One way I've done it is to count pixels using a current image and noting the date it was taken as it's angular diameter changes during its apparition. GIMP works. The imaging forum is a good place to find nice current images to work with. You do not have to be completely accurate with measurements, just enough significant digits to get a good approximation.
We know the equatorial diameter of Jupiter is 143,000km and on 25 July 2019, the date of the image above, Jupiter was 4.54 AU (679,000,000 KM). I chose to use the equatorial diameter knowing the longitudinal diameter varies and I am measuring a feature along its latitude.
Now we have all the information we need to use the small angle approximation. Plugging in those numbers, we find that Jupiter was 43.4" arc in diameter. The link below converts AU as well as KM, miles, etc.
Now, it's simply a matter of ratios. In pixels, I find Jove to be about 740+/- pixels across it's equator and an average white oval is about 20 pixels to the accuracy I care to shoot for. Close enough for a good approximation. Doing the math, comparing Jupiter's known angular dimension to the feature we wish to measure, that particular white oval is ~ 1.2" arc. The GRS is about 90 pixels across its width which gives ~ 5.28" arc across its latitudinal dimension.
Rayleigh and Dawes really do not apply to extended object resolution. It's all about contrast and seeing. Is it possible to resolve extended features less than the Dawes limit. Can a 3" aperture to see a low contrast feature on Jove 1" arc across? I dunno, you tell me.
Edit: I understand the maximum spatial frequency is k = 1 at Lambda/D or 113/Dmm and 1.4" arc with an 80mm aperture. An average white oval of 1.2" arc is smaller than the maximum spatial frequency, so it may not resolve it (though an obstructed aperture might). Even if it could, the white oval would need to be much higher contrast on this tiny scale to survive diffraction effects even in a perfect aperture. An 80mm may well resolve some of the larger ones, like Mickey's Head a few years back. I've seen about 5 of the 9 or so average white ovals in a 6", and surely a 4" can grab a few. At smaller apertures, it becomes less likely to see them. In any case, doing so will require some extraordinary seeing.
Edited by Asbytec, 31 August 2019 - 08:35 PM.