Really, this took much longer to put together than I had imagined. There were a few technical snags — most of which are explained by the fact that I'm a bad programmer — but we finally have something worth discussing.
In Part 1, I talked about the basic science behind the Radio Science campaign that Opportunity undertook from January through the middle of May. Now, we have the results from that. Where in the sky was the Earth when Oppy was doing the experiments? Why does it matter? How did that change over time? How do the various variables relate? How can we easily represent all of this?
I've boiled it down to three plots. First, a few disclaimers and notes:
1) Since I'm not allowed to use operations data or products to create these plots, I have to play stupid and guess at which times of the Martian day to look at the data. As always, I used the SPICE toolkit for the geometric computational heavy lifting. Based on this data and what I remember from all those tactical shifts, I could piece together the relative time of Martian of day at which these happened. I looked at the orientation data of the High Gain Antenna (HGA) to see when it was moving and then — by hand! by hand! — picked out the ones that were "obviously" RS-DTE experiments rather than just the regular DTE/DFE's (see Part 1) when the HGA is also moving. The RS-DTE's are easy to pick out simply by time of day.
2) No durations shown here, just middle of the guessed window. Close enough! Most windows were about half an hour in length.
3) All Martian times of day (TOD) are Hybrid Local Solar Time (HSLT; we also just say "LST"), which is consistent with the rover's flight software.**
4) The plots of position of Earth in the sky (azimuth, elevation) are just showing where the Earth is, not where the antenna was actually pointing. I've done this for simplicity, and because backing out the real position of the HGA difficult. There are ~5 degrees of error here, which, for the purposes of this blog, is well under my "do I care?" radar.
The Evolution of Earth Elevation
We like to schedule DFE/DTE communications with our rover at the same time of Martian day. This gives us predictability, consistency, and flexibility in the plans from sol to sol. However, even if we could get the time on the DSN to do that (nobody can, it's a shared resource), geometry plays a big role. Both planetary geometry and the relationship of Earth and Mars time (i.e., the length of their day) have effects on when we can schedule communications passes — and remember, RS-DTEs are simply communications passes without much data going between the rover and Earth.
First, as you may know, the Mars day is not equivalent to the Earth day — though it is very close. It's roughly 24 hours and 40 minutes, depending on what you mean by "day". Are we talking solar day? Mean solar day? Hybrid solar day? Then we get different values. The variance of this couples with the fact that, simply due to the relationship of Earth's position to Mars' position over time as they move through the solar system, the Earth will be at different parts of the sky at different times of the year.
Put it all in a big confusing pot, and baby you got a stew goin'.
Right. So. How we best show this? The plot below shows this basic relationship: I've plotted elevation of the Earth from the local-level horizon at Opportunity's position on Mars at the same time LST (hybrid! hybrid!) from Sol 2800 to Sol 2971, which corresponds roughly to the times of the Radio Science experiments.
I could have picked any arbitrary time of day. The point is to show how the same time of day doesn't give you the same Earth position. We can see that sometime in the middle of February the elevation peaked. This pattern would repeat over and over if I had simply extended the time back.
The lesson here is this: Earth elevation and Martian time of day only approximate proxies for one another.
Right, so, we see that elevation drifts. How did the RS-DTEs take account for this, or take advantage of this?
The RS-DTE Observations
One of the key characteristics of good RS-DTEs is a low Earth elevation angle. This exaggerates the Doppler-shifted signal, reducing the noise and clarifying the meaning of the data. We know that the Earth will probably be at low elevation angles in the morning and late afternoon, so it would be prudent to schedule our RS-DTEs there. When you slap on operational constraints — can we get that time with the DSN? do we have the solar energy to do it at that time of day? are we doing other things on the rover that preclude HGA movement? etc. — you get large variation from sol to sol in the time of day, and consequently the elevation angle of Earth, for each observation.
The plot below shows all of the measurements that I gleaned from the SPICE kernels (see above). Details:
1) Left axis (blue): Elevation angle of Earth in degrees during the observation
2) Right axis (green): HLST Time of Day of the observation
3) Bottom axis: Time (duh)
Here are my observations:
> We tried for a lot of elevations under 30 degrees. Notice how we were getting those early on — then the power got too low, and we had to sacrifice the quality of the data for the survival of the rover, so we scheduled the RS-DTEs at an earlier time of day when there was more sun on the arrays.
> Another driver for the earlier and earlier times of day of the observation is found in the first plot from above: The Earth was lower and lower in the sky at the same time of day, and we wanted to hit particular windows of elevation angles, we ended up moving observation times to get the elevation angles right.
> The earlier the measurements got, the more we (presumably) doubled these tracking passes with the DSN as uplink passes to load the next sol's set of plans on board. Win win!
Finally, where was the Earth in the azimuthal direction relative to North? Here we have a plot of azimuth angle clockwise from North and elevation in concentric circles,
North is up (0 degrees azimuth); East is to the right (90 degrees azimuth). For each of the observations, the azimuth was roughly the same; this has mostly to do with the orbits of Earth and Mars, less to do with local solar time. Of course, you can't tell the direction of time in this plot, but that's not the point!
The End of RS-DTEs
There is an incredible amount of input going into these observations; a hundred constraints and a hundred desires. Now we're driving and hunting down veins, leaving radio science to next Martian winter — about an Earth year and a half from now.
I hope this was educational!
*No, I don't have a Twitter account. No, I don't want one. hashtag PleaseLeaveMeAloneAboutIt
**Fun fact: MSL will be using "mean" solar time — "LMST". It matters.