Re: Hawking and distance of stars

peter wrote:
> Tom McDonald wrote:
>
>>peter wrote:
>>
>>>Ye Old One wrote:
>>>
>>>>>>He can
>>>>>>even do it himself, a small telescope with a camera mount is all that
>>>>>>is needed. Take two photos, six months apart, that include a know
>>>>>>nearby star and he will SEE for HIMSELF the parallax
>
> .
>
>>>I agree with Martin that you're oversimplifying the problem. I guess
>>>there could be some question as to what you mean by a "small"
>>>telescope, i.e. for a professional astronomer a 24" scope would still
>>>be considered small. With that kind of instrument and its solid
>>>permanent mounting structure the problem is indeed trivial. But I'd
>>>think the term "small telescope" would generally be thought to refer to
>>>something more like those readily available in camera shops that might
>>>be 3" in lens diameter and maybe about 4' long. The 3" diameter is
>>>what determines the resolving power and if that instrument had perfect
>>>optics (doubtful), the resolving power would be about 1.5 seconds of
>>>arc, i.e. two stars of equal magnitude and separated by 1.5" of arc can
>>>just barely be detected to be separated provided you have a good
>>>observer. Photographing those barely distinguishable stars is a good
>>>deal trickier. Such small telescopes rarely have a mount that will
>>>keep them perfectly steady, and even the small vibration of the camera
>>>taking the photo is likely to blur the image enough to wipe out the
>>>tiny gap between those two stars. The atmosphere itself is also
>>>frequently not steady enough to get such high resolution photos,
>>>especially when viewing from in or near cities. So I'd expect the
>>>quick photo taken as you described through a typical small telescope of
>>>a double star with a separation of 1.5" of arc to just show a single
>>>slightly blurry ball instead of the two distinct stars.
>>>
>>>Now the parallax motion of even the closest star is only about 0.75" of
>>>arc, so it's less than the inherent blurriness of that hypothetical
>>>optically perfect 3" diameter "small" telescope. So when comparing two
>>>photographs taken 6 months apart you won't get images where one of the
>>>little stars on the photo jumps from one spot to a clearly different
>>>spot. Instead the movement will only be a fraction of the size of the
>>>star's dot on the photo.
>>>
>>>Might you be able to detect the motion by careful back and forth
>>>examination of the images? Maybe. Would anyone skeptical of the
>>>technique think that you're seeing an imaginary difference? Probably.
>>>
>>
>> These days, vast stampeding hordes of amateur astronomers start
>>with 8" telescopes with focal lengths of 1500-2000mm. I have an
>>8" Meade SCT with a focal length of about 2000mm. I don't have
>>the formula to determine what sort of separation I could
>>theoretically achieve, but with light gathering capacity a little
>>over 7 times that of a 3" scope, I like my chances.
>
>
> Light gathering power (which goes as the square of diameter) isn't the
> issue, resolution (which is only linear) is what matters here. I also
> have an 8" telescope and have friends with ones up to 18", but I still
> think the image most people have if you mention a "small telescope" is
> 3" at most and more likely the typical 2.4" department store variety.
>
> But even with an 8" aperture, the theoretical resolving power is just
> under 0.6" of arc, so even if you took a perfect photo just at a time
> of very steady seeing, the amount of movement due to parallax of a very
> close star would only move the image of that star over by about its own
> width. So the two comparison photos would show a few stars in the
> field as little dots and if you look very closely you might be able to
> see that one of those dots has been displaced by about one 'dot-width.'
> And that's being very generous that the telescope is better than
> average Meade quality, that the seeing is excellent that night (most
> nights I can't even resolve 1.0" doubles much less 0.6" ones, and I've
> never been able to properly photograph such a close double), that the
> mount is more rigid than the standard one that Meade supplies, and that
> the photographer knows exactly what he's doing.
>
> Although the original claim that parallax can't be measured at all is
> absurd, the angles involved are very small so making the observations
> does require properly selected equipment (with special attention to the
> quality of the mounting). A couple quick photos through a typical
> 'small telescope' is unlikely to provide convincing evidence.
>

I would think one would do best to set the two images in a (real
or virtual) blink comparator, and use a high-enough magnification
to get a background star field that's essentially motionless, for
these purposes.

I agree that the canonical starter telescope won't be useful for
this, but I think the issue isn't the small end of telescope
sizes so much as the size of telescope (and stability of the
associated mount and imaging equipment) widely available to most
people. Or at least to most people with star-gazer acquaintances.

IOW, one need not necessarily rely on professional astronomers.
If one is especially wary of scientists, one may find someone in
their area who could actually help them do a parallax experiment
of their own.

.

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