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Wandering geosynch satellites.

In "Observing Geosynchronous Satellites" (October issue, page 66), Randy Rhea states, "A satellite's north-south excursion from a fixed point on the sky is caused by orbital inclination, whereas an east-west excursion is caused by eccentricity."

The first statement is true; the second is mostly not. Even if a satellite in an inclined orbit has zero eccentricity (a circular orbit), it still appears to move in a figure-8 that includes some east-west motion. This happens for the same reason Earth's own axial inclination causes the Sun to go through east-west excursions to form the familiar figure-8 of the analemma. (The analemma is the Sun's position on the sky as seen at the same time of day through the year). In both cases, the reason has to do with the fact that at high or low latitudes (or declinations), lines of longitude (or right ascension) are spaced more closely together.

If the orbit is circular, the figure-8 will be symmetric, with its lines crossing in the middle at the equator. Non-zero eccentricity makes the figure-8 asymmetric. For instance, the small top and big bottom of the Sun's analemma shows that Earth's orbit is not a perfect circle.

In the case of a geosynch satellite, each time the satellite crosses the equator its longitude must be within an assigned "longitude box" 0.1[degrees] to 0.2[degrees] wide. To ensure this, the satellite must do station-keeping maneuvers to maintain an eccentricity of zero to within several ten-thousandths.

So, the east-west excursions that we see geosynchronous satellites performing are dominated by the effect of orbital inclination, not eccentricity (unless the inclination is so small that the orbit is better described as geostationary).

Robert D. Furber

Manhattan Beach, California

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Title Annotation:Letters
Author:Furber, Robert D.
Publication:Sky & Telescope
Article Type:Letter to the editor
Date:Jan 1, 2012
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