Internal reference system

The internal cartesian reference system is a right-handed equatorial system with the particularity that the axes labels are unorthodox. Usually, $X$ points to the fundamental direction ($\alpha =0,\delta =0$), $Z$ points “up” and $XY$ is the fundamental plane ($\delta =0$), with $Y=Z\times X$.

In our case, it is $Z$ which points to the fundamental direction ($\alpha =0,\delta =0$), $Y$ points up and $XZ$ is the fundamental plane ($\delta =0$), with $X=Y\times Z$. In order to convert from common equatorial cartesian coordinates $(XYZ)$ to Gaia Sky coordinates $(X^{\prime }{Y}^{\prime }{Z}^{\prime })$, you just need to swap the axes:

• $X^{\prime }=Y$

• $Y^{\prime }=Z$

• $Z^{\prime }=X$

The reason for this is that this is the OpenGL convention as far as coordinate systems go.

Description

So, in Gaia Sky $XZ$ is the equatorial plane ($\delta =0$). $Z$ points towards the vernal equinox point ($\alpha =0,\delta =0$). $Y$ points towards the north celestial pole ($\delta =+{90}^{\circ }$). $X$ is perpendicular to both $Z$ and $Y$ and points to $\alpha =+{90}^{\circ }$ so that $X=Y\times Z$.

Gaia Sky reference system

All the positions and orientations of the entities in the scene are at some point converted to this reference system for representation. The same happens with the orientation sensor data in mobile devices.

Internal units

Internally, the objects in Gaia Sky are positioned using Internal Units. The default Internal Units ($iu$) are defined as follows:

• $1iu=1\ast {10}^{9}m$

When running in Virtual Reality mode, and only for the duration of the session, the Internal Units are scaled as follows:

• $1iu=1\ast {10}^{5}m$