Measure the brightness within the shadow of the gnomon and just outside, and take the ratio. The higher the atmospheric tau is, the greater the brightness of the sky relative to that of the sun. Therefore, that shadow ratio should be correlated with tau. In principle you could do a calibration using the real tau measurements to convert the ratio into an estimate of tau.

Of course this would be much more work than 5 minutes of scripting! I can't imagine automating this. This is a job for a summer student! In practice, shadows are brighter (less distinct) when the sun is lower, so you'd want to use just the pics with the sun around some fixed altitude.

This is actually an effect that's pretty easy to notice if you pay attention to shadows over time. A sudden brightening of the shadows is a sure sign of a jump in tau.

Touché I retract my previous post.

Fantastic - what fun!! Thanks again Paolo.

Have fun! (Pulling the tau data would screen out the transits based on both seq ID and filter-- R8 vs. L8).

Most likely. A DN brightness threshold would be sensitive to exposures. The images are manual exposures, adjusted episodically to account for dust on optics and seasonal expectation of atmospheric dust load. High tau or high window dust -- relative to expectations at the last exposure update -- would make the solar brightness smaller, which would propagate to a low radius. And, of course, vice versa.

Well, since this is an obscure side topic I figured it would be a decent place for my first UMSF contribution. See attached chart.

I used the JPL HORIZONS web interface to get the predicted apparent solar diameter as seen from Mars and plotted it for sols 1-3000. Using a value of .28 mrad/pixel (=57.75 arcsec/pixel) for Pancam which appeared in several sources I googled, I aligned this with Paolo's chart. The alignment was done manually so no guarantees it's precise.

Click to view attachment

As I would expect from some dust etc. the apparent diameter is a bit larger than the purely geometric prediction. Interestingly as siravan mentioned the magnitude of the variation is less than the prediction.

Comments/criticism/corrections welcome. This is not my field of expertise.

Very nice comparison, Greenish. I've confirmed your numbers, but I've seen 0.27 mrad/px which improves the agreement a bit. That leaves 2 pixels excess in Paolo's measurements, ie one pixel on each limb, which sounds reasonable considering exposure/psf/binarization effects.

Paolo's results clearly show that Mars periodically gets closer and farther from the sun, like Kepler's 1st law predicts. But they also show more. If you look closely, the minima are broader than the maxima. This is because Mars moves more slowly (and so spends more time) near aphelion than near perihelion, according to Kepler's 2nd law.

You can see this clearly in Greenish's predicted curve. This gif flips back and forth from the normal curve to the curve reflected vertically. This makes it easy to see the asymmetry in width between the peaks and the troughs:
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Repeating with Paolo's measurements, again you can see that the minima are broader than the maxima:
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So we find evidence for two of Kepler's laws, all from just 5 minutes of scripting!

This thread has also proved something else: how great you guys are! I knew it already but this is further proof of it (just in case there was any doubt). Thank you all.

Paolo

Paolo was the graph created with all 4779 images from your first gif? or just the 747 separated by one sol?

The latter animation includes only 747 images, the plot includes all 4779 data points.

Paolo

Paolo sent me the actual data (thanks!) so I re-did the plot. Thankfully, it looks the same.

The green points show what happens iif you subtract 3 pixels from the observed diameter: the maxima line up. (It looks similar if you use .27 mrad/px and subtract 2 pixels). I don't know if that's legit but it illustrates fredk's note above.

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Surface close up...

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Gorgeous detail visible on the Faraway Hills now, too...

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I was working on those exact same images when you posted them.
Especially like the one, maybe two, tiny natural arches.

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o_O

Is that vertically stretched at all?

-m

It looks like a straight zoom, Matt.

Astro - nice catch! It's too bad but we're just barely missing R2 coverage of that feature. Here's the best anaglyph I could come up with, combining L2 and navcam R0:
Click to view attachment
Not quite enough detail to confirm an arch, I'd say.

No, that's a straight crop of a panoramic mosaic, Matt.

Have a quiet word in someone's ear and suggest that now would be a **really** good time to take a full super-res panorama of the farside of Endeavour...that would be glorious...

I'm not sure, but I think we are still flash volume limited but the area where we are moving to should still provide quite a view.

Paolo

The full Greenly Pan was released by NASA on the 5th July:

http://marsrovers.nasa.gov/newsroom/pressr.../20120705a.html

The pan currently has top billing on the Daily Mail's web site:

http://www.dailymail.co.uk/sciencetech/art...ian-winter.html

The deck pan has been flawlessly merged with the Greenly Pan despite the two pans being taken a few cm apart.

Just... beautiful... (the place and the geology, not my picture! )

Click to view attachment

Edit: actually, I think I like this version more... http://roadtoendeavour.files.wordpress.com...-july-2012d.jpg ?

...and another nice chunka gypsum...

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Stu, in that gorgeous pic from your Post 270 -- fascinating that some of the layered rock is vertical, and some looks smeared or shaved horizontally.

Yep..

http://qt.exploratorium.edu/mars/opportuni...FFBRQ2P2935M2M1

Astro0, I'm going to go out on a limb here and say I don't think your features are arches. This looks like the famous case of O'Neill's Bridge on the Moon. An arcing shadow with an illuminated lump in front of it looks very much like an arch with illuminated terrain behind it. I think the arch shadow should be more forward in the image than it is if it were real.

Phil

A bit late to the party (I was on vacation last week), but some time back I realized that, if you use pancam photogrammetry to measure the various linear distances among the corners of the square aluminum base plate of the calibration target, you can use these distances as a means of estimating the changes in temperature of the plate. I even did a quick validation check of this using AlgorimancerPG, but decided that it would take more time than I was willing to spend to do anything of interest with this notion, though it was clear that the changes in dimension predicted due to fairly small changes in temperature were quite accessible with this method, and the fact that you can measure between combinations of corners provides a foundation for some good statistics on the estimates. Is the temperature of the base plate of any real interest to anyone? Considering that it is affected by solar irradiation effects moderated by dust?

That's a good one. I would have to look at what is the actual resolution you can get from the PANCAM. The pointing of the PMA is not very accurate. For example when we do RAT activities we point the PMA to the turret but we do not repoint until all the RAT activity is complete because when we blink the images we do not want to be distracted by the pointing inaccuracies. Another source of error would be the changing sistance from the CalTarget plate and the PMA due to thermal dilation/contraction. Recovering the footprint of the caltarget automatically would be quite difficult but not impossible. For starters one could analyze a few selected images taken early in the morning or late in the afternoon and compare the plate size to images taken at noon. I'm going to leave this exercise to the reader ;-)

Paolo

The Sundial base is 8cm across, and about 215 pixels across at its nearest side. Roughly 0.37mm/pixel - but at this range it's out of focus - the PSF is probably a couple of pixels across.

Aluminium's thermal expansion is about .023mm/meter per degree K. So 0.00184 mm / degree.

Given a 100 degree change - you might see something like 0.2mm change

I would doubt, very much, that it would be visible.

Slipped out of the habit of doing these again, especially seeing how good and how quick Stu is these days.

Need to get back to it ready for MSL, so her is my take of Veladero:

The trick here is that you can take advantage of measurements along each edge and diagonal of the base, then do pairwise comparisons between these measurements on different dates. So it is not so critical to observe the change on a single edge -- let's say you measure the 4 edge lengths and the 2 diagonals, then scale the diagonal lengths to match the edges (divide by sqrt(2)), so you've essentially got 6 samples of the edge length of this square base on that occasion. Do the same thing on a different occasion. Perform a paired t-test by pairing the equivalent measurements from the 2 occasions. From this you've got a mean change in the edge length, and you can get an associated confidence interval and p-value. The "noise" in the measurements is essentially averaged out, and since you can quantify the noise (since you can get a standard deviation) you can do some good statistics; handily, this sort of measurement error should be very "normal".

Paolo, the pointing of the pancam need only be such that the target is included in both L & R images taken on that occasion, the exact orientation of the pancam is not critical, we're depending on the camera model to identify the xyz coords of each vertex on the plate, then finding the 3D distances between those vertices. Where this gets potentially complicated is if you stop to consider whether the change in temperature also changes the camera model enough to be a problem.

My back-of-envelope estimates at the time I first looked at this suggest that a 100 degree C change in temperature should be easily measurable, and likely even a 20 degree change. Below that it looked "iffy".

Sharp edges can be located to significantly better than a pixel by appropriate modelling, as is routinely done in astronomy by limb-fitting routines. I don't know the details but they must be readily available. Measuring along the edge, you would be taking advantage of lots of pixels, not just the end points of an edge or diagonal. Every pixel on the edge would contribute to fixing the position.

Phil

One of the reasons I was going with a natural arch was because of the rock feature immediately to the right in that pan of Stu's.
The next rock has hollows in it. So assuming that the 'arch rock' is a piece of that same rock type, then the arches may well be there.
I guess unless they take something higher res and perhaps a different angle (unlikely), we'll never know.
Maybe we'll luck out and get another shot of the area under different lighting conditions.
But it is interesting to look at this area and try to interpret what we are seeing without having the benefit of actually being there.

That's the fun part!

If you look at it in a false color composite, it seems clear that we are seeing the "blue" soil through two holes in the rock.
Click to view attachment

Very convincing Cosmicrocker: definitely looks like arches to me. The rightmost arch even seems to be composed partially of vein material, doesn't it?

The one on the left is more convincing, certainly. I might believe in that one, eventually! The one on the right looks like it's casting its shadow backwards if it's an arch. I don't find that one very convincing.

Phil

Quite true, and I have seen this used elsewhere in photogrammetry, so in principal the dimensions of the base plate can be determined rather precisely, and its changes in temperature estimated likewise. Estimating temperature changes is a neat trick -- would this be of value in the absence of an external thermometer on the MER rovers, or would it just be a neat thing to do?

Incidentally, if anyone is curious to try this using distances between the corners of the plate (as described in an earlier post) with the AlgorimancerPG application, one difficulty I encountered when I initially looked into this (December 2010) was that many of the images of the calibration target were sub-frame images, rather than the full-frame 1024x1024 images required by the software in its current incarnation. If this is important, the software could be modified to handle sub-frame images in conjunction with the pancam tracking database.

This brings up another issue -- in the absence of an available camera model for MSL, there will likely be a lengthy post-landing delay in revising AlgorimancerPG for MSL.

I agree with Phil's original claim, that the light patch (white arrow in pic below) is the top of a pebble sitting in front of the alleged arch, rather than the ground behind viewed through a hole. The pebble's flat top is tilted towards us.

My reasons: the shadow of the supposed arch (grey arrow) looks too narrow, and seems to have a break in it (black arrow). Also, we're looking down at quite a steep angle at this rock. So the bottom floor of the arch would have to be sloping coincidentally at least at the same angle so we can't see the floor of the arch. Or the floor would have to be extremely narrow, front to back, which seems unlikely.

I've taken the average of L5 and L7 frames to reduce noise (adding L2 doesn't help). This allows us (barely!) to zoom to 200%:
Click to view attachment
Once I picture the light patch as a pebble in front of the "arch", I can't believe it's an arch. The thin shadow now makes sense.

Another drive NE tosol - I think we're now sitting in the "mininotch" feature. This looks like its mouth:
http://qt.exploratorium.edu/mars/opportuni...0M1.JPG?sol3008
Very nice shadow shot:
http://qt.exploratorium.edu/mars/opportuni...0M1.JPG?sol3008

Looks like part of the ground may be sinking in that area.

Anaglyph of the glorious mess beside us now:
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Mini notch? Or mini graben? What would cause such a slumping on such a small scale as this?

Just got word ODY is in safe mode again. They do not know what is the cause of the safe mode yet.

Paolo

Drat. Thanks for the update, Paolo.

Hey DFinFrock ... that's what I thought as I saw that image, a minor fault graben !

From sol 3008, inward slope of Cape York now more in view, as well as its angle of slope compared to distant horizon.

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(Edit: I'm afraid I may have cropped it so the distant horizon is not exactly level. But maybe it's not level anyway, considering the massive craters just beyond the horizon and how the landscape may have been adjusted on a much larger scale?)

It definitely looks like the mini-notch is bounded by a pair of parallel faults. A graben might make sense near a crater rim, but so also might a pair of normal faults, or perhaps even a horst. Since these faults are presumably billions of years old and the current topography is largely the result of differential erosion, the topography will not reveal the directions of fault movement.

It would be nice to get a full pancam panorama here and turn it into a polar projection, but maybe even a navcam panorama to polar would reveal something interesting. As of yet, a key navcam is still not down yet.

Nice indeed, here below a colorized/unvignetted version:
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My version of the Sol 3008 Horizon Pan.

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And here's a polar view made from a navcam mosaic created with MMB "Export panorama" option. Unfortunately, there are still several images missing.
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While we wait for ODY to cme out of its latest sulk and start talking to us again, there's a fascinating - and very welcome - "Beginners Guide to the Geology of Endeavour" in an interview with MER's Dr Barbara Cohen, over on my blog now, if anyone wants a look...

http://roadtoendeavour.wordpress.com/2012/...r-barbara-cohen

Thanks Stu and Dr. Cohen: I just improved my knowledge of Endeavour by about 1000%.