# Positions and Coordinates¶

Skyfield is careful to distinguish the position of an object from the several choices of coordinate that you can use to designate that position with numbers. There are only three basic kinds of position that Skyfield recognizes, but several different ways in which each position can be turned into coordinates.

Here is a quick reference to the three basic kinds of position, together with all of the attributes and methods that they support:

```Three positions

obj.at(time)        →  Barycentric position (BCRS)
└─ observe(obj2)   →  Astrometric position (ΔBCRS)
└─ apparent()  →  Apparent position (GCRS)

ICRF, Barycentric, Astrometric, or Apparent position
│
├── position.au         →   x, y, z
├── position.km         →   x, y, z
├── position.to(unit)   →   x, y, z
│
├── velocity.au_per_d   →   xdot, ydot, zdot
├── velocity.km_per_s   →   xdot, ydot, zdot
├── velocity.to(unit)   →   xdot, ydot, zdot
│
├── radec(epoch=t)      →   ra, dec, distance
├── radec()             →   ra, dec, distance
├── distance()          →   distance
│
├── ecliptic_position() →   x, y, z
├── ecliptic_velocity() →   xdot, ydot, zdot
├── ecliptic_latlon()   →   lat, lon, distance
├── galactic_position() →   x, y, z
└── galactic_latlon()   →   lat, lon, distance

Apparent position only
│
└── altaz(…)            →   alt, az, distance

Angle like ra, dec, alt, and az
│
│
├── hours               →   23.934469599999996
├── hstr()              →   '23h 56m 04.09s'
├── hstr(places=4)      →   '23h 56m 04.0906s'
├── hms()               →   (23.0, 56.0, 4.0)
├── signed_hms()        →   (1.0, 23.0, 56.0, 4.0)
│
├── degrees             →   359.017044
├── dstr()              →   '359deg 01' 01.4"'
├── dstr(places=3)      →   '359deg 01' 01.358"'
└── signed_dms()        →   (1.0, 359.0, 1.0, 1.0)
```

The rest of this page is designed to explain all of the features outlined in the quick reference above. All hyperlinked attributes and method names, both in the text above and in the explanations below, lead to the low-level API Reference which explains each option in even greater detail.

## Quick reference to generating positions¶

Skyfield already supports three kinds of object that can compute their position. Each object offers an `at()` method whose argument can be a Time object that either holds a single time or a whole array of different time values. Objects respond by returning either a single scalar position or else by generating a whole series of positions.

Instantiating positions from numeric coordinates

If you already possess x, y, and z coordinates oriented along the ICRF axes, then you can directly instantiate any of the position classes by providing those coordinates as a vector of length 3. Here, for example, is how to instantiate the `ICRF` class:

```from skyfield.positionlib import ICRF

x = 3141.0
y = 2718.0
z = 5820.0
vec = ICRF([x, y, z])
```

This also works with more specific position classes like the `Barycentric` class. The resulting position object will support all of the main features described on this page.

The planets

The eight planets and Pluto are all supported, thanks to the excellent work of the Jet Propulsion Laboratory (JPL) and Skyfield’s support for their major solar system ephemerides. Read more

```from skyfield.api import Topos, load

t = ts.now()

mars = planets['mars']

# From the center of the Solar System (Barycentric)

barycentric = mars.at(t)

# From the center of the Sun (Heliocentric)

sun = planets['sun']
heliocentric = sun.at(t).observe(mars)

# From the center of the Earth (Geocentric)

earth = planets['earth']
astrometric = earth.at(t).observe(mars)
apparent = earth.at(t).observe(mars).apparent()

# From a place on Earth (Topocentric)

boston = earth + Topos('42.3583 N', '71.0603 W')
astrometric = boston.at(t).observe(mars)
apparent = boston.at(t).observe(mars).apparent()
```
The stars

Stars and other fixed objects with catalog coordinates are able to generate their current astrometric position when observed from a planet. Read more

```from skyfield.api import Star, Topos, load

t = ts.now()

boston = earth + Topos('42.3583 N', '71.0603 W')
barnard = Star(ra_hours=(17, 57, 48.49803),
dec_degrees=(4, 41, 36.2072))

# From the center of the Earth (Geocentric)

astrometric = earth.at(t).observe(barnard)
apparent = earth.at(t).observe(barnard).apparent()

# From a place on Earth (Topocentric)

astrometric = boston.at(t).observe(barnard)
apparent = boston.at(t).observe(barnard).apparent()
```
Earth satellites

Earth satellite positions can be generated from public TLE elements describing their current orbit, which you can download from Celestrak. Read more

```from skyfield.api import EarthSatellite, Topos, load

t = ts.now()

line1 = '1 25544U 98067A   14020.93268519  .00009878  00000-0  18200-3 0  5082'
line2 = '2 25544  51.6498 109.4756 0003572  55.9686 274.8005 15.49815350868473'

boston = Topos('42.3583 N', '71.0603 W')
satellite = EarthSatellite(line1, line2, name='ISS (ZARYA)')

# Geocentric

geometry = satellite.at(t)

# Geographic point beneath satellite

subpoint = geometry.subpoint()
latitude = subpoint.latitude
longitude = subpoint.longitude
elevation = subpoint.elevation

# Topocentric

difference = satellite - boston
geometry = difference.at(t)
```

What can you do with a position once it has been generated? The rest of this document is a complete tour of the possibilities.

## Barycentric position¶

When you ask Skyfield for the position of a planet or star, it produces a three-dimensional position that is measured from the Solar System barycenter — the center of mass around which all of the planets revolve. The position is stored as x, y, and z coordinates in the International Celestial Reference System (ICRS), a permanent frame of reference that is a high-precision replacement for the old J2000.0 system that was popular at the end of the 20th century.

The ICRS is one of three related concepts that you will often see mentioned together in technical publications:

• Barycentric Celestial Reference System (BCRS) — a coordinate origin whose relativistic frame of reference is the one that was carefully defined in IAU 2000 Resolution B1.3 which puts the coordinate origin at the gravitational center of the Solar System. The direction in which the coordinate axes might point is left unspecified.
• International Celestial Reference Frame (ICRF) — a precision reference frame that radio astronomers have helped us define, that will become forever more exact as we measure better and better positions for a list of very distant radio sources. Wherever the origin of your coordinate system might lie, you can use the ICRF to define where your x-axis, y-axis, and z-axis should point.

• International Celestial Reference System (ICRS) — A coordinate system whose origin is defined by the BCRS and whose axis directions are defined by the ICRF. In essence, the ICRS = ICRF + BCRS.

Instead of using an acronym, Skyfield uses the class name `Barycentric` for coordinates expressed in the ICRS. You can view the raw x, y, and z coordinates by asking Skyfield for their `position` attribute:

```# BCRS positions of Earth and Venus

earth = planets['earth']
mars = planets['mars']

t = ts.utc(1980, 1, 1)
print(earth.at(t).position.au)
print(mars.at(t).position.au)
```
```[-0.16287311  0.88787399  0.38473904]
[-1.09202418  1.10723168  0.53739021]
```

The coordinates shown above are measured using the Astronomical Unit (au), which is the average distance from the Earth to the Sun. You can, if you want, ask for these coordinates in kilometers with the `km` attribute. And if you have the third-party AstroPy package installed, then you can convert these coordinates into any length unit with the `to()` method.

## Astrometric position¶

You might think that you could determine the position of Mars in the night sky of Earth by simply subtracting these two positions to generate the vector difference between them. But that would ignore the fact that light takes several minutes to travel between Mars and the Earth. The image of Mars in our sky does not show us where it is, right now, but where it was — several minutes ago — when the light now reaching our eyes or instruments actually left its surface.

Correcting for the light-travel time does not simply fix a minor inconvenience, but reflects a very deep physical reality. Not only the light from Mars, but all of its physical effects, arrive no faster than the speed of light. As Mars tugs at the Earth with its gravity, we do not get pulled in the direction of the “real” Mars — we get tugged in the direction of its time-delayed image hanging in the sky above us!

So Skyfield offers a `observe()` method that carefully backdates the position of another object to determine where it was when it generated the image that we see in our sky:

```# Observing Mars from the Earth's position

astrometric = earth.at(ts.utc(1980, 1, 1)).observe(mars)
print(astrometric.position.au)
```
```[-0.92909581  0.21939949  0.15266885]
```

This light-delayed position is called the astrometric position, and is traditionally mapped on a star chart by the angles right ascension and declination that you can compute using the `radec()` method and display using their `hstr()` and `dstr()` methods:

```# Astrometric RA and declination

print(ra.hstr())
print(dec.dstr())
print(distance)
```
```11h 06m 51.22s
+09deg 05' 09.2"
0.96678 au
```

As we will explore in the next section, objects never appear at exactly the position in the sky predicted by the simple and ideal astrometric position. But it is useful for mapping the planet against the background of stars in a printed star atlas, because star atlases use astrometric positions.

If you have several bodies for which you want to generate positions, note that it’s more efficient to generate the observer’s position only once and then re-use that position for each object you want to observe.

```# Observing Mars from the Earth's position

mercury, venus = planets['mercury'], planets['venus']

here = earth.at(ts.utc(2018, 5, 19))
print(here.observe(mercury).position.au)
print(here.observe(venus).position.au)
```
```[0.894231   0.67436002 0.24448674]
[0.02134722 1.22511631 0.57114432]
```

## Apparent position¶

To determine the position of an object in the night sky with even greater accuracy, two further effects must be taken into account:

Deflection
The object’s light is bent, and thus its image displaced, if the light passes close to another large mass on its way to the observer. This will happen if the object lies very near to the Sun in the sky, for example, or is nearly behind Jupiter. The effect is small, but must be taken into account for research-grade results.
Aberration
The velocity of the Earth itself through space adds a very slight slant to light arriving at our planet, in the same way that rain or snow seen through the windshield while driving appears to be slanting towards you because of your own motion. The effect is small enough — at most about 20 arcseconds — that only in 1728 was it finally observed and explained, when James Bradley realized that it provided the long-awaited proof that the Earth is indeed in motion in an orbit around the Sun.

Skyfield lets you apply both of these effects by invoking the `apparent()` method on an astrometric position. Like an astrometric position, an apparent position is typically expressed as the angles right ascension and declination:

```# Apparent GCRS ("J2000.0") coordinates

apparent = astrometric.apparent()

print(ra.hstr())
print(dec.dstr())
print(distance)
```
```11h 06m 51.75s
+09deg 05' 04.7"
0.96678 au
```

But it is actually unusual to print apparent coordinates in a permanent unchanging reference frame like the ICRF, so you are unlikely to find the two values above if you look up the position of Mars on 1980 January 1 in an almanac or by using other astronomy software.

Instead, apparent positions are usually expressed relative to the Earth’s real equator and poles as its rolls and tumbles through space — which, after all, is how right ascension and declination were defined through most of human history, before the invention of the ICRF axes. The Earth’s equator and poles move at least slightly every day, and move by larger amounts as years add up to centuries.

To ask for right ascension and declination relative to the real equator and poles of Earth, and not the ideal permanent axes of the ICRF, simply add the keyword argument `epoch='date'` when you ask the apparent position for coordinates:

```# Coordinates relative to true equator and equinox

print(ra.hstr())
print(dec.dstr())
print(distance)
```
```11h 05m 48.68s
+09deg 11' 35.7"
0.96678 au
```

These are the coordinates that should match other astronomy software and the data in the Astronomical Almanac, and are sometimes said to be expressed in the “dynamical reference system” defined by the Earth itself.

## Azimuth and altitude¶

The final result that many users seek is the altitude and azimuth of an object above their own local horizon.

• Altitude measures the angle above or below the horizon, with a positive number of degrees meaning “above” and a negative number indicating that the object is below the horizon (and impossible to view).
• Azimuth measures the angle around the sky from the north pole, so 0° means that the object is straight north, 90° indicates that the object lies to the east, 180° means south, and 270° means that the object is straight west.

Altitude and azimuth are computed by calling the `altaz()` method on an apparent position. But because the method needs to know whose local horizon to use, it does not work on the plain geocentric (“Earth centered”) positions that we have been generating so far:

```alt, az, distance = apparent.altaz()
```
```Traceback (most recent call last):
...
ValueError: to compute an apparent position, you must observe from a specific Earth location that you specify using a Topos instance
```

Instead, you have to give Skyfield your geographic location. Astronomers use the term topocentric for a position measured relative to a specific location on Earth, so Skyfield represents Earth locations using `Topos` objects that you can add to an Earth object to generate a position relative to the center of the Solar System:

```# Altitude and azimuth in the sky of a
# specific geographic location

boston = earth + Topos('42.3583 N', '71.0603 W')
astro = boston.at(ts.utc(1980, 3, 1)).observe(mars)
app = astro.apparent()

alt, az, distance = app.altaz()
print(alt.dstr())
print(az.dstr())
print(distance)
```
```24deg 30' 27.2"
93deg 04' 29.5"
0.678874 au
```

So Mars was more than 24° above the horizon for Bostonians on 1980 March 1 at midnight UTC.

The altitude returned from a plain `altaz()` call is the ideal position that you would observe if the Earth had no atmosphere. You can also ask Skyfield to estimate where an object might actually appear in the sky after the Earth’s atmosphere has refracted its image higher. If you know the weather conditions, you can specify them.

```alt, az, distance = app.altaz(temperature_C=15.0,
pressure_mbar=1005.0)
print(alt.dstr())
```
```24deg 32' 34.1"
```

Or you can ask Skyfield to use a standard temperature and pressure when generating its rough simulation of the effects of refraction.

```alt, az, distance = app.altaz('standard')
print(alt.dstr())
```
```24deg 32' 37.0"
```

Keep in mind that the computed effect of refraction is simply an estimate. The effects of your local atmosphere, with its many layers of heat and cold and wind and weather, cannot be predicted to high precision. And note that refraction is only applied to objects above the horizon. Objects below −1.0° altitude are not adjusted for refraction.