Issue 89

16 Jan: Newer Flash readers may not be aware that for a few months in 2022 we had Jack Anthony as a contributing author. I sent Jack a head’s up on what we saw with the SY-24 triplets and SJ-6 05B in early January, and he was nice enough to give us his thoughts on what was going on. More on that below. I also want to recommend the following articles Jack wrote for the Flash covering the Classic Orbital Elements:

• Jack’s Astro Corner: It’s Elemental (Part I)
• Shaping up with Eccentricity (Part II)
• Inclination – The Tilted Element (Part III)
• Right Ascension of the Ascending Node (RAAN) – Let’s Do the Twist (Part IV)
• Argument of Perigee — Let’s get close with our orbit (Part V)
• How To Rendezvous With Another Satellite
• True Anomaly — “Where are we?” (Part VI)
• Applying your Orbital Element Knowledge

Many thanks to Jack for coming out of retirement to help out our Flash readers (and editor).

I’m baaaaack! Remember all those “Jack’s Astro Corner” articles I wrote? Hope so! We covered a lot of topics that can help you understand threat astrodynamics that confront us these days. The preceding “Shiyan-24A/B/C & Shijian-6 05B: A Closer Look” article gives me a chance to illustrate some astro rules of thumb. I particularly wish to look at the 24A, B and C trio “fly-by” of 6-05-B that occurred 7 – 8 January 2024. I’ll call the trio the Chasers, and the SJ 6-05-B satellite the Target for my discussion. When I watched the LSAS prepared video, I saw an opportunity to explain the 10:1 rule, plus expand on the explanation of the out of plane motion (both crosstrack and radial). This 10:1 rule of thumb is applicable to Low Earth Orbits. If you have not watched the video, please do so. Pretty cool video to learn from! Watch it several times… start and stop it and try to formulate how YOU would narrate it to a fellow US Space Force Guardian. All Guardians should seek to learn and be able to step up and be the astro hero, and say with confidence “let me explain what we are seeing here.”

10:1 Rule: What you talking about, Jack? In his 1999 book Space Power Theory, James Oberg introduces the concept, based on his many years as a NASA Flight Controller at Johnson Space Center. Jim is an space expert of the highest order, and one of the best “explainers of astro stuff.” Here’s a pdf of the section of his book. Note he uses the term “Orbitology”, which is a term I hate, with one exception… when Jim Oberg uses it. His explanation of the 10:1 Rule is on the third page. Give it a read, in its entirety — you’ll learn a lot.

I called upon my astro and RPO dynamo friend Jason Westphal, who leads a company named TenOne Space. Wow, Jason named his company after the 10:1 Rule! He spelled it out “TenOne.” That’s pretty cool! His team are RPO experts, and the 10:1 Rule is a key concept used by RPO mission teams as they seek to get their Chaser close to a Target (for example, getting into position to dock for servicing).

Here’s how Jason explains it:

“The majority of missions we undertake involve spacecraft rendezvous with other objects, so it seemed appropriate to name our company after the 10:1 rule. The 10:1 ratio enables us to estimate the timing for the convergence of co-elliptic drift phasing orbits. To illustrate, if we’re trailing a target spacecraft by 10 km with the objective of reaching the target inserting into a safety ellipse in close proximity after one orbit, we know our spacecraft needs to attain an orbit with a semi-major axis 1 km below that of the target to achieve the desired drift rate using the 10:1 rule.”

Let’s dive into the recent RPO situation involving the trio drifting by the Target. I want to draw you attention to what’s being shown in the video at T+ 4 to 22 seconds, as well as the three Chasers Range to Target over Time plot, at T+33 sec.

You see a lot of zig-zagging, up-down and sideways; I’ll talk about that in a second. But, did you see how the Chaser trio are in a row, moving forward relative to the Target? That’s what excited me to shout out “that’s the 10:1 Rule!” The zig-zagging ellipse is moving forward. If you study the range vs time plot, and measure the distance moved in one orbit (a sine wave cycle), you maybe be able to figure out it moves about 35 km per orbit (the orbit period is ~95.6 minutes). I grabbed the TLEs for these spacecraft from Celestrak (thank you TS Kelso), and calculated their mean orbit altitudes. My calculator tells me the Target’s mean altitude is 544 km, and the trio each is at ~540.5 km. The difference is 3.5 km. OK, get ready for the 10:1 Rule. If we multiply the 3.5 Km difference in mean altitude by 10, we get 35 km. So, since the trio is below the Target, they advance on it 35 km per orbit. See that, the 10:1 ratio works. Clark Keith (1952-2013), the RPO legend from the XSS-11 days, called it linear drift when we did it a lot in the 2005-2007 pioneering AFRL RPO experimental space mission.

They also employed a safety ellipse in their linear drift approaches to their target. More on that next. So here’s a thinking question: what if the Chaser trio was above the Target by 3.5 km? “Bueller, Bueller, Bueller…..who knows?” Of course you know: the Chaser trio would be moving back relative to the target, and at 35 km per orbit. Pretty cool stuff!

So, what is all the zig-zagging going on? It’s a repetitive ellipse. There’s relative motion happening in both crosstrack and radial, as you can see in the video. There is an ellipse repeat going on here. China launched the trio into the orbit plane of SJ 6-05-B, but not exactly. So you are seeing the effects of their orbit having a slightly different orbit tilt (inclination) and twist (Right Ascension of the Ascending Node). Again mathematically monkeying with the TLE data, I mashed my calculator excitedly and found the trio had close alignment in inclination (I got 0.0109°) and not as close in RAAN (My estimate 0.6567°). You can see the out of plane “zig- zagging.” indicative of the offset in inclination and RAAN. There are also some big differences between the Target’s Argument of Perigee and the Chasers’. This is wise, in that it helps set up this drifting ellipse, and ensures as the Chasers go by the Target such that they don’t collide. This is the safety ellipse concept that all of us RPO enthusiasts use to keep it safe out there, as we get close to others (with permission of course). In the preceding “A Closer Look” article they talk about setting up where the Chaser is in the safety ellipse, to get the Sun in a good position for imagery. Wow, this RPO and fly-by activity requires some orbital element thinking. Do YOU know all about orbital elements? (I wrote a six part series a while ago in the Flash… a fun read. Go find it if you need a tune up.)

Now, go explain the 10:1 rule to some General officer, or your kids, or your neighbor. They will declare YOU ARE AN ASTRO DYNAMO… maybe invite you to parties to wander around explaining astro! I hope you enjoyed my “I’m baaaack” return, and sharpened your astrodynamics understanding and awesomeness. Thank you, Jason Westphal of TenOne Space, and Jim Oberg, NASA mission control pioneer and astro “explainer of stuff.” Stay awesome for America in space!