Geometry dialog box (Dome | Setup | Geometry button)

This dialog box allows you to specify the dome geometry for your dome, telescope and optical system.

Three-dimensional dome drawing courtesy Gene Kochanowsky.

Use the drawings above and definitions below to determine the geometry for your dome, telescope and optical system.

Roll Axis Elevation (radians)

The longitude, or "roll" axis is the polar axis in the case of an equatorial mount and the azimuth axis in the case of an alt-azimuth mount. This parameter is not defined in the above diagram. See Technical Description of Required Parameters below for more information.

Dome Radius (Rdome)

Enter the radius of the dome. All measurements should be the same units. See above diagram for details. See Technical Description of Required Parameters below for more information.

Offset of Mount from Dome

The arguments xm, ym, zm specify the offset of "the mount" from "the dome." See Technical Description of Required Parameters below for more information.

Xm

Enter the distance from the N-S centerline of "the dome" to "the mount." See above diagram for details. Also, see Technical Description of Required Parameters below for more information.

Ym

Enter the distance from the E-W centerline of "the dome" to "the mount." See above diagram for details. Also, see Technical Description of Required Parameters below for more information.

Zm

Enter the distance from "the dome" to "the mount." This parameter is not defined in the above diagram. See Technical Description of Required Parameters below for more information.

Offset of Telescope from Mount

The arguments xt, yt specify the offset of the telescope from the mount. See Technical Description of Required Parameters below for more information.

Xt

Enter the distance from the N-S centerline of "the mount" to the "optical center." See Technical Description of Required Parameters below for more information.

Yt

Enter the distance from the E-W centerline of "the mount" to the "optical center." This parameter is not defined in the above diagram, and is normally zero. See Technical Description of Required Parameters below for more information.

Offset of Optical Axis from Telescope (yo)

Enter the offset of the optical axis within the telescope. This value is typically zero for most amateur telescopes.

Use these dome and telescope mount geometry options to define the position of your telescope mount with respect to the center of the dome. These parameters are required to predict the azimuth and elevation of the dome aperture for any asymmetrically mounted telescope. See Technical Description of Required Parameters below for more information.

 Technical Description of Required Parameters

Notes:

1. The routine supports all types of mount based on two axes at right angles. The longitude, or "roll", axis is the polar axis in the case of an equatorial mount and the azimuth axis in the case of an alt-azimuth mount. The latitude, or "pitch", axis is the declination axis in the case of an equatorial mount and the elevation axis in the case of an alt-azimuth mount.

2. The tilt of the roll axis is specified through the phi argument, which is the elevation above the horizon of the north, or positive, direction of the roll axis. For an equatorial mount, phi is equal to the latitude; for an alt-azimuth mount it is equal to pi/2. Except in the alt-azimuth case, the tilt of the roll axis defines "north" for the dome. If the roll axis is not, in fact, aligned north-south then an appropriate adjustment needs to be made to the returned azimuth.

3. The dome is presumed to be hemispherical (or some other portion of a sphere). The radius of the sphere is specified through the Rdome argument. Any desired units can be used as long as the other "length" arguments are in the same units.

4. The arguments xm, ym, zm specify the offset of the mount from the dome. "The dome" is the center of the sphere. "The mount" is that point along the roll axis (and hence fixed in space) that lies nearest to the telescope (Note 5). The x, y, z coordinate system is oriented east, north, up.

5. The arguments xt, yt specify the offset of the telescope from the mount. "The mount" is the fixed point defined in Note 4. "The telescope" is that point along the pitch axis (and hence fixed within the moving part of the mount) that lies nearest to the optical axis (Note 6).

6. The argument yo specifies the offset of the optical axis within the telescope. "The telescope" is the point defined in Note 5. "The optical center" is the point along the optical axis that lies nearest to the pitch axis. It is the intersection of the optical axis with the dome that defines the point the azimuth and elevation of which are to be calculated.

7. The telescope roll/pitch coordinate system matches hour angle and declination in the equatorial case. This means that it is left-handed, longitude increasing clockwise as seen from the positive pole. It means also that zero roll occurs when a northern-hemisphere telescope is pointing south. Thus the telescope roll/pitch system matches azimuth/elevation in handedness but there is an azimuth zero-point offset of 180 degrees. Note that the roll/pitch are mechanical rather than celestial, so that above/below pole and east/west of the pier cases are distinguished.

8. The coordinate systems for the offsets are as follows.

9. • They are all right-handed.

   • The xm, ym, zm axes point east, north, up.

   • The orientation of the xt, yt axes is such that they coincide with xm, ym for the case of an alt-azimuth mount pointing south. Other types of mounting follow suit. For an equatorial mount in the Northern Hemisphere, when the telescope is pointing at the meridian north of the zenith, xt points east (i.e. aligned with xm), and the horizontal component of yt points north (i.e. aligned with ym).

   • The yo axis is coincident with yt when the telescope is pointing at the positive pole.

   • The units of rdome, xm, ym, zm, xt, yt, xo and yo must all be the same.

9. The dome azimuth/elevation coordinate system follows the normal convention. Azimuth increases clockwise from zero in the north, through 90 degrees (pi/2 radians) in the east. The value returned is in the range zero to 2pi. At the zenith, zero is returned.

10. Small "pointing corrections", minor non-perpendicularities and misalignments, are ignored.

Example Geometry Setup for a German Equatorial Mount (GEM)

The optical axis and the declination axis intersect. The declination axis and the polar axis intersect. The distance from the polar axis to the optical axis is 505 mm. The point at which the polar axis and declination axis intersect is 35 mm west of, 370 mm north of, and 1250 mm above the center of the dome, which is 3.8 meters in diameter. The telescope site is at latitude +36.18 degrees. The telescope is pointing at a star 10 minutes west of the meridian, at declination +37.9 degrees, and is east of the pier.

The arguments are as follows: