Why doesn't surface brightness work on solar system objects?

[Demonperformer]

I've got to grips with the idea that surface brightness is more important than visual magnitude for photographing DSOs.

I was having a general look around the moons of the solar system, and was directed here: http://ssd.jpl.nasa....orizons.cgi#top and, being the inquisitive sort of guy I am, I typed in Elara (one of the faint moons of Jupiter). To my surprise, it lists not only a visual magnitude (of about 16.85 for Jan 2014), but also a surface brightness of 8.64. And therein lies my problem.

I can see that with a visual magnitude of 16.85, it would be way beyond seeing visually, but, if surface brightness is the important figure for photography, why is it any more difficult to photograph than any 9th magnitude star (which I presume it must be, otherwise the internet would be full of 'look at the small moon of Jupiter I've imaged' photos)?

I realise that it has a really small angular size, but it must be measurable for jpl to produce a surface brightness figure.

Any thoughts?

[Knight of Clear Skies]

Looking at the data, surface brightness is measured in units of visual magnitude per square arcsecond. Elara must be less than one square arcsecond in size for its surface brightness to be higher than its magnitude. For point sources surface brightness isn't very useful. Hope that explanation makes sense.

[Demonperformer]

I hear what you are saying, and I'm sure it's got to be something along those lines.

But, as far as the camera is concerned, every object is a point-source (if you define a pixel as a point). True some objects we see as "extended", but to the camera they are merely a bunch of individual point-sources?

It is, indeed, a very miniscule object, and I was extremely surprised to find a surface brightness figure in the output. I wonder if it could be something along the lines of it being so small that you could fit a load of them in a single pixel on the camera and the surface brightness is only useful if the object is providing a full pixel's-worth of size?. From the magnitude figures, its measured radius must be (very approximately) about 3/4 arc-sec.

[Knight of Clear Skies]

I wonder if it could be something along the lines of it being so small that you could fit a load of them in a single pixel on the camera and the surface brightness is only useful if the object is providing a full pixel's-worth of size?. From the magnitude figures, its measured radius must be (very approximately) about 3/4 arc-sec.

That's it exactly. The surface brightness is higher than the magnitude because the light from the body is only coming from a fraction of the unit area. The surface brightness figure makes no allowances for the performance of real-world optics.

Consider a star with the same magnitude as Elara: the surface brightness would be absolutely huge, because it's apparent size is a tiny fraction of an arcsecond. Through an ideal telescope with unfeasibly high resolution Elara would appear large and dim compared to the star, although their magnitude (total light received) is the same.

[Demonperformer]

From the magnitude figures, its measured radius must be (very approximately) about 3/4 arc-sec.

Oops! Serious calculation error there. Actually works out as a radius of 0.013". I now suspect that this has been calculated from the measured size from probe(s) - Galileo? Voyager? - and distance rather than from ground-based observations.

All-in-all then, the SB figure would appear to be of academic interest (maybe!) but of little practical value, for any object that has a smaller arc-sec size than the arc-sec-per-pixel figure for any particular telescope/camera set up.

[AlexB67]

You may find this article useful if you are into that sort of thing.

http://www.uv.es/jrtorres/index.html

I am sure somewhere in the depths such models are further developed in research papers compared that article no doubt, but it is quite a good run down on that topic. You can actually do some reasonable estimates, but from what I can see, the approximation still assumes a constant brightness across the object as one of the inherent problems.

I had the thought that perhaps some sort of Gaussian distribution of light to describe the light distribution across the galaxy, or at least something that represents the brighter inner core to develop on the ideas presented there. May be one day something to have fun with, but I suspect someone must have already done it somewhere, or something along those lines

edit: The direct link does not seem to work but if you jump to the bit where it says

visibility of stellar or nonstellar objects

you'll find it. Also it is for visual work mainly I should have pointed that out, so perhaps it is not as much use to you for what you are after.

[Demonperformer]

Thanks for the link, Alex. Looks a really interesting article, but I'm going to have to devote a bit of time to it to be able to think through the math. I enjoy the mathematical side to our hobby, but my appetite exceeds my skill-level, so I find it a bit of a struggle at times.