t, a, d

To begin using the Zenith Method, two tracking data points (observed positions) and knowledge of the satellite's direction of travel are required. This would normally involve a minimum of two images obtained near the observer's local zenith. It is highly recommended that Equatorial coordinates (R.A. and Dec.) be used since they are truly inertial coordinates.

Below is an example image of a Low Earth Orbit (LEO) satellite obtained by the author near his local zenith. The direction of travel is indicated by the arrow. The exposure time was 5 seconds. The identity of the satellite in the image will be revealed in the final step. The tracking data coordinates required are shown at each end of the satellite streak, as shown by the red circles in the image.

It is highly recommended that images of the satellite rather than naked eye or eyepiece observation be used since the observation errors will be much lower when using image analysis. Like any other orbit determination method, accurate astrometric analysis is absolutely essential. For this example, I used my own astrometric analysis method that involved six stars (three stars near each endpoint).

The example tracking data presented in the table below has the Equatorial coordinates in J2000.0. To use this method, both the R.A. and Dec. have to be in angular units. To convert the R.A. coordinate from hours to degrees, use the following equation:

a_i (^o) = [15^o/hr] [a_i (hms)]

where i = the observation number (1 or 2).

The convention for this method is that the second observation (a₂, d₂) follow the first observation (a₁, d₁) along the apparent direction of travel, as shown in the first table below.

The observer's geodetic latitude also has to be known. This is provided (for this example) in the second table below.

PROCEED TO STEP #2