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WARNING. To view the Sun safely you must use an approved solar filter at the front of the telescope before any light passes through the optics. Not having an approved filter at the front and even having an ND5 filter at the eyepiece or diagonal end will cause excessive heat build up at the filter, eyepiece, eye!
Approved filters typically have a metal alloy, i.e. Nickel Chromium, Aluminised Mylar to block harmful IR and UV.
As for Moon filters and especially for binoviewing, you wont need one as the binoviewer splits the beam. In fact even for mono viewing of the Moon you will find no filters fine.
Note your binoviewer doesn't add to your focal length so your 500mm telescope will still have a 500mm focal length whether the binoviewer is used or not (without Barlow attachment). The binoviewer does chew up approx. 100mm (depending on model) of focal length so you will have to rack inward an extra 100mm to achieve focus with the binoviewer attached than without. Depending on you telescope you may or may not have that much inward travel available in which case you must have a Barlow attachment (say 2x) or one of your 1.7 or 2.5 correctors which are in essence a Barlow attachment. This will push out the focal plane and allow you to achieve focus within the focal travel of your focuser. It will give you higher powers, 1.7x or 2.5x depending on which corrector you use.
With your telescope you get the following:
102mm aperture
500mm focal length
f4.9 focal ratio (It will likely be labelled f5).
Magnification = telescope focal length/eyepiece focal length
exit pupil = aperture/magnification
exit pupil = eyepiece focal length/focal ratio
true field of view =apparent field of view/magnification.
(There is another method to calculate TFOV but requires field stop diameter of eyepiece)
No binoviewer or with binoviewer but no corrector, 30mm Plossl/50 deg.
Mag=500/30=16.7x
TFOV=50/16.7=3deg. (nice and wide especially for Pleiades)
Exit pupil=102/16.7=6.1mm
Exit pupil=30/4.9=6.1mm
With binoviewer and 1.7x corrector and using results above:
Mag=16.7x1.7=28.3x (Note Mag. is 1.7x greater)
TVOV=3/1.7=1.8deg. (Note TFOV is 1.7x smaller)
Exit pupil=6.1/1.7=3.6mm (Note exit pupil is 1.7x smaller)
Note the image with a 3.6mm exit pupil will be dimmer but there will be more contrast. In fact at 6.1mm in the city will give you a more grey sky background less than say a 7x50 binocular gives. (50/7=7.1mm).
With binoviewer and 2.5x corrector and using results above:
Mag=16.7x2.5=41.2x (Note Mag. is 2.5x greater)
TVOV=3/2.5=1.2deg. (Note TFOV is 2.5x smaller)
Exit pupil=6.1/2.5=2.4mm (Note exit pupil is 2.5x smaller)
With a 15mm Superview eyepiece (68deg apparent field) magnification for above is doubled in all cases and exit pupil is halfed. However as apparent field is 68 and not 50 the true field is 68/50=1.36x greater.
e.g. 15mm/68deg eyepiece and 2.5x corrector in binoviewer
Mag=500/15x2.5=83.3x
TFOV=68/83.3=0.82deg. (nice for the Moon)
Exit pupil=102/83.3=1.2mm
Exit pupil=15/4.9/2.5=1.2mm
83x will show you the bands on Jupiter and the rings of Saturn but it is a little on the low side for planetary viewing so you may consider a shorter focal length pair of eyepieces if that is what you like viewing. (Say 7-10mm). However your telescope is a fast (f5) refractor designed for low power wide field viewing will show all objects nicely at low power but does have chromatic aberration (as all achromatic refractors do) and is is particularly severe and shows itself when viewing bright objects (e.g. planets) at high powers. It is not an ideal planetary 'scope but nonetheless can provide pleasing views and can provide that wow factor especially if you've never seen a planet in a telescope before. Adding Barlow to change the effective focal length does not make it a slower focal ratio for the purposes of chromatic aberration effects. It is still f5 for this unfortunately.
As for light pollution filters nothing beats a dark sky but a broad band filter may work to provide a little darker background in your case without taking out too many stars. If you can borrow and try it would be better than buying as there are so many filters out there with so many different uses. I would perhaps try a Lumicon Deep Sky or Astronimik UHC-E on the 30mm at low power viewing and perhaps a Lumicon UHC for mid range power on objects such as Eta Carina and Orion Nebula. The original Tele Vue Bandmate Nebustar type works well on smaller refractors and would be idea for your telescope. Note though if you keep the 1.7x corrector in place your exit pupil will be 3.6mm which is ideal and will produce a nice darker background and you may not need a light pollution filter, (depends on your city lights).
Whatever you choose, enjoy and remember safety first for solar viewing (and don't forget to remove of cover you finder telescope if solar vielwing with the main 'scope (proper filter attached on it).
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