OK, so here are the results for a simulation of the first 10 years of the stage orbit. On my laptop, using a GRAIL gravity model with degree/order set to 200/200, it takes about 9 hours to run this simulation. As described in an earlier post I am only plotting the low "perilune" points of each orbit.
We can still see the 25-day cycles of oscillation in the orbit eccentricity that we saw in the first year, but now they start to blur together. The longer 5-month cycles are still easy to discern. But the key point of this plot is that there is no downward trend. Here and there you see the perilune dropping below 20 km, but overall there is no sign that the stage will be impacting the surface any time soon.
If we zoom in to look at the data for year 10, the pattern closely resembles the pattern of the first year in orbit.
So it seems possible that as John Young guided the first Space Shuttle flight to a successful landing in 1981, the stage he had last seen in lunar orbit ten years earlier might still have been orbiting the moon.
All right then, let's run this simulation out to the present day. The 50th anniversary of the mission was in May of 2019, and that is when I first got the hair-brained idea to go looking for this stage.
At the resolution of this image, the individual 25-day oscillations are no longer visible, and the 5-month oscillations are nearly lost. We see the orbit dipping below 20 km four or five times in any given decade. But the key takeaway from this plot is that the simulation gives no hint of any decay of the stage orbit.
And once more, zooming in on the results of the simulation for the year leading up to the 50th anniversary of Apollo 10, there is nothing to distinguish the behavior of the orbit in that year from the first year or the tenth. The same pattern of oscillating eccentricity is present.
It seems possible from this result that on the 50th anniversary of the mission, in May of 2019, the stage was still orbiting the moon, screaming along at over a mile a second, just as easily, as silently, as majestically as it was in May of 1969.
Could this really be true? If the stage were still in orbit, isn't there some way to detect it? That will be the subject of my next post.