Talk:Polar mount

Geometry of tracking path
The geostationary orbit lies in the plane of the earth's equator. If the dish is not on the equator, it has to be aimed slightly "downward" in order to point at any geostationary satellite. This means that the directions in which the dish aims, as it slews around the axis, trace out the surface of a cone, with the dish at the vertex of the cone. The locus of the points in the equatorial plane at which the dish aims is the intersection of this cone and the equatorial plane. It is therefore a conic section, a circle, ellipse, or (theoretically, though not in practice in this situation) a parabola or hyperbola.

If the dish's rotation axis is parallel with the earth's axis, the conic section is a circle, but, unless the dish is at one of the earth's poles (which is impossible, since the geostationary orbit cannot be seen from there), its centre is not at the earth's centre. It is located on the polar axis through the dish. Since the geostationary orbit is a circle centred at the earth's centre, a dish slewing around a polar axis cannot accurately point at geostationary satellites at different longitudes (unless the dish is on the equator).

The situation can be improved by making the dish slew around an axis that is slightly more vertical than a polar axis. If done correctly, this changes the conic section to an ellipse whose centre (the mid-point of its major axis) is at the earth's centre. This is close to the true shape of the geostationary orbit, but they are not precisely the same. The orbit is a circle and the locus of points in the equatorial plane at which the dish aims is an ellipse. It is impossible for a dish slewing around a single axis to aim precisely at geostationary satellites at all longitudes (unless the dish is on the earth's equator). However, the error can be small enough to be negligible for practical purposes of radio communication.

DOwenWilliams (talk) 21:55, 17 November 2010 (UTC) David Williams

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