# 10. Units and Coordinate Systems¶

## 10.1. Coordinate Systems¶

Astronomy is well known for its confusing coordinate systems: nature and math don’t always look at things through the same mirror. For example, the so-common (mathematical) right handed coordinate system that we call X-Y-Z does not neatly fit in with our own Galaxy, which rotates counter-clockwise (meaning the angular moment vector points to the galactic south pole). Sky coordinates (e.g. Right-ascension Declination) are is pinned on the sky, looking up, instead of on a sphere, looking down, and become a left-handed coordinate system where the “X” coordinate increases to the left.

Here are some examples, and their respective NEMO programs that deal with this. See also their {it manual} pages for more detailed information.

mkgalorbit

orbits in our galaxy have to deal with the UVW space velocities
in the galactic coordinate system. There is no formal definition of a spatial XYZ
system, other than Z=0 being the galactic plane. So, where to put the sun if
the galactic center is (0,0,0) is purely by convention. It so happens that
(-R0,0,0) is convenient since galactic longitude and latitude can be
easily expressed as `atan2(y,x)`

and `atan2(z,sqrt{x^2+y^2})`

resp.

mkspiral, mkdisk

These programs use
the `sign=`

keyword to set the sign of the angular moment vector. Positive
means thus counter-clockwise rotation in this convention. Of course with
tools like `snapscale`

and `snaprotate`

snapshots can always be
re-arranged to fit any schema.

snaprotate

in order for a known object (e.g. a disk) to be viewed as an ellipse with given position angle and ellipticity this program uses a series of Eulerian angle rotations. Apart from the astronomical convention to using position angle as a counter clockwise angle measured from north, these numbers do no trivially convert to the angles we use on the projected sky. There are some examples in the manual page, which we briefly highlight here.

item
The first example describes the projection of disks of spiral galaxies.
If kinematic information is also known,
the convention is to use the position angle of the receding
side of the galaxy. The inclination still has an ambiguity, which could
be used to differentiate based on which is the near and far side, but this would
result in values outside the commonly used 0..90 range. Thus the sense
of rotation (sign of the angular momentum)
is a more natural way, with
again `sign=-1`

for counter-clockwise rotating (as seen for us projected on
the sky)

Here are NEMO commands to create an example velocity fields of these two galaxies with the right orientation and velocity field (with an arbitrary rotation curve of course):

```
mkdisk - 1000 sign=+1 mass=1 |\ # clock wise rotating
snaprotate - - theta=-30,-160 order=yz |\
snapgrid - vel-m33.ccd moment=-1
mkdisk - 1000 sign=-1 mass=1 |\ # counter clock wise rotating
snaprotate - - theta=+22,170 order=yz |\
snapgrid - vel-m51.ccd moment=-1
```

The second example is that of a barred galaxy, or two nested disks if you wish. Here an addition angle, the difference between the major axis and that of the bar), is a parameter.

snapgalview

ccdfits

## 10.2. Units¶

Perhaps better to refer to a few man pages we have on this: units(1NEMO) , units(5NEMO) , and constants(5NEMO) .