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In the video Why Does it take BepiColombo 7 Years To Get To Mercury? Scott Manley nicely explains some of the basic orbital mechanical aspects of the mission and compares it to the Messenger mission.

At roughly the six-minute mark he shows some graphics including a crude trajectory plot and then a nice plot of perihermion (also here) for the last three months of the mission.

This plot has a strange shape, it starts flat then starts accelerating downward, then levels off, then starts accelerating downward again, with an occasional orbit-raising maneuver not really changing the rate of descent.

It also looks like the predicted decay during conjunction (where I'm assuming it was out of contact with Earth) was not fast enough and the curve suddenly drops down at a bit when emerging from the Sun's exclusion area.

What is the source of this plot, where can I read further? Optionally an explanation here would be great as well!

fyi: The fundamentals of what is happening is described in @DavidHammen's answer to Through what process does MESSENGER undergo orbital decay?

enter image description here

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    $\begingroup$ Have you asked him? $\endgroup$ – Hobbes Oct 25 '18 at 15:49
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    $\begingroup$ @Hobbes It looks like that technique worked here for that user, but I'm too shy for social media. SE is about as far as I go. $\endgroup$ – uhoh Oct 25 '18 at 16:07
  • $\begingroup$ Not even worth an answer: messenger.jhuapl.edu/About/… $\endgroup$ – David Hammen Oct 26 '18 at 5:50
  • $\begingroup$ @DavidHammen and I'll write the rest of the answer myself. $\endgroup$ – uhoh Oct 26 '18 at 8:21
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Since nobody has jumped in so far to answer except @DavidHammen's incredibly helpful comment I'll write an answer to my own question.

Other/different answers are more than welcome!

His link http://messenger.jhuapl.edu/About/Mission-Design.html#final-extended-mission points to the final extension of the Messenger mission. This is a really nice summary and explains things so well that I don't know how to summarize.

Instead I will point out certain aspects of these strange wiggles shown in the screenshot.

Messenger was in a highly elliptical polar orbit around a low mass body near an extremely massive body (the Sun) so its orbit is constantly being pulled-on and reshaped, and there were many orbit correction maneuvers as well.

The maneuvers were used to

a) offset the perturbation effects that would have prematurely ended the mission by moving the periapsis down to the surface, causing end of mission.

b) keep the periapsis over latitudes (and longitudes) of interest to better study certain features. While the periapsis altitudes were of order 100 km or less, apoapsis was way up at roughly 10,000 km altitude.

It's important to note that proximity to the Sun had other impacts on mission design. Messenger had a sunshade and that needed to be kept pointing towards the Sun to avoid overheating while the antenna needed to be pointed towards the Earth.

Also, communications was lost whenever the line-of-sight came to close to the Sun as seen from Earth, when Mercury would be at superior conjunction.

NASA messenger dot jhuapl dot edu

NASA messenger dot jhuapl dot edu

NASA messenger dot jhuapl dot edu

Maneuver Calendar date dV(m/s) Purpose

MOI      18 Mar 2011   861.7   insert spacecraft into orbit around Mercury
OCM-1    15 Jun 2011    27.8   lower minimum altitude to 200 kilometers
OCM-2    26 Jul 2011     4.1   increase orbit period to 12 hours
OCM-3    07 Sep 2011    25.0   lower minimum altitude to 200 kilometers
OCM-4    24 Oct 2011     4.2   increase orbit period to 12 hours
OCM-5    05 Dec 2011    22.2   lower minimum altitude to 200 kilometers
OCM-6    03 Mar 2012    19.2   lower minimum altitude to 200 kilometers

First Extended Mission

OCM-7    16 Apr 2012    53.3   Decrease orbit period to 9.1 hours; deplete oxidizer
OCM-8    20 Apr 2012    31.5   Decrease orbit period to 8 hours

Second Extended Mission

OCM-9    17 Jun 2014     5.0   Target 25-km minimum altitude on 12 September 2014
                                Met 25.2-km minimum altitude on 12 September 2014

OCM-10   12 Sep 2014     8.6   Target 25-km minimum altitude on 24 October 2014
                                Met 25.4-km minimum altitude on 24 October 2014

OCM-11   24 Oct 2014    19.3   Target 25-km minimum altitude on 21 January 2015
                                Met 25.7-km minimum altitude on 21 January 2015

OCM-12   21 Jan 2015     9.7   Target 15-km minimum altitude on 1 March 2015
                                Met 14.9-km minimum altitude on 1 March 2015

Final Extended Mission

OCM-6    03 Mar 2012    19.2   lower minimum altitude to 200 kilometers
OCM-13   18 Mar 2015     3.1   Target 5.7-km minimum altitude above terrain on 2 April 2015
OCM-14   02 Apr 2015     3.0   Target 13.1-km minimum altitude above terrain on 6 April 2015
OCM-15   06 Apr 2015     1.8   Target 6.9-km minimum altitude above terrain on 14 April 2015
OCM-15A  08 Apr 2015     1.9   Target 6.9-km minimum altitude above terrain on 14 April 2015
OCM-16   14 Apr 2015     1.0   Target 9.0-km minimum altitude above terrain on 24 April 2015
OCM-17   24 Apr 2015     1.5   Raise minimum altitude to delay Mercury impact to 30 April 2015
OCM-18   28 Apr 2015     0.45   Raise minimum altitude to delay Mercury impact to 30 April 2015 at 19:26:01 UTC

Here is some data from the simulated orbit in JPL's Horizons database. This solution was revised in 2015. Messenger's orbit around Mercury was every 12 hours. I downloaded the osculating orbital for Messenger in orbit around Mercury at a cadence of 1 hour. Each data point is the median of 24 values over one day, which smooths the tiny wiggles do do the fact that the orbit is not purely Keplerian and so osculating elements wiggle.

The strange curved undulations in periapsis distance are likely due to the highly elliptical orbit bringing Messenger far from Mercury so that the Sun's influence is stronger. You can see the periapsis wiggles decrease when the apoapsis drops down, However, I am not sure why those wiggles pick up again towards the end even though apoapsis only increases a little.

I believe that these changes will correlate with the angle between Messenger's orbital plane and the direction of the Sun's gravitational attraction, but I've run out of steam here...

This is a very complicated and interesting Mission!

Messenger orbital elements JPL Horizons

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