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Based on How much time does it take to circularize a GTO orbit using ion propulsion? and the launch and entry into service dates, it takes about 6 months of continuous ion propulsion to transfer a GTO to a GEO.

According to a spacenews.com article, the journey was 7 months for the all-electric Eutelsat 117 West B. They have an illustration, which suggests the GTO's apogee was higher than GEO:

enter image description here
Source: spacenews.com

The post Thrust and rotation strategy to circularize a standard GTO orbit using ion propulsion? offers a theoretical approach. To a mere Kerbonaut, who only knows how to circularize an orbit by firing at apogee: when a continuous very, very, very small thrust is used in practice such as that payload (Eutelsat 117 West B) aboard the June 2016 Falcon 9 launch, how does the orbit look like as it circularizes, since the thrust is not always at apogee?

Of note, I think, is the movable arms with the thrusters:

enter image description here

(...) these twin arms can be moved freely about its body so their thrusts can always be aligned precisely with the satellite's center of gravity for orbit raising and stationkeeping – saving propellant to elongate mission life (eoportal.org).

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    $\begingroup$ Not sure it's the same but to do it on the TDRS-1 rescue using 1 lbf thrusters took months commons.erau.edu/cgi/… $\endgroup$ Mar 14, 2021 at 23:17
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    $\begingroup$ @OrganicMarble your post on that $\endgroup$
    – uhoh
    Mar 15, 2021 at 1:00
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    $\begingroup$ @uhoh I didn't say they were duplicates, just related. More importantly (to me) that's quite strange, the OP edit history currently shows EDIT#5 as being the current version and that this was made 5 hours ago, vs 2 hours ago for my comment. However I could see the EDIT#4 when I added the comment! Time is now 16th March 2021 00:32GMT $\endgroup$
    – Puffin
    Mar 16, 2021 at 0:36
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    $\begingroup$ @Puffin since everybody can read and react to comments, mine is for the drive-by close-voters who think it might be grounds for duping. $\endgroup$
    – uhoh
    Mar 16, 2021 at 1:00
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    $\begingroup$ @uhoh OK, good point to remember in future $\endgroup$
    – Puffin
    Mar 16, 2021 at 11:35

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I don't have an exact GTO-to-GEO transfer on hand, but I have this figure from a class assignment from a few years back. While definitely not a practical trajectory, it shows the characteristics of how to transfer from an elliptical to a circular orbit.

Elliptical-to-circular low-thrust transfer

This solution was computed using indirect optimization. This problem assumed constant thrust magnitude (so the thruster is always firing), with the control variable being the thrust angle. The objective function was min(t_f).

As the figure shows, the thrust vectors are approximately in the velocity direction near periapsis and apoapsis, and they are approximately perpendicular between the apses. In general, when the thrust vectors are in line with the velocity vector (parallel or anti-parallel), they are adjusting the orbital energy (and therefore increasing/decreasing semi-major axis). When the thrust vectors are perpendicular to velocity, they are adjusting the eccentricity (shape) and argument of periapsis (orientation) of the orbit.

For a 6-month transfer from GTO to GEO, you would have a LOT of spirals. A GTO has a period of around 10.7 hr, and GEO has a 24 hr period. If you take their average, you're looking at around 250 spirals.

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  • $\begingroup$ Welcome to Space SE! Please feel free to post this as a supplementary answer to Thrust and rotation strategy to circularize a standard GTO orbit using ion propulsion? as well. Do the arrows point in the direction of acceleration? $\endgroup$
    – uhoh
    Mar 23, 2021 at 0:52
  • $\begingroup$ I added a dot in the center of the image which may make it easier to understand at first glance. Feel free to roll back. $\endgroup$
    – uhoh
    Mar 23, 2021 at 0:58
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    $\begingroup$ Yes, the yellowish arrows point in the direction of acceleration from thrust. The dot is fine! Unfortunately the code to generate this is lost to time so I can't clean it up anymore in MATLAB. $\endgroup$
    – Paul W
    Mar 23, 2021 at 1:26

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