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Computation and plotting of azimuth and elevation for astronomical objects

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Computation and plotting of azimuth and elevation for astronomical objects


Azely (pronounced as "as-elie") is a Python package for computation and plotting of horizontal coordinates (azimuth and elevation; az/el, hereafter) of astronomical objects at given location and time. While computation and plotting are realized by astropy and matplotlib, what Azely provides is high-level API to use them easily. In fact Azely offers one-liner to compute and plot, for example, one-day elevation of the Sun in Tokyo:

>>> azely.compute('Sun', 'Tokyo').el.plot(ylim=(0, 90))



  • High-level API: Azely provides a simple yet powerful compute() function. Users can complete most of operation with it (e.g., information acquisition and computation).
  • Handy output: Azely's output (from compute()) is pandas DataFrame, a de facto standard data structure of Python. Users can convert it to other formats like CSV and plot it by matplotlib using builtin methods.
  • Web information acquisition: Azely can automatically acquire object and location information (i.e., longitude and latitude) from online services (e.g., catalogues or maps). Obtained information is cached in a local TOML file for an offline use.
  • User-defined information: Azely also offers to use user-defined object and location information written in a TOML file.


  • Python: 3.6, 3.7, or 3.8 (tested by author)
  • Dependencies: See pyproject.toml


$ pip install azely

Basic usage

This section describes basic az/el computation using compute() function.

Compute function

Azely's compute() function receives the following parameters and returns pandas DataFrame (df):

>>> import azely
>>> df = azely.compute(object, site, time, view, **options)

This means that azely will compute az/el of object observed from site at (on) time in view. For example, the following code will compute az/el of Sun observed from ALMA AOS on Jan. 1st 2020 in Tokyo.

>>> df = azely.compute('Sun', 'ALMA AOS', '2020-01-01', 'Tokyo')

Acceptable formats of each parameter and examples are as follows.

Parameter Acceptable format Description Examples
object <obj. name> name of object to be searched 'Sun', 'NGC1068'
<toml>:<obj. name> user-defined object to be loaded (see below) 'user.toml:M42', 'user:M42' (also valid)
site 'here' (default) current location (guess by IP address)
<loc. name> name of location to be searched 'ALMA AOS', 'Tokyo'
<toml>:<loc. name> user-defined location to be loaded (see below) 'user.toml:ASTE', 'user:ASTE' (also valid)
time 'today' (default) get one-day time range of today
'now' get current time
<time> start time of one-day time range '2020-01-01', '1/1 12:00', 'Jan. 1st'
<time> to <time> start and end of time range '1/1 to 1/3', 'Jan. 1st to Jan. 3rd'
view '' (default) use timezone of site
<tz name> name of timezone database 'Asia/Tokyo', 'UTC'
<loc. name> name of location from which timezone is identified same as site's examples
<toml>:<loc. name> user-defined location from which timezone is identified same as site's examples

Output DataFrame

The output DataFrame contains az/el expressed in units of degrees and local sidereal time (LST) at site indexed by time in view:

>>> print(df)
                                  az         el             lst
2020-01-01 00:00:00+09:00  94.820323  68.416756 17:07:59.405556
2020-01-01 00:10:00+09:00  94.333979  70.709575 17:18:01.048298
2020-01-01 00:20:00+09:00  93.856123  73.003864 17:28:02.691044
2020-01-01 00:30:00+09:00  93.388695  75.299436 17:38:04.333786
2020-01-01 00:40:00+09:00  92.935403  77.596109 17:48:05.976529
...                              ...        ...             ...
2020-01-01 23:20:00+09:00  96.711830  59.146249 16:31:49.389513
2020-01-01 23:30:00+09:00  96.185941  61.431823 16:41:51.032256
2020-01-01 23:40:00+09:00  95.664855  63.719668 16:51:52.674998
2020-01-01 23:50:00+09:00  95.147951  66.009577 17:01:54.317740
2020-01-02 00:00:00+09:00  94.634561  68.301349 17:11:55.960483

[145 rows x 3 columns]


Here is a sample script which will plot one-day elevation of the Sun and candidates of black hole shadow observations at ALMA AOS on Apr. 11th 2017 in UTC.

import azely
import matplotlib.pyplot as plt'seaborn-whitegrid')

fig, ax = plt.subplots(figsize=(12, 4))

site = 'ALMA AOS'
time = 'Apr. 11th 2017'
view = 'UTC'

for obj in ('Sun', 'Sgr A*', 'M87', 'M104', 'Cen A'):
    df = azely.compute(obj, site, time, view)
    df.el.plot(ax=ax, label=obj)

ax.set_title(f'site: {site}, view: {view}, time: {time}')
ax.set_ylabel('Elevation (deg)')
ax.set_ylim(0, 90)


Advanced usage

This section describes advanced usage of Azely by special DataFrame accessor and local TOML files. Note that Azely will create a config directory, $XDG_CONFIG_HOME/azely (if the environment variable exists) or ~/.config/azely, after importing azely for the first time. TOML files for configuration (config.toml) and cached information (objects.toml, locations.toml) will be automatically created in it.

Plotting in local sidereal time

The compute() function does not accept local sidereal time (LST) as view (i.e., view='LST') because LST has no information on year and date. Instead an output DataFrame has in_lst property which provides az/el with a LST index converted from the original time index. For example, the following code will plot elevation of an object in LST:

>>> df.in_lst.el.plot()

In order to use LST values as an index of DataFrame, LST has pseudo dates which start from 1970-01-01. Please ignore them or hide them by using matplotlib DateFormatter when you plot the result. Here is a sample script which has JST time axis at the bottom and LST axis at the top of a figure, respectively.

import matplotlib.dates as mdates

fig, ax = plt.subplots(figsize=(12, 4))
twin = ax.twiny()

df = azely.compute('Sun', 'Tokyo', '2020-01-01')
df.in_lst.el.plot(ax=twin, alpha=0)

ax.set_ylabel("Elevation (deg)")
ax.set_ylim(0, 90)

formatter = mdates.DateFormatter('%H:%M')


User-defined information

Azely offers to use user-defined information from a TOML file. Here is a sample TOML file (e.g., user.toml) which has custom object and location informaiton.

# user.toml

name = "ASTE Telescope"
longitude = "-67.70317915"
latitude = "-22.97163575"
altitude = "0"

name = "Galactic center"
frame = "galactic"
longitude = "0deg"
latitude = "0deg"

If it is located in a current directory or in the Azely's config directory, users can use the information like:

>>> df = azely.compute('user:GC', 'user:ASTE', '2020-01-01')

Cached information

Object and location information obtained from online services is cached to TOML files (objects.toml, locations.toml) in the Azely's config directory with the same format as user-defined files. If a query argument is given with '!' at the end of it, then the cached values are forcibly updated by a new acquisition. This is useful, for example, when users want to update a current location:

>>> df = azely.compute('Sun', 'here!', '2020-01-01')

Customizing defualt values

Users can modify default values of the compute() function by editing the Azely's config TOML file (config.toml) in the Azely's config directory like:

# config.toml

site = "Tokyo"
time = "now"

Then compute('Sun') becomes equivalent to compute('Sun', 'Tokyo', 'now').


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