Element Symbol Value
Epoch to 05:54:21.171 UTC December 16, 2007
Inclination i 51o.9970
R.A. of the Ascending Node aW0 251o.0219
Eccentricity e 0.0001492
Argument of Perigee w0 33o.8641
Mean Anomaly at TLE Epoch Mo 326o.2322
Mean Motion n 12.62256095 orbits / solar day
Propagation Time Dt 1.7677141 solar days
Mean Anomaly at Time t M(t) 1.37777389 radians (78o.940629)
True Anomaly at Time t n(t) 78o.95065818
Semi-major Axis a 7791.787473 km
Perigee Distance P 7790.624938 km
Geocentric Distance r(t) 7791.564499 km
Precessed R.A. of Asc. Node aW(t) 245o.6400244
Precessed Arg. of Perigee w(t) 37o.77767416
Argument of Latitude m(t) 116o.7283323
R.A. Difference Da 129o.278845
Geocentric R.A. ag 14o.9188694
Geocentric Declination dg +44o.73125163
Geocentric Cartesian x xg 5348.663965 km
Geocentric Cartesian y yg 1425.05581 km
Geocentric Cartesian z zg 5483.565179 km
Observer Geodetic Longitude q -75o.6883
Observer Geodetic Latitude l +44o.5903
Observer Geocentric Dec. di +44o.5903
Observer Geocentric R.A. ai 15o.419875
Observer Geocentric Cart. x ag 4371.468712 km
Observer Geocentric Cart. y bg 1205.734692 km
Observer Geocentric Cart. z cg 4470.310913 km
Topocentric Cartesian x xs 977.195253 km
Topocentric Cartesian y ys 219.321118 km
Topocentric Cartesian z zs 1013.254266 km
Topocentric R.A. a 12o.64980763 (00h 50m 35s.95)
Topocentric Declination d +45o.32255686 (+45o 20' 02".84)

With the coordinates of the GlobalStar M047 satellite predicted, it is often beneficial to compare these coordinates with actual observation. This is normally done to measure how trustworthy the propagation equations are for different satellite orbit types and different observation conditions.

Using Steps 1 to 14 we calculated the following coordinates for the GlobalStar M047 satellite:

a = 00h 50m 35s.95
d = +45o 20' 02".84

The original CASTOR image of the GlobalStar M047 satellite was used to determine the observed coordinates:

aobs = 00h 49m 26s.6
dobs = 45o 56' 10"

The errors of each coordinate were then calculated by subtracting the observed from the measured. These values are commonly known as "Residuals" and are also used in Orbit Determination.

Da = 1m 9s.35 = 12' 15".57
Dd = -36' 07".16

The total error was then calculated using the following equation:

cosD = sindsindobs + cosdcosdobscos [15o/hr (a - aobs) ]

D = 0o 38' 05".58

The image above shows an illustration of the predicted satellite streak location vs. the actual satellite streak detected by CASTOR. The dot at the endpoint of the predicted streak depicts the predicted location of the GlobalStar M047 satellite at the time selected for this example. The white arrow denotes the apparent direction of satellite travel in both cases.

This error would certainly enable the CASTOR wide-field camera (11.3 degrees FOV) to successfully detect this object using the predicted satellite coordinates calculated in this example. For a higher accuracy prediction, a higher precision orbit element propagator model would be required.

This single orbit propagation example is an introduction to the steps that automated orbit propagators contain in order to give you satellite location predictions based on your location and selected observation time(s). These steps are followed by every satellite prediction software and service that you use.

Contact CASTOR with your questions, comments and possible corrections.








Step 15: Comparing with Actual Was Last Modified On April 01, 2014