h

 Variable Symbol Value Radius of Earth at Observer Latitude rE 6,367.75 km Gravitational Parameter m 398,600.442 km3/s2 Apparent Angular Velocity of Satellite wapp 0.0123037 rad/s
 When observed at zenith, the satellite range from the observer is approximately the same as the satellite altitude above the Earth's surface. The orbit range (AKA height or altitude at zenith) is found by using the equation below: h = (rE / 3) { 2cos [ cos-1 ( 5381105.9 / r3E w2app  - 1 ) / 3 ] - 1 } This equation can only be used if the following condition is true: wapp > [ 2690553 / rE3 ]1/2 For the observer's latitude, [ 2690553 / rE3 ]1/2 = 0.003228 rad/s. Since wapp for this example is indeed greater than 0.003228 rad/s, it is alright to proceed with the calculation. h = 614.1 km   The determined value suggests that the satellite in the image was approximately 614 km from the observer when the image was obtained. The orbit radius (approximately the semi-major axis for a LEO orbit) can be determined by adding this determined altitude to the radius of the Earth at the observer's latitude.  rorbit ~ a = h + rE a ~ 6981.9 km   The satellite's orbit period can therefore be found from the determined semi-major axis by using Kepler's Third Law. T = 2p [ a3 / 398600.44 ]1/2 T = 5806 s = 96.8 m = 1.613 h From the orbit period, the mean motion (n) of the satellite's orbit can be found: n = 1 / T n = 14.881157 orbits/day These results look adequate for a typical LEO satellite. We have determined the first of the six Keplerian orbit elements (semi-major axis) for this satellite using a single image! The satellite streak endpoint coordinates will be used again to determine the satellite's inclination, right ascension of ascending node (RAAN) and the mean anomaly. GO BACK TO STEP #3

 SITE MAP Step 4: Satellite Range Was Last Modified On December 30, 2013