Monday, February 7, 2022

A Reality Check

 What about that Apollo 16 subsatellite?

In this blog I have shown that two Apollo spacecraft were left in orbits that are stable over decades. That’s really surprising and unexpected. Some people have asked if I can simulate an object that is known to have decayed out of orbit, as a reality check, to show that these simulations aren’t out of whack. That’s what we’ll do in this post.

One very notable case is the Apollo 16 Particles and Fields Subsatellite, otherwise known as PFS-2, which decayed out of lunar orbit in 1972 after only 5 weeks in orbit. Weighing just 36 kg, it was jettisoned from the Apollo 16 Service Module not long before the crew left lunar orbit to return to Earth. Originally it was planned to raise the orbit of Apollo 16, so that PFS-2 would remain in orbit for a year. Due to problems during the mission, that orbit change was skipped, and the expected orbital lifetime of PFS-2 was cut down to a few months. PFS-2 was equipped with a transmitter so that it could be tracked, and its data could be sent back to Earth. Only 34 days after it was jettisoned, the transmissions ceased, and PFS-2 impacted the Moon. 

Let’s run a simulation of PFS-2 and see what happens. As with previous simulations we can get the initial conditions from the Mission Report. The Figure 1 shows the data from the report. I believe the report is showing the state of the Command-Service Module (CSM) rather than the PFS-2, but it should be close enough to see if we are in the right ballpark. After converting the parameters to metric and getting them into the right coordinate frame, I get a GMAT script like this one, posted on GitHub.

Figure 1: Showing the initial conditions of PFS-2 from the Mission Report.

For starters, we’ll just record the low point in each revolution, as we have done previously. Figure 2 shows how it looks over time. We see the minimum altitude dropping for several weeks, and then there is a reversal and it starts to rise up again around the middle of May. About a week later the orbit starts to become more eccentric, and the perilune altitude begins dropping again. Sure enough, just 5 weeks after jettison, at the end of May 1972, the low point of the orbit is below the average radius of the altitude...and that is a sure sign that impact has occurred. (The simulator doesn’t check for impact while it is running…it will happily simulate an object that is actually beneath the surface, so we’ll have to look in greater detail to see exactly when and where the impact occurs. I’ll explain how to do that in a future blog post.)

Figure 2: Simulated perilune altitude.

A more detailed analysis of the simulation results gives the location and time of impact, and it comes out as below. Tracking data from the satellite ended shortly after 10:31 PM on May 29th, with an estimated impact at 111° East longitude, and 10° North latitude. This simulation puts the impact about 14 hours later, and about 13 degrees further west. That's not bad! 

Figure 3: Impact times and locations reported by NASA and estimated by simulation

There is another source of information on the PFS-2 initial orbit, at this page. It describes the orbit in a different way, and the parameters don’t completely agree with those in the Mission Report. If we run again with those initial conditions, we get the results labelled “Nominal 2”. This time we get closer to the 1972 estimated impact location and time…impacting about three hours earlier and about 4° more to the west, with the latitude agreeing almost exactly.

In my view, the basic answer is “yes”, these simulations do compare well against reality. We are able to predict the impact of PFS-2 within a few hours of the actual time, and within a few degrees of the estimated location. Considering the uncertainty of the initial conditions, with two different NASA sources that don’t agree, errors of a few hours either way don’t seem too surprising. Having gone through this exercise, I have even greater confidence in the results obtained for Eagle and Snoopy.

By the way, if you are looking for a lunar sleuthing challenge, the actual impact crater of PFS-2 has never been located. This web page states that the original raw PFS-2 tracking data has been preserved, and if you were to obtain that data and fit a simulation to it, I suspect you would be able to map out a very small area where the PFS-2 impact occurred on the surface of the Moon almost 50 years ago. You might be the person to identify the final resting place of the infamous short-lived Apollo subsatellite. Good luck and happy hunting!

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