Satellite observing, the basics

[aphh]

<p>I'm trying to figure out what is needed to get some orbital parameters of a satellite by observing the satellite in the sky.<br /><br /> Here is the basic schematic for a best case scenario, where the observer has unobstructed both horizons, sun is&nbsp; perpendicular to the satellite's orbit and the satellite passes directly overhead:<br /><br /><br /> <img src="http://sitelife.space.com/ver1.0/Content/images/store/13/8/8dae2b3a-c1a6-4319-a892-c412b6359552.Medium.jpg" alt="" /><br /><br />The blue area is the visible portion of the satellite's orbit in the best case scenario. Knowing the altitude makes it possible to calculate the time it takes for the satellite to complete the visible arc.</p><p>Let's say the satellite is the ISS, and you are in a position to get a direct overhead pass. The visible arc would then be 2 * ((6375km / (6375km + 330km) * cos^-1)) = 36 degrees.</p><p>If one orbit takes 5441 seconds to complete, then the visible pass would take 544 seconds in optimal conditions.</p><p>How far the satellite is when the visible pass begins in this scenario is (xkm)^2 + (6375km)^2 = (6705km)^2. Solving the x gives 2076 kilometers distance to the satellite when the visible pass begins or ends.</p><p>The length of the visible arc in this case is 2pi * 6705km / 10 = 4212km (because the visible arc is one tenth of the full circle in this scenario).&nbsp; </p><p>This is for a satellite, who's orbital parameters are known. The next step would be to determine the orbital parameters by observing how long it takes for the satellite to complete the visible pass.</p><p>For this we need reference points in the sky, stars. By observing how long it takes for the satellite to go between two fixed reference points in the sky should allow us to determine the time it takes for the satellite to complete one complete orbit and thus the mean altitude.&nbsp;</p>

 

[aphh]

<p>There's more;</p><p>let's say the satellite who's orbital parameters you'd like to know makes a direct overhead pass. During the visible pass the satellite goes right past familiar stars Altair and then Deneb.</p><p>When the satellite reaches Altair, you start clocking it with a time piece and the clock stops when the satellite reaches Deneb. You now have timed the portion of the satellite's orbit, that goes through 2 fixed reference points in the sky.</p><p>Now we need to know how far apart stars Altair and Deneb are in the sky. For this we need to know their celestial coordinates, which are R.A 297.70 degrees and declination (dec 1) 8.87 degrees for Altair and R.A. 310.36 degrees and declination (dec 2) 45.28 degrees for Deneb.</p><p>This means, that the stars are 12.66 degrees apart at the equator of the celestial sphere, we will call this distance Delta A.</p><p>Using a little bit of spherical trigonometry we can calculate the angular distance between these stars. The formula in it's simplest form is cos (distance) = cos Delta A * cos (dec 1) * cos (dec 2) + sin (dec 1) * sin (dec 2) = cos 12.66 * cos 8.87 * cos 45.28 + sin 8.87 * sin 45.28 = 0.79.</p><p>Using inverse cosine gives 38 degrees for the distance between stars Altair and Deneb on the celestial coordinates on a arc that would stretch directly overhead.</p><p>Now we only need to translate this distance to your local horizontal coordinates, which the satellite follows. With 2 unobstructed horizons your viewable portion of the sky is 180 degrees on the ground, but not on the celestial sphere. On the celestial sphere that would be the tangent in the schematic above.</p><p>Now we need to calculate the portion of the sky arc in degrees limited by your local horizons, or the tangent. Since the stars are infinitely far away, you are in fact seeing 180 degrees of the celestial sphere, right?</p><p>This means that if it took 544 seconds for a satellite to complete full 180 degree overhead pass, then the distance of 38 degrees between Altair and Deneb should take 115 seconds.</p><p>This scenario only works if you're positioned so that the stars Altair and Deneb are fully aligned for a overhead pass.</p><p>So it's not complete yet, but needs a translation between coordinates, celestial coordinates and observer's local horizontal coordinates.</p><p>More about that when I have the conversions figured out. <img src="http://sitelife.space.com/ver1.0/content/scripts/tinymce/plugins/emotions/images/smiley-smile.gif" border="0" alt="Smile" title="Smile" /> </p>