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This answer to How are co-located satellites positioned relative to each other? links to the paywalled paper Separation of Geostationary Satellites with Eccentricity and Inclination Vector with the abstract:

Nowadays, locating several satellites in a narrow station-keeping window is a good way to make advantage of the geostationary orbit source problem. To avoid collision,drawbacks of close approach and mutual interferences, a method of multi-satellites separation using eccentricity vector and inclination vector is discussed in this paper. The principle and constraint equation of combined separation is investigated. The initial qualification, the eccentricity and inclination control strategy in W/E maneuver and N/S maneuver is given. Simulation shows that minimum distance separation more than 10 Km, and two Chinese geostationary satellites work in orbit with secure operation.

Question: Is it possible to explain and/or illustrate how this technique works; how it maintains a safe distance between colocated GEO satellites?

I'm thinking that in the synodic (rotating) frame the two satellites will appear to rotate around each other, but I'm having difficulty visualizing how this actually works.

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I think each person will visualise this problem differently. Personally, whilst formal papers describing separation strategies can be interesting I often find that they miss out on the basics (though I couldn't comment on the article you mention).

Here is a simple explanation that applies between any pair of orbits but is particularly used at GEO, hopefully a clear enough starting place:

  1. Each satellite orbit is a plane, if the two planes are non-coplanar then they have a line of intersection. The only chance of a collision is somewhere along that intersection.
  2. Each orbit has a varying radius from Earth, i.e. it is eccentric to a degree. The only chance of a collision is where the radii are the same.
  3. Putting the above together then to avoid a collision we simply need to make sure we have radial separation at the plane crossing.

More details

The rest of this is will hopefully help bridge the gap to understanding dicussions of a separation strategy that have been written more formally:

  1. It happens that the plane is defined by inclination and RAAN, and so if you want to you can define the plane by the inclination vector which accounts for the inclination and RAAN

  2. The orbit radii are defined by the eccentricity and argument of perigee. Together these make up the eccentricity vector.

  3. Both the inclination and eccentricity vectors will progress through the year, and this can be constrained through station-keeping (ok, I admit this is where fancy diagrams help a bit).

  4. There is a notion of relative inclination and eccentricity vectors, i.e. between the two satellites.

  5. Thereafter the precise language for one method or another may well involve such tortuous notions as "keeping the relative inclination vectors and relative eccentricity vectors" at some angle to one another throughout the year.

  6. (EDIT) There will be quite a lot of variations of actual strategies according the number of satellites to be co-ordinated and any special needs if they are owned by different operators.

  7. (EDIT) So far, all of this applies at any timescale, daily or yearly because its just a concept. At some point the relative station-keeping cycles of the satellites involved will become relevant so that they can monitor the continuing progress - i.e. plan manoeuvre, check separation distances, execute manoeuvre(s), ranging and orbit determination, check it all worked.

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    $\begingroup$ +n! This is a really beautiful explanation! By the time I read through to item 2 I can already imagine the pair corkscrewing around the Earth. $\endgroup$ – uhoh Oct 17 '19 at 0:17
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    $\begingroup$ Many thanks, glad it worked for you. Just added last thoughts. $\endgroup$ – Puffin Oct 18 '19 at 10:45

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