Positional Measurements

Orbital elements of hundreds of secret objects, like the NOSS satellites, are not available from official sources. An informal network of amateurs specializes in finding and keeping track of such satellites. Regular accurate positional measurements are needed for this kind of detective work.

Positional observers are also the primary public source of brightness data for all kinds of satellites. Prediction services, such as the Heavens-Above web site, make use of the standard magnitude data produced by amateurs to provide accurate magnitude estimates of satellites.

Positional observers make precise measurements of the position and time of a satellite at several points along its track, enabling its orbital elements to be determined or updated. Skilled observers routinely meet or exceed positional accuracy of 0.03 degrees, and timing accuracy of 0.1 second.

The required investment in equipment is modest - a pair of 7 x 50 binoculars, a stopwatch, and an accurate star atlas are sufficient to try your hand at the hobby. Experienced observers graduate to larger binoculars, of at least 80 mm aperture, not only to observe fainter satellites, but to reveal a greater number of closely spaced reference star-pairs, which are key to achieving precise observations, as explained below.

The easiest way to determine the position of a satellite is when it passes between two not too distant stars, say at most half a degree apart. You start the stopwatch at the moment that the satellite intersects the imaginary line joining the two stars; at the same time, you judge the fraction of the distance of the point of intersection from star A to star B. For example, 40 percent of the distance from A to B, down from A toward B. The most accurate measurements are possible when the line connecting the two stars is perpendicular to the path of the satellite.

Skilled observers are able to judge the point of intersection between a pair of stars to an accuracy of about 5 percent of the distance between the stars. For example, using stars spaced 0.5 deg, yields accuracy of about 0.025 deg. Star pairs that close are infrequently seen using 7x50 binoculars, which tends to limit the accuracy you can achieve. Using 80 mm binoculars will reveal many more faint star-pairs, enabling you to more consistently achieve accuracy of 0.03 deg or better.

The accuracy of a position does not only depend on the way it is measured, but on the angular velocity of the satellite. A low orbiting satellite (lower than 500 km) moves across the observer's sky with an angular velocity of 0.5 to 1 degree per second. During a time interval of 0.1 s (our timing precision) the satellite moves between 3 and 6 arc minutes, which will ultimately be our positional accuracy. Naturally, for higher objects the angular velocity will be smaller and the positional accuracy will accordingly be better.

To determine the actual time of your observation, stop the stopwatch at a known reference time, provided by an accurate time signal, such as radio station WWV, and subtract the recorded duration from the reference time. For best accuracy, use a time source that provides audible ticks at each second. You should try to achieve 0.1 seconds precision or better. Always report observations using Universal Time (UT) (also called Greenwich Mean Time - GMT).

To determine the actual position of your observation, look up the reference stars in a star atlas that has sufficient scaling to enable estimating accuracy of 1 or 2 arc minutes. Now you plot the satellite's position in the star atlas. For example, if we call '1' the full distance on the segment joining the two stars, and if you estimated that the satellite passed at '0.4' from one star, you can easily plot the satellite's position in the star atlas (with a ruler). You can then estimate the coordinates of the satellite's position from the plotted position in the star atlas.

Alternatively, you can look up the coordinates of the reference stars in a star catalogue and calculate the satellite's position using spherical trigonometry.

Ted Molczan has written ObsReduce, an MS Windows program that reduces observations of satellites relative to the background stars into their precise coordinates. Observers identify their reference stars in a simulated binocular or telescope field of view, select them using the mouse, enter the observed geometric and positional data, and the program automatically produces a formatted observation report.

Several reporting formats have been devised to facilitate the exchange of positional observations. Each observation report should include :

  • the equipment used

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