splitting math

There was some discussion on the RASC Toronto Centre Yahoo!Group listserv about double stars and being able to resolve them. Or not. I shared some math...

There's a formula often used to calculate telescope resolution:

resolution = 4.56 / aperture

where:
resolution = seconds of arc
aperture = inches

According to SkyTools 3 Professional, with double star data as of August this year, the epsilon Lyrae pairs are at the following Position Angles and Separation. I've also including the preliminary orbit Period, which is kinda cool...

AB: PA 347°; Sep 2.50"; P=1165.6 yr
CD: PA 77°; Sep 2.38"; P=724.3 yr

So, now, let's we work it backwards:

aperture = 4.56 / resolution

If I'm doing my math right, you need this much minimum aperture, in inches, to split the pairs...

AB    1.8
CD    1.9

Or for you Metric heads, in mm.

AB    46
CD    49

[ed: I.e. a 2-inch or 50 mm telescope. That's also in the range of large binoculars...]

And now, the disclaimer. YMMV. Your mileage may vary.

I often view the Double Double aka Tim Horton "star" in my 8" SCT at around 110x. Easy to split, usually, with decent conditions. And, at times, with poor conditions, one of the pair cannot be cleanly split, despite the aperture and/or power.

But occasionally I look through other instruments. In particular, while at Mew Lake in 2011, through Adam's Tele Vue 85 apo refractor doublet (600mm focal length, f/7), we viewed epsilon Lyr at 100x or so. We were able to just split the tight pairs. Nice view.

Finally. One other "magic number" to consider. According to Sky and Telescope, "Doubles look their best at a magnification that is approximately 750 divided by the separation in arcseconds."