Ground based telescopes have two main types of mounts.  One is the hour angle declination mount, which has its axes lining up with the axes of right ascension and declination.  This means that its axes are in reference with the celestial sphere.  This mount is preferred because once the declination is set no more adjusts need to be made along that direction, and compensation for right ascension can be handled with a simple hour angle timing device.  The other type of mount is the azimuth-elevation mount.  This mount has its reference points at the local horizon and due North.  Azimuth is rotational motion from North along the horizontal plane, while elevation is the motion from the horizon along a vertical plane.  The azimuth-elevation mount must always track the apparent motion of stars in both planes, even once they are locked on.  This, of course, is not as easy as with the hour angle declination mount which must only move one axis to compensate for the earth's rotation.  However, large and heavy telescopes are usually based on the azimuth-elevation mount because of the simpler, less costly structural requirements.

The SOFIA is a unique hybrid of the azimuth-elevation mount and a spherical bearing, since it is not a ground-based observatory but a stratospheric observatory. The airplane itself provides a coarse rotating platform for the azimuth axis (directional heading and yaw) and the telescope bulkhead suspension provides limited coarse rotation (from 20 to 60 degrees) for the elevation axis. The SOFIA telescope is precisely moved (within +/- 3 degrees) on a large, low friction spherical bearing, which is controlled in three dimensions. These three perpendicular directions are called the line-of-sight (LOS), elevation, (Figure 1) and cross-elevation (Figure 2). The telescope cross-elevation is not along the horizontal azimuth plane, since it is elevated at some angle above the plane's horizontal. The pointing direction of cross-elevation, together with the elevation and the aircraft heading and yaw is difficult to visualize, but it can be precisely converted with trigonometric transformation:

true-azimuth(deg) = heading - 90 + yaw + cross-elevation*cosine(elevation)

Likewise the true elevation must include a correction for aircraft roll. The azimuth-elevation can, in turn, be converted to hour-angle-declination coordinates for a standard portable telescope according to the latitude of the aircraft; figure 3 gives an example of the relations for 35-degree north latitude. The spherical mount, together with a stable inertial reference, allows decoupling of the telescope motion from the incidental motions of the aircraft to provide precise pointing and is what makes SOFIA unique. The total observation area in the night at any one moment is less than a good Earth-based telescope because elevation angles are limited to between 20 degrees and 60 degrees, but because of the aircraft platform, if one selects the correct latitude and time, all areas of the celestial sphere can be observed.

 A ground-based telescope using an azimuth-elevation mount can also have three axes of rotation called line of sight (LOS), elevation, and azimuth, which correspond to the normal x, y, and z-axes.  A telescope can rotate about all three of these axes.  These axes and rotation about them are all perpendicular to each other .  To help you understand the value of  the third axis think about target shooting.  To hit the target you must have the proper elevation and azimuth.  These rotations are obviously perpendicular.  Now, imagine rotating 180 degrees about the LOS.  If your azimuth and elevation are correct the LOS rotation will have no effect on hitting the target, even though your view is now upside down.  Now imagine a more general target , like a flock of geese, and that you would like to shoot a picture of them, centered on the lead goose.  If the geese were flying along a path which appeared diagonal to the horizon, you would rotate the camera along the LOS in order to take a rational picture.  Similarly, Astronomers who are imaging object clusters may want to rotate the LOS to compare images taken on different nights and at different hour angles.

SOFIA Observations Require more than Meets the Eye

We must remember the fact that SOFIA is an airborne observatory and this makes targeting a star in the SOFIA a unique experience. Many factors must be considered together to provide precise targeting: Earth's rotational velocity (the date and time), velocity of the aircraft, pitch & yaw of the aircraft, longitudinal and latitudinal coordinates of the aircraft. Ground based telescopes only adjust for date and time, with fixed translations for location, to compute a star position. However, the SOFIA flight must account for all these other factors.