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The picture above is eccentricity evolution for one year of a GEO satellite. Based on that eccentricity evolution, I want to do maneuvers to correct the eccentricity. But I have problems, I am confused in what time I should do the maneuver. At some literatures written that eccentricity maneuver is done based on the eccentricity evolution. I have had the eccentricity evolution, but still don't know what the time it is.

Thank you.

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    $\begingroup$ Can you mention what exactly is plotted? Are these components of the eccentricity vector? Without knowing the total eccentricity (magnitude of the vector) the problem might be incompletely specified. What does the origin (0, 0) represent? What does "correct the eccentricity" mean? Do you want zero eccentricity, or just to have the eccentricity vector point at the origin of your plot (i.e. have your periapsis point in a specific direction? $\endgroup$ – uhoh Feb 11 at 9:47
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    $\begingroup$ different but possibly related: How does the “eccentricity-inclination vector separation” technique work for colocated GEO satellites? $\endgroup$ – uhoh Feb 11 at 9:58
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    $\begingroup$ Where is this satellite positioned relative to the two "stable" locations or the two "anti-stable" ( $\frac{\pi}{2}$ apart ) ? $\endgroup$ – Carl Witthoft Feb 11 at 13:29
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This is relatively straight-forward but the OP needs to determine/find out mission requirements to start with. It looks like a homework problem so I will leave you to fill in some gaps yourself (plus, in retrospect, its not that great an explanation!).

NB assuming the unlabelled plot is that of eccentricity vector then the eccentricity magnitude is simply the distance from the origin to the line. Clearly the magnitude varies from more or less circular (i.e. at the origin) to about 0.0005 or 0.0006 (by eye).

The size of this circle comes from the satellite shape plus any regularly applied control. If the satellite is left uncontrolled this circle's radius is a characteristic of the area to mass ratio and reflectivity. (This isn't any kind of quote, I just wanted to give the whole point more emphasis)

It would help to know whether this previous year has already had eccentricity control or not. Lets assume the last year of progression has occurred with the satellite doing no eccentricity control of its own and that the longitude manoeuvres have been arranged to have no influence on eccentricity (actually rather a contrived situation but hey no). In that case the satellite will continue to do a similar circular pattern each year, with some scope for the big "curly circle" to drift around from year to year. Basically each January it will be at the same point on the circle even though the circle as a whole is mobile.

Have a look at the eccentricity evolution over two or three years in order to see what is typical for a few objects that are either:

a) some controlled geostationary satellites and

b) some uncontrolled geo debris

What is the mission target eccentricity? This will depend upon:

  1. the form of station-keeping: the longer the East-West cycle the more of the satellite's allocated longitude box that will take up and thus there will be less space for longitude librations that derive from eccentricity. The latter is likely to be the smaller quantity if the East/West manoeuvres are weekly or more.
  2. if there are nearest satellite neighbours also in the same orbital slot. If so there should be some agreed separation strategy that is bound to involve eccentricity control.
  3. whether the needs of the satellite user community in terms of doppler effects on modem operation imply a limitation on eccentricity evolution.

Finally: control.

If one were able to reset this pattern so that instead of being lopsided it is a circle centred on 0,0 then its clear it will have a through-year magnitude of 0.00025 or 0.0003. This would already be typical of a controlled commercial communications satellite. You might want it tighter but its ok. This is where it is important to know if that past year was already controlled.

Step 1

You have to look at this eccentricity vector and now visualise the real orbit. It has an argument of perigee as well as magnitude. You will have to look at the dates that it achieves each point on the current circle and then set the new argument of perigee so that it follows the same pattern but geometrically shift the circle so that it sits symmetrically around 0,0 then you will need to put the argument of perigee in the right direction (i.e. place on the circle) for the time of year.

If the previous circle was obtained without manoeuvres and you are happy with the circle radius then you will just need to reset this circle once a year the same way.

Step 2

If the existing circle was achieved with manoeuvres then without manoeuvres the natural circle will be larger. You will need to regularly constrain the new circle to the radius value you want. You can achieve this the same way as for step 1. Just envisage where you want the circle to be and look up the dates from the old circle so that you can transpose the position around the circle from the old one to the desired one.

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