e.g. x = t.tt.copy()
.
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 the observed values provided by the International Earth Rotation and Reference Systems (IERS) Service. Astropy will automatically download and use values from the IERS which cover times spanning from 1973-Jan-01 through one year into the future. In addition the astropy package is bundled with a data table of values provided in Bulletin B, which cover the period from 1962 to shortly before an astropy release.
When the delta_ut1_utc
attribute is not set
explicitly then IERS values will be used (initiating a download of a few Mb
file the first time). For details about how IERS values are used in astropy
time and coordinates, and to understand how to control automatic downloads see
IERS data access (astropy.utils.iers). The example below illustrates converting to the UT1
scale along with the auto-download feature:
>>> t = Time('2016:001')
>>> t.ut1
Downloading http://maia.usno.navy.mil/ser7/finals2000A.all
|==================================================================| 3.0M/3.0M (100.00%) 6s
<Time object: scale='ut1' format='yday' value=2016:001:00:00:00.082>
Note
The IERS_Auto
class contains machinery
to ensure that the IERS table is kept up to date by auto-downloading the
latest version as needed. This means that the IERS table is assured of
having the state-of-the-art definitive and predictive values for Earth
rotation. As a user it is your responsibility to understand the
accuracy of IERS predictions if your science depends on that. If you
request UT1-UTC
for times beyond the range of IERS table data then the
nearest available values will be provided.
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))
>>> t.utc.iso
'2006-01-15 21:24:37.500'
>>> t.ut1.iso
'2006-01-15 21:24:37.834'
>>> t.tai.iso
'2006-01-15 21:25:10.500'
>>> t.tt.iso
'2006-01-15 21:25:42.684'
>>> t.tcg.iso
'2006-01-15 21:25:43.323'
>>> t.tdb.iso
'2006-01-15 21:25:42.684'
>>> t.tcb.iso
'2006-01-15 21:25:56.894'
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 13.08952187 hourangle>
>>> t.sidereal_time('apparent')
<Longitude 13.08950368 hourangle>
>>> t.sidereal_time('apparent', 'greenwich')
<Longitude 5.08950368 hourangle>
>>> t.sidereal_time('apparent', '-90d')
<Longitude 23.08950368 hourangle>
>>> t.sidereal_time('apparent', '-90d', 'IAU1994')
<Longitude 23.08950365 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 |
datetime | TimeDeltaDatetime |
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>
Barycentric and Heliocentric Light Travel Time Corrections¶
The arrival times of photons at an observatory are not particularly useful for accurate timing work, such as eclipse/transit timing of binaries or exoplanets. This is because the changing location of the observatory causes photons to arrive early or late. The solution is to calculate the time the photon would have arrived at a standard location; either the Solar system barycentre or the heliocentre.
Suppose you observed IP Peg from Greenwich and have a list of times in MJD form, in
the UTC timescale. You then create appropriate Time
and SkyCoord
objects and
calculate light travel times to the barycentre as follows:
>>> from astropy import time, coordinates as coord, units as u
>>> ip_peg = coord.SkyCoord("23:23:08.55", "+18:24:59.3",
... unit=(u.hourangle, u.deg), frame='icrs')
>>> greenwich = coord.EarthLocation.of_site('greenwich')
>>> times = time.Time([56325.95833333, 56325.978254], format='mjd',
... scale='utc', location=greenwich)
>>> ltt_bary = times.light_travel_time(ip_peg)
>>> ltt_bary
<TimeDelta object: scale='tdb' format='jd' value=[-0.0037715 -0.00377286]>
If you desire the light travel time to the heliocentre instead then use:
>>> ltt_helio = times.light_travel_time(ip_peg, 'heliocentric')
>>> ltt_helio
<TimeDelta object: scale='tdb' format='jd' value=[-0.00376576 -0.00376712]>
The method returns an TimeDelta
object, which can be added to
your times to give the arrival time of the photons at the barycentre or
heliocentre. Here, one should be careful with the timescales used; for more
detailed information about timescales, see Time Scale.
The heliocentre is not a fixed point, and therefore the gravity continually changes at the heliocentre. Thus, the use of a relativistic timescale like TDB is not particularly appropriate, and, historically, times corrected to the heliocentre are given in the UTC timescale:
>>> times_heliocentre = times.utc + ltt_helio
Corrections to the barycentre are more precise than the heliocentre, because the barycenter is a fixed point where gravity is constant. For maximum accuracy you want to have your barycentric corrected times in a timescale that has always ticked at a uniform rate, and ideally one whose tick rate is related to the rate that a clock would tick at the barycentre. For this reason, barycentric corrected times normally use the TDB timescale:
>>> time_barycentre = times.tdb + ltt_bary
By default, the light travel time is calculated using the position and velocity of Earth and the Sun from built-in ERFA routines, but one can also use more precise calculations using the JPL ephemerides (which are derived from dynamical models). An example using the JPL ephemerides is:
>>> ltt_bary_jpl = times.light_travel_time(ip_peg, ephemeris='jpl')
>>> ltt_bary_jpl
<TimeDelta object: scale='tdb' format='jd' value=[-0.0037715 -0.00377286]>
>>> (ltt_bary_jpl - ltt_bary).to(u.ms)
<Quantity [0.00058527, 0.00058518] ms>
The difference between the builtin ephemerides and the JPL ephemerides is normally of the order of 1/100th of a millisecond, so the builtin ephemerides should be suitable for most purposes. For more details about what ephemerides are available, including the requirements for using JPL ephemerides, see Solar System Ephemerides.
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]...)
>>> 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 makes a small change to the date format. For instance one could insert T
in the yday
format with the following TimeYearDayTimeCustom
class. Notice how
the subfmts
definition is modified slightly from the standard
TimeISO
class from which it inherits:
>>> from astropy.time import TimeISO
>>> class TimeYearDayTimeCustom(TimeISO):
... """
... Year, day-of-year and time as "<YYYY>-<DOY>T<HH>:<MM>:<SS.sss...>".
... The day-of-year (DOY) goes from 001 to 365 (366 in leap years).
... For example, 2000-001T00:00:00.000 is midnight on January 1, 2000.
... The allowed subformats are:
... - 'date_hms': date + hours, mins, secs (and optional fractional secs)
... - 'date_hm': date + hours, mins
... - 'date': date
... """
... name = 'yday_custom' # Unique format name
... subfmts = (('date_hms',
... '%Y-%jT%H:%M:%S',
... '{year:d}-{yday:03d}T{hour:02d}:{min:02d}:{sec:02d}'),
... ('date_hm',
... '%Y-%jT%H:%M',
... '{year:d}-{yday:03d}T{hour:02d}:{min:02d}'),
... ('date',
... '%Y-%j',
... '{year:d}-{yday:03d}'))
>>> t = Time('2000-01-01')
>>> t.yday_custom
'2000-001T00:00:00.000'
>>> t2 = Time('2016-001T00:00:00')
>>> t2.iso
'2016-01-01 00:00:00.000'
Another special case that is relatively common 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.
Custom string formats with strftime
and strptime
¶
The Time
object supports output string representation
using the format specification language
defined in the Python standard library for time.strftime
.
This can be done using the strftime
method:
>>> from astropy.time import Time
>>> t = Time('2018-01-01T10:12:58')
>>> t.strftime('%H:%M:%S %d %b %Y')
'10:12:58 01 Jan 2018'
Conversely, to create a Time
object from a custom date string
that can be parsed with Python standard library time.strptime
(using the same format language linked above), use the
strptime
class method:
>>> from astropy.time import Time
>>> t = Time.strptime('23:59:60 30 June 2015', '%H:%M:%S %d %B %Y')
>>> t
<Time object: scale='utc' format='isot' value=2015-06-30T23:59:60.000>
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 |
TimeDatetime64 (val1, val2, scale, precision, …) |
|
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. |
TimeDeltaDatetime (val1, val2, scale, …[, …]) |
Time delta in datetime.timedelta |
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]]”. |
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…”. |
TimeInfo ([bound]) |
Container for meta information like name, description, format. |
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 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.