**Field Rotation**

Field rotation limits the maximum exposure possible with an Alt-Az mount. The field rotation depends upon the latitude of the observer, as well as, the Azimuth angle and Altitude of the object being observed. The following field rotation formula and plot are copied from an excellent discussion of the topic on the RASC Calgary Center and reproduced here in short:

Field Rotation Rate (arcmin/min) = 15.04 COS(Latitude)*COS(Azimuth Angle) / COS(Altitude Angle)

The plot shows the field rotation that you can expect in arcsec per sec for different Azimuth and Altitude angles for an observer at latitude 37 degrees. Field rotation is largest looking north and due south and for objects at higher altitudes. Field rotation is zero due east and due west, but remember the sky is constantly moving so objects in those directions begin to have field rotation immediately. An observer at latitude 37degrees looking at an object at an Altitude of 60 degrees due south, will see the field rotate 24arcsec/sec; while looking at an object in the NE, 45 degrees Azimuth, at an Altitude of 40 degrees will see a field rotation of 11arcsec/sec.

Field rotation limits the maximum exposure possible with an Alt-Az mount. The field rotation depends upon the latitude of the observer, as well as, the Azimuth angle and Altitude of the object being observed. The following field rotation formula and plot are copied from an excellent discussion of the topic on the RASC Calgary Center and reproduced here in short:

Field Rotation Rate (arcmin/min) = 15.04 COS(Latitude)*COS(Azimuth Angle) / COS(Altitude Angle)

The plot shows the field rotation that you can expect in arcsec per sec for different Azimuth and Altitude angles for an observer at latitude 37 degrees. Field rotation is largest looking north and due south and for objects at higher altitudes. Field rotation is zero due east and due west, but remember the sky is constantly moving so objects in those directions begin to have field rotation immediately. An observer at latitude 37degrees looking at an object at an Altitude of 60 degrees due south, will see the field rotate 24arcsec/sec; while looking at an object in the NE, 45 degrees Azimuth, at an Altitude of 40 degrees will see a field rotation of 11arcsec/sec.

The field rotation rate varies as the cosine of the latitude of the observer. As the graph below shows, this means that the rotation rate is maximum at the equator and zero at the north and south poles.

To put this into perspective we need to translate this into the number of pixels of movement per exposure. To do that, we need the Field Rotation Rate result from above, the exposure time in seconds and the number of pixels from the center to edge of corner of our particular video camera. The equation for this is:

Field Rotation Rate (pixels/exposure) = Field Rotation Rate (arcmin/min) * 2 * PI * Exposure (seconds) / 1296000

where PI is 3.1415... and the 129600 = 360 x 3600 is to convert the units from degrees to radian and from hours to seconds (but you may not care about these details).

Once again, using the Mallincam Xtreme and looking at the Video Sensor Specs page on this web site, there are 768 pixels along the width of the camera, so from the center to edge is half that, or 384 pixels. Plugging this into the equation above for an observer at latitude 37degrees we find that, for an object at 60degrees Altitude due south, a 30 second exposure will result in 3.9 pixels of rotation. However, at 40 degrees Altitude that is reduced to 1.3 pixels of rotation.

Field Rotation Rate (pixels/exposure) = Field Rotation Rate (arcmin/min) * 2 * PI * Exposure (seconds) / 1296000

where PI is 3.1415... and the 129600 = 360 x 3600 is to convert the units from degrees to radian and from hours to seconds (but you may not care about these details).

Once again, using the Mallincam Xtreme and looking at the Video Sensor Specs page on this web site, there are 768 pixels along the width of the camera, so from the center to edge is half that, or 384 pixels. Plugging this into the equation above for an observer at latitude 37degrees we find that, for an object at 60degrees Altitude due south, a 30 second exposure will result in 3.9 pixels of rotation. However, at 40 degrees Altitude that is reduced to 1.3 pixels of rotation.

© 2015 Curtis V. Macchioni

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