Exploring the Angle of Resolution in the Mercury Transit and Beyond

[nightcleaner]

Hi

I have been thinking about the transit of Mercury, in which, so I have read, the exact time of crossing of the limb of the sun is difficult to determine due to an apparent tear-drop shape distortion of the orb of the planet. A symetrical distortion of the limb of the sun at the point of transit also occurs. This distortion is an unexplained optical phenomena, not an actual change in the shape of the planet or of the sun.

My question has to do with the angle of resolution of the event. I'm not sure I have the right terminology here. What I mean to inquire about has to do with the magnification of the image. The tangent of the angle would be 1/2 the width of the image divided by the distance to Mercury.

How does this angle compare to the angle used in far-field observations of galaxies at the limits of the observable universe? And of the recent images of large planets orbiting local area stars? My guess is that all of these images are near the limits of current resolution available to our technology. Am I correct? Or is the Mercury image relitively much wider than the others?

Thanks for any information,

nc

 

[Nereid]

This is a good question nightcleaner (do you really?), let's see if I can help.

There are many factors which go into determining how 'sharp' an image a telescope working in the optical (or near IR or UV; they're pretty much the same set of factors) can be. Down here on the ground, the major limiting factor is something called 'seeing', which is what causes the twinkling of stars, and the jumping around of the star images when you look at them through a telescope. This is caused by pockets of air of different temperature between your eye and the top of the atmosphere - some in the telescope itself, some quite a ways off. For most amateur astronomers, in most places, seeing rarely gets better than 2" (that's 2 arc-seconds) for extended periods of time; for brief moments it can be as good as 0.5".

Big, dedicated telescopes - both the night-time kind (Keck, Gemini, VLT, etc) and solar ones - have had a great deal of effort put into getting sharp images, particularly choosing sites with good seeing, and controlling temperatures in the domes, in the optical paths, and in making mirrors that can have their shape changed many times a second to compensate for seeing. As a result, cameras on these telescopes can often take images with a resolution of 0.3"; the best solar telescopes can take advantage of particularly good seeing (and adaptive optics) to get solar images better than 0.1".

Up in space, there's no seeing to worry about, but other factors still limit the resolution of telescopes; the most famous one is the misconfiguration of the Hubble Space Telescope's primary mirror. With the present set of cameras, which correct for the incorrect shape of Hubble's main mirror, resolution in the UV can be as good as 0.05"; most of the really cool Hubble images have resolutions of ~0.1 to 0.2".

So what about the transit of Mercury (and Venus)? First, the 'black-drop effect' so widely reported last time Venus transited, turns out to have been mostly an artifact - today's telescopes with much better optics (than over a century ago) recorded few, if any, 'black-drop's! Mercury, when it transits the Sun, has an apparent diameter of ~10", and Venus ~1' (60"; I don't have the exact figures to hand). So, if a Venus transit image, taken through a good solar telescope in superb seeing, had a pixel size equal to the resolution, Venus would be ~600 pixel across!

 

[nightcleaner]

Thank you. I misremember reading about this in the popular press. Venus, eh? I am in fact a nightcleaner and have lots of time to think about odd bits of this and that. I had been trying to imagine the events in terms of quanta of light, and later realized that the planetary transits are at best a very temporary phenomena, so that the number of quanta of light must be limited to the width of the angle you can collect, but of course those far field images of early galaxies can be exposed over many hours, even over many nights, I suppose, so the number of quanta you can collect will be very much higher. Was this problem corrected, do you know, by computer assisted enhancements? I don't suppose you have a reference for the paper that explains the black drop effect at hand? Of course I can and should google it up for myself, and will try to do so, but sometimes I get lost in searches and forget what it was I was looking for, distracted by all the other fascinating stuff.

If I do find anything I'll try to rememer correctly to bring it back here.

Thanks,

nc