Issue 99

Of course I couldn’t let Robin have all the fun…in interesting cases like this I have found it very helpful to consult with our Orbital Mechanics Guru Jack Anthony. Many are familiar with Jack’s articles in the Flash answering all of the orbital mechanics questions you were afraid to ask. Here’s his take on TJS-10 and TJS-3…and GEO maneuvering in general. Thanks Jack! TJS-10 has been moving relative to TJS-3 and changing its position on the GEO belt quite a bit. The Celestrak plot of altitude, semi-major axis and longitude is an excellent depiction of what’s going on and from it you can see that altitude above or below the TJS-3 holding its position is the key to determining how fast TJS-10 is “drifting” (that’s not a astro word, but it is used often in chit chatting about movement of GEO satellites.) So, let’s have a quick lesson on how this occurs. The “magic” number is 78…78 kilometers that is. If you maneuver to 78 Km above Geo reference altitude (which is 35,786 KM, but remember when doing astro calculations, the radius is key to use…and it’s 42,164 km) and re-circularize at the new altitude you will drift 1 deg/day west per day. One degree in GEO arc is about 736 km in distance along the orbit path. I bet you know what happens if you maneuver to 78 Km below the GEO reference altitude. “Bueller, Bueller, Bueller?” You will get 1 deg/day east drift. So let’s say you boost up and re-circularize at 39 Km above GEO. What’s the drift rate? Well, it’s west and we simply take 39 divided by 78 and get 0.5 deg/day. Go back to the Celestrak plot and play with this rule of thumb. Quiz question: you are circular and 312 Km below GEO reference. Which was and at what rate? (east, 4 deg/day). OK, on more thing. How do you get to your new “drift” orbit? Well, I bet you all know who Walter Hohmann is. That whiz kid from Germany who in 1925 wrote a paper on the minimum energy transfer between two circular orbits (he was a visionary; he knew someday soon human-made satellites would be out there). I bet you are well aware of the Hohmann Transfer. So, it involved 2 positive In-Track Delta-V’s. To climb & re-circularize 78 Km higher all it takes is two 1.4 m/s Delta-Vs , separated by 11 hours 58 minutes, thus 2.8 m/s total. If you want to descend, well, make the Delta-V negative. Down ya go! I’m sure TJS-10 will continue to entertain us as it dances with TJS-3, and armed with this basic review above you’ll be more “in the know” as they move around relative to each other and the position on the GEO belt. TJS-3 Two Line Element Set (TLE) 1 43874U 18110A 24161.76367480 .00000001 00000+0 00000+0 0 9991 2 43874 0.6363 88.9008 0001447 54.5022 203.0600 1.00272505 20086 257.5 TJS-10 Two Line Element Set (TLE) 1 58204U 23169A 24161.76353244 .00000000 00000+0 00000+0 0 9996 2 58204 0.6322 88.6861 0001118 286.4253 331.1645 1.00272749 2278 257.5 This orbital element compare is time synchronized, the epoch times are about the same. So we can now compare orbital elements. What do we see here? Well, the yellow heighted compare shows these two spacecraft are Orbit Plane Matched” … essential to rendezvous and proximity ops. We see the eccentricity (blue highlight) is somewhat circular and equal. So far, so good. Now, this next step is a wee bit tricky, but if you add argument of perigee and mean anomaly you get the position of the satellite relative to the right ascension of the ascending node. We see in adding them and then converting to be less than 360, they pretty much match. Sooooo, just by doing a orbital element compare when the epoch times are the same we see they are “matched up”…cozy near each other. Hooray for taking the time to do a orbital element compare to see “what’s going on.”