APOD: Opportunity's Mars Analemma (2014 May 16)

[APOD Robot]

Opportunity's Mars Analemma

Explanation: Staring up into the martian sky, the Opportunity rover captured an image at 11:02 AM local mean time nearly every 3rd sol, or martian day, for 1 martian year. Of course, the result is this martian analemma, a curve tracing the Sun's motion through the sky in the course of a year (668 sols) on the Red Planet. Spanning Earth dates from July, 16, 2006 to June 2, 2008 the images are shown composited in this zenith-centered, fisheye projection. North is at the top surrounded by a panoramic sky and landscape made in late 2007 from inside Victoria crater. The tinted martian sky is blacked out around the analemma images to clearly show the Sun's positions. Unlike Earth's figure-8-shaped analemma, Mars' analemma is pear-shaped, because of its similar axial tilt but more elliptical orbit. When Mars is farther from the Sun, the Sun progresses slowly in the martian sky creating the pointy top of the curve. When close to the Sun and moving quickly, the apparent solar motion is stretched into the rounded bottom. For several sols some of the frames are missing due to rover operations and dust storms.

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[Nitpicker]

Very, very cool.

I was trying to make some measurements directly from the image, before I realized that the zenith is not at the image dead-centre, but closer to the centre of the "sky dome". Opportunity is about 39 Mars-minutes (2.7% longer than minutes) ahead of the longitude from which its local mean time is measured, so the analemma appears a bit further West (to the right) than 11:02AM would otherwise suggest, making it appear to be almost time for lunch.

[Boomer12k]

Fascinating.....who'd a thunk?

I wonder if you can do this with an astronomy program, and make an Analemma for each planet....would be interesting to find out.

:---[===] *

[neufer]

I wonder if you can do this with an astronomy program, and make an Analemma for each planet....would be interesting to find out.

http://asterisk.apod.com/viewtopic.php? ... 89#p184089
http://www.analemma.com/

[Nitpicker]

Simulating or modelling an analemma is a fine thing to do. But it is somehow more beautiful to record one directly.

And to see one recorded authentically from Mars ... well, it's a good time to be alive.

[neufer]

Simulating or modelling an analemma is a fine thing to do. But it is somehow more beautiful to record one directly.

And to see one recorded authentically from Mars ... well, it's a good time to be alive.

We now have the means, motive, and Opportunity.

[Nitpicker]

Simulating or modelling an analemma is a fine thing to do. But it is somehow more beautiful to record one directly.

And to see one recorded authentically from Mars ... well, it's a good time to be alive.

We now have the means, motive, and Opportunity.

And the all important evidence. Good to see you back, Your Honor.

[BDanielMayfield]

We now have the means, motive, and Opportunity.

Which would make us guilty your honor, of what, interplanetary trespass?

P.S. Not a crime, I would argue.

[Chris Peterson]

We now have the means, motive, and Opportunity.

And of course, we have Curiosity. Although sadly, we are now lacking Spirit.

[Beyond]

Red rover, red rover, send your Analemma over.

[neufer]

Click to play embedded YouTube video.

We now have the means, motive, and Opportunity.

Which would make us guilty your honor, of what, interplanetary trespass?

P.S. Not a crime, I would argue.

https://www.youtube.com/watch?v=wxIHV-R0YVE
https://www.youtube.com/watch?v=4q6k4KdpMUg

[neufer]

[starsurfer]

Simulating or modelling an analemma is a fine thing to do. But it is somehow more beautiful to record one directly.

And to see one recorded authentically from Mars ... well, it's a good time to be alive.

We now have the means, motive, and Opportunity.

Opportunity rover:
"If it wasn't for those pesky dust storms, I would have gotten all the frames. Drat and double drat!"

[walker1001]

Simulating or modelling an analemma is a fine thing to do. But it is somehow more beautiful to record one directly.

And to see one recorded authentically from Mars ... well, it's a good time to be alive.

We now have the means, motive, and Opportunity.

But sadly no canals, no Martians, no War of the Worlds.

[Beyond]

YEA

[geoffrey.landis]

The caption is a little misleading. It's not that the martian sky is "blacked out" around the solar images; what you're seeing is that when we're pointing the camera directly at the sun, we use a neutral density solar filter, which is so dark that the sky comes out black.

[Nitpicker]

The caption is a little misleading. It's not that the martian sky is "blacked out" around the solar images; what you're seeing is that when we're pointing the camera directly at the sun, we use a neutral density solar filter, which is so dark that the sky comes out black.

I would not have called that misleading. "Blacked out" and "underexposed" are more or less synonymous in this context.

[JEH1138]

So forgive me fore being dense, but does the sun in a Martian analemma cross back on itself at all? Is it just too hard to see from greater distances? Probably my lack of understanding about what actually causes the shape over time.

--j

[Chris Peterson]

So forgive me fore being dense, but does the sun in a Martian analemma cross back on itself at all?

No.

[Nitpicker]

No, it does not cross itself. This is because the higher eccentricity of Mars's orbit has a much more dominant effect on the analemma, than the inclination of Mar's polar axis to the Ecliptic. These two components of the more circular Earth orbit, are much more closely matched in magnitude (but the effect of the inclination has twice the frequency).

See also:
http://en.wikipedia.org/wiki/Equation_of_time (for Earth)
and:
http://en.wikipedia.org/wiki/Timekeeping_on_Mars

[neufer]

No, it does not cross itself. This is because the higher eccentricity of Mars's orbit has a much more dominant effect on the analemma, than the inclination of Mar's polar axis to the Ecliptic. These two components of the more circular Earth orbit, are much more closely matched in magnitude (but the effect of the inclination has twice the frequency).

No, it does not cross itself... because the equation of time effect due to the inclination of Mars' polar axis (i.e., the close spacing of time zones near the poles) is closely matched in magnitude with that due to the high eccentricity of Mars' orbit (such that they nearly cancel each other at aphelion).

[neufer]

---

But sadly no canals, no Martians, no War of the Worlds.

They sought it with thimbles, they sought it with care;
They pursued it with forks and hope;
They threatened its life with a railway-share;
They charmed it with smiles and soap.

[Nitpicker]

No, it does not cross itself. This is because the higher eccentricity of Mars's orbit has a much more dominant effect on the analemma, than the inclination of Mar's polar axis to the Ecliptic. These two components of the more circular Earth orbit, are much more closely matched in magnitude (but the effect of the inclination has twice the frequency).

No, it does not cross itself... because the equation of time effect due to the inclination of Mars' polar axis (i.e., the close spacing of time zones near the poles) is closely matched in magnitude with that due to the high eccentricity of Mars' orbit (such that they nearly cancel each other at aphelion).

Not convinced. Show me the "equation of time" graph for Mars, including the two components from which it is formed.

A sundial on Mars would become a lot slower/faster over the course of a year, than a sundial on Earth (compared to an accurate clock). But Mars and Earth have similar inclinations, and both have the line of apsides far from the nodes. The big difference is the high eccentricity of Mars's orbit.

[alter-ego]

No, it does not cross itself. This is because the higher eccentricity of Mars's orbit has a much more dominant effect on the analemma, than the inclination of Mar's polar axis to the Ecliptic. These two components of the more circular Earth orbit, are much more closely matched in magnitude (but the effect of the inclination has twice the frequency).

No, it does not cross itself... because the equation of time effect due to the inclination of Mars' polar axis (i.e., the close spacing of time zones near the poles) is closely matched in magnitude with that due to the high eccentricity of Mars' orbit (such that they nearly cancel each other at aphelion).

Not convinced. Show me the "equation of time" graph for Mars, including the two components from which it is formed.

A sundial on Mars would become a lot slower/faster over the course of a year, than a sundial on Earth (compared to an accurate clock). But Mars and Earth have similar inclinations, and both have the line of apsides far from the nodes. The big difference is the high eccentricity of Mars's orbit.

As you stated, the figure-8 shape is lost due to the dominant eccentricity component within the analemma. Per your request, I've calculated the EOT and analemma components for Mars. Instead of using Earth months on the EOT X-axis, I used orbital position angle which works the same. I personally like viewing the analemmas.

Mars Equation of Time & Components.JPG

Mars Analemma & Components.JPG

1. Edit: At first, I mistakenly annotated the "Eccentricity Only" graph as being a 0° inclination case which is not true. The declination would remain 0° if that were the case. Just think of it as having axis tilt component removed.

Mars Analemma - Half Eccentricity.JPG

• Edit: I decided to add the analemma for the case where the eccentricity is ½ the actual value. The figure-8 is beginning for form.

As an aside, geosynchronous satellites show the same gamut of analemmas too, and for the same reasons. From nice figure eights (circular orbits with non-zero orbital inclinations) to the pointy type (high eccentricity).

[Nitpicker]

Thank you alter-ego. Nice work.