Sky and Telescope - November 2015 - 29

Sissy Haas

Want something new to do with
your telescope? If I can interest you in joining our project,
please know we'd love to add your help. And now with that
much said, let me back up and start at the beginning.
You and I know the sky is ﬁlled with double stars.
Almost every time we study star ﬁelds in our telescope,
we'll see that one of the stars is actually two stars, barely
separated with magniﬁcation. If you've seen showcase
pairs like Albireo or Epsilon (ε) Boötis, you know they can
have breathtaking colors. But we don't always know that
we'll see a double star, even when the star is known to be
one. If a pair is made of stars not fainter than 6th magnitude and not drastically unequal in brightness, you can
use the Dawes limit as the guideline for your aperture:
116/aperture in mm = the smallest separation in arcseconds (″) possible to resolve. For example, the Dawes limit
for my 60-mm telescope is 1.9″, since 116/60 = 1.9. Any
pair at least this wide should look double in my 60-mm,
so long as it's not faint or unequal. Of course, my 60-mm
may not perform at the Dawes limit because of bad
weather or other factors, but the rule holds true in ideal
observing circumstances.
But what if the stars are very unequal in brightness?
What's the limit of my telescope then? There have been
many formulas published over the years devoted to
answering this question. It was the subject about which I
was most frequently asked when I had a regular column

in this magazine, and Chris Lord of the United Kingdom
spent 20 years of his life on it. He gathered personal
observations for many years and used his background in
mathematics to extrapolate a predictive formula between
aperture and separation for unequal double stars; all it
requires is a ruler and chart (see S&T: Jan. 2002, p. 120).
And now with all this said, I'll go back to the ﬁrst
sentence and talk about the Binary Star Observing Project
and the Uneven Double Stars Project. Like Lord, we're
looking to ﬁnd the smallest realistic aperture for a speciﬁc
separation and magnitude diﬀerence. But we're simply
gathering observations: no predictive formula is intended
from them. We've determined test pairs in increments of
0.5, starting at 1.0. All we ask you to do is look at them -
as few or as many as you have time for - and see whether
or not the pair splits in your aperture. That's it!
Even if our ﬁndings prove redundant to what Lord
found or predicted, they'll reinforce his study and won't
be wasted. What we'd like to have is so many observations, from so many diﬀerent observers, that we can give
a speciﬁc aperture for a speciﬁc separation/magnitude
diﬀerence without fear of being wrong. We can already do
that for a bright pair that is 3.0″ apart and unequal by 2.0
magnitudes, using Epsilon Boötis as the case example.
We have 17 conﬁrmations, from many diﬀerent observers, that it can be split with 60-mm instruments, and 12
conﬁrmations that it splits with still smaller apertures.

Test Pairs by Separation and Magnitude Diﬀerence
Separation

ΔM = 1.0

ΔM = 1.5

ΔM = 2.0

ΔM = 2.5

ΔM = 3.0

ΔM = 3.5

ΔM = 4.0

1.0″

Σ2054 (Dra)*
130-mm?

Hrg 47 (Car)*
no data

Σ2403 (Dra)*
no data

41 Oph
no data

42 Ori
200-mm?

8 CMa
no data

69 Her*
no data

1.5″

Dun 39 (Car)*
no data

Hu 544 (Per)*
80-mm?

θ Gru
no data

Σ2303 (Ser)
150-mm?

β 67 (Cyg)*
no data

90 Her*
150-mm?

no star
-

2.0″

33 Ori
80-mm?

μ Cyg*
60-mm

49 Leo
100-mm

κ Lep
130-mm

3 Mon
200-mm

Σ1171 (Cnc)
no data

Hu 1136
no data

2.5″

CapO 16 (Cir)
no data

Σ389 Cam*
80-mm

38 Lyn
80-mm

no star
-

H Vel
no data

h3874 Pic
no data

no star
-

17 Dra*

CapO 9 (Vel)*

ε Boo

ψ Cyg*

23 Aql

π Cap*

φ Ori

60-mm?

no data

60-mm

80-mm?

100-mm

100-mm?

100-mm

3.5″

90 Leo
60-mm?

Σ2671 (Cyg)*
60-mm

Σ1881 (Vir)
100-mm

See 180 (Cen)
no data

h4178 (Car)
no data

h5188 (Sgr)*
100-mm?

no star
-

4.0″

ρ Her*
60-mm

65 UMa
80-mm

Σ750 Ori
80-mm

Σ2958 (Peg)*
90-mm?

Σ1878 (Dra)
100-mm

5 Aur*
100-mm?

Σ3116 (UMa)
100-mm?

3.0″

* visible now

Sk yandTelescope.com November 2015

http://www.SkyandTelescope.com

Sky and Telescope - November 2015

Table of Contents for the Digital Edition of Sky and Telescope - November 2015