John Pazmino
 NYSkies Astronomy Inc
 2009 October 12 initial
 2011 March 11 current
    Double stars, both true binary stars and lined-up unrelated pairs, 
were a favorite target of stargazing until the late 20th century. One 
reason was that the usual deepsky objects like nebulae and galaxies 
were out of reach of the small scopes among home astronomers for most 
of that century. It was only in the last couple decades that large 
well-built opticly-good telescopes became affordable to the rank-&-
file home astronomer. 
    With the large aperture instrument in hand, home astronomers could 
realisticly hunt up deepsky objects and skip the easy targets: double 
stars. Double stars were never fully ignored and they were featured in 
articles on observing continuously thru today. They just fell out of 
mainstream favor and were only weakly highlighted at stargazing meets 
and starparties. 
    There is one niche of stargazer who never left double stars behind 
in quest of ever fainter and fuzzier targets. The New York astronomer, 
confined to small scopes by structural and institutional constraints, 
maintained a lively interest in double stars. 
    Apart from the lesser size of scope, the City astronomer suffers 
from grayed sky due to luminous graffiti that impedes the view of many 
nebulae and galaxies. Oh, there are an amazingly large number that can 
be observed with satisfaction from the City, but orthodox stargazing 
litterature dissuades against trying for them. 
    For these main reasons double stars remain a significant part of 
the New York astronomer's target list for his observing efforts. 
    Deepsky objects are considered as static fixtures in the sky that 
can be examined with equal benefit in any year. Changes are due to 
local observing conditions like haze, air turbulence, bright sky. 
There are a couple nebulae that have real changes over time, like 
Hubble Variable Nebula in Monoceros, but such examples are rare for 
home astronomy 
    A double star is an evolving object. As its component stars orbit 
each other they change their orientation and separation. This applies 
to both true binary stars and stars that happen to line up. In the 
latter case the changes are due to the independent proper motion of 
the stars. 
    As much as this behavior is now known for quite two hundred years, 
most observing guides simply fail to appreciate it. They give the 
orientation and separation as if they were fixed parameters. This is 
further implied by missing out the year for which these parameters are 
    For the newcomer to observing, such a practice is insidiously 
disinforming. Unless the specs are really recent and the star evolves 
really slowly, the aspect of a given double star can be far off that 
stipulated in the guide. 
    The pair can have widened or narrowed its separation, making the 
star harder or seem too easy to resolve. The orientation may have 
rotated to some other angle, confusing your directions in the eyepiece 
    The most common specification of a double star are its angles of 
separation and of orientation. The former is cited in arcseconds 
because the idea of a 'double star' is that under bare eye or low 
magnification the star looks like a single star. High power breaks it 
into its two constituents. 
    The orientation is expressed in degrees around a compass rose 
centered on the brighter of the pair. Celestial north is 0d; east, 
90d; south, 180d; west 270d. I never saw an orientation cited as a 
clock hour, with north being 12 o'clock, as is sometimes done for 
other celestial alignments. 
    By long convention the brighter star -- regardless of its 
astrophysical character -- is the primary component and the other, 
fainter, is the secondary. It is also called the companion or, in 
Latin, 'comes' (KO-mess). If there be several companions in a multiple 
star system, they are 'comites' (KO-mih-teez). I rarely see them 
called by higher ordinal numbers. 
    The specs help you to assess if the star can be split with your 
telescope. Too close a pair will remain singular. The orientation, or 
the position angle, helps to look in the proper quadrant of the 
eyepiece field for the comes. 
    Note carefully the two distinct meaning of angle, which carries 
over to all other facets of skywatching. One is the 'surface' distance 
on the celestial sphere between two points. The other is the direction 
from the one point to an other. 
    Thee angles are similar to the distinction on Earth. The 
separation of two places can be expressed in degrees along the surface 
and the direction from the one to the other is in degrees round from 
north. These are the navigators run and bearing. 
    On Earth you usually cite distance in linear units, kilometers. 
This is only because the Earth has a fixed known size, so each degree 
on it correspond to a linear unit. One surface degree is 111 
kilometers. One minute of arc is 1,800 meters, the sailor's 'nautical 
mile'. On the Moon, in comparison, one surface degree is 30 kilometers 
and one surface minute is 500 meters. 
    How rapidly can a double star's aspect change? For some the orbit 
period is thousands of years or there was no sensible change in the 
last century or so. There are lots of other stars whose timescale of 
change is decades. Within a lifetime you can follow the shifting 
direction and distance. 
    There are clues for the timescale. If the two stars are so far 
apart that in a small scope you actually see them separately, they are 
likely to be far apart linearly. This implies a long period of 
revolution by the same Kepler principle that planets farther from the 
Sun have longer periods than nearer ones. 
    Hence, an easily split double reasonably has a period so long that 
you may not sense any change of its parameters over a lifetime. Stars 
with very close components, discernible only under strong 
magnification, tend to have shorter periods. There is the chance that 
you can detect the mutation by keeping careful records of your 
observations over the decades. 
    Pairs so close they can not be resolved by ordinary telescopes can 
have periods of months or days. The typical example of this star is an 
eclipsing binary. The stars are so close that they can mutually hide 
each other in turn, causing periodic fluctuations of apparent 
    The absence of a period can not be so causally assigned to an 
excedingly slow pair of stars. A period more than a thousand years 
could be missed with the short time of observation in the order of a 
couple decades or a century. 
    A missing period may also mean a sheer lack of observations. Too 
few astronomers had the interest or purpose to examine the star and 
lay out its orbit. A missing period may also mean that the pair is not 
a true binary. The stars are a perspective pair that happens to sit 
along our line of sight. 
Home observations
    More so than ever in the 21st century there are very few campus 
astronomers taking care of double stars. Their work is increasingly 
occupied by other fields of astronomy. At the same time, home 
astronomers are gradually obtaining the means to capture valuable 
information about double stars with larger aperture of telescope, 
stable fixed mounts, imaging apparatus, electronic astrometry and 
photometry, general computation power. 
    There could be a new endeavor for home astronomers to keep tabs on 
critical stars and compute their orbits. This work has to be 
coordinated with a facility that has an abiding interest in double 
    In the United States, the US Naval Observatory is one such center 
for double star work. It could promulgate standards and procedures for 
observing double stars, collect observations in a competent format, 
and blend them with other observations.
    So far it hasn't. In fact, there is a deep absence of campus 
extension to the home astronomer for double star observations and 
little effort to render submitted data into orbits or databases. 
    The home astronomer as a result has no easy way to know what a 
given binary is doing now, as agains reading what is was doing many 
decades or a century ago. 
    Apart from dedicated recording and documenting double stars, these 
stars are plain enjoyable as casual targets of admiration. For one 
thing, they are one of the few celestial objects that show obvious 
colors, even if two observers do not agree on which colors they are. 
    The planets and bright nebulae have colors but they tend to be 
subtile and pale. Just     There are, to be fair, temporary 
apparitions with strong color. Their appearance is rare and can not be 
reliably foretold. These include aurorae, large meteors, bright 
comets. Just about everything else in the heavens is white or neutral. 
    Home astronomers tend to think of 'orbit' as a nearly circular 
path around a central body. This is based on long experience with the 
planets around the Sun and the larger moons around planets, Even the 
orbit of Mars looks pretty circular when drawn to scale on a letter 
sheet. You have to measure with a ruler to learn that it is really 
an ellipse. 
    Double stars have orbits that can be extremely excentric, like 
most comets. Near their closest approach to each other, perisastron, 
the two stars can swing around rapidly within a decade or so. When far 
apart, near apoastron, their specs may linger almost fixed for many 
decades. Unless you know where in its orbit a given binary is now, you 
can't tell for sure from the period and spec's epoch what the star is 
    You can from a set of observations work out an orbit either by 
hand or with computer programs. This is usually an exercise, lke in a 
college astronom class, using canned mesurements culled from 
observatory records. For well-obseved short-period stars, the data are 
accessible to try your hand at this work. 
    One ambiguity is that from our remote perspective an orbit by be 
tilted one way or mirroed to an equibalent tilt in the opposite 
direction. Supplemental information, like radial velocity data, is 
needed to obtain the correct tilt. 
Gamma Virginis
    The wonderful and awesome prototype of rapid change in a binary 
system is gamma Virginis. This star went thru its periastron in the 
mid 2-thous. The two components closed to about 1/3 second apart and 
rotated by quite 120 degrees. Home and campus astronomers watched this 
star until it collapsed into a single solid point. 
    In 2009 it broke apart again into two stars discernible by small 
telescopes. For the next, uh, 160[!] years gamma Virginis will be a 
wide pair ranging up to about 5 seconds separation near apoastron. 
    gamma Virginis is, believe it or not, the ONLY instance where 
within a couple years you actually witness real gravitational motion 
of whole stars! For all other binary stars you must wait decades or 
rely on reports over a century. 
    For a detailed discussion of gamma Virginis, please read my 
articls about gamma Virginis in the NYSkies website at 
'www.nyskies.org/articles/pazmino/gamvir1.htm' and '.../gamvir2.htm'. 
    Barnard's star is an other example but mainly for linear proper 
motion. It is also not an easy target to find. Its 10 arcsecond per 
year proper motion results partly from its proximity to us. 
    For many binary stars the orbit is well enough determined to allow 
elements to be worked up. These are defined similarly to, but a bit 
differently than, those fo the planets. From them you can plot out the 
star's aspect for any given date. 
    Dedicated computer program do this, as do some computer 
planetarium programs. In the early days of home computers, I and 
others wrote our own orbit programs in BASIC. 
    The main difference between the dynamics for a binary star and a 
planet is that the stars are of the same order of mass, whole suns 
apiece. Planets are at the best only one thousandth the mass of the 
Sun. This means that placing the origin of coordinates in the Sun is a 
very good approximation to the real situation where you should bank 
off of the barycenter between the Sun and planet. The barycenter of 
the solar system is always within the globe of the Sun. 
    When a double star is newly observed, and in the centuries before 
astrophysics, the masses of the stars are not known. We know now that 
they are of roughly equal mass so the barycenter is midway between 
them. Stricta mente, the elements of BOTH stars must be worked up and 
tied to this barycenter. 
    In practice we hold the brighter, primary, star fixed and put all 
of the orbital motion into the secondary, dimmer, star. The elements 
are RELATIVE elements as seen from the primary star. While this sounds 
sloppy, it does favor the observer on Earth because he instinctively 
fixates on the primary and looks around it for the secondary. 
    You can see what's going on. It is sort of reversion to the 
geocentric world where all motion is banked off of a fixed Earth. As a 
matter of sheer fact, you can do this with all good results. The 
dynamics, by gravity, are all wrong, but the kinetics, with the 
planets are massless points, is quite valid. 
    For history sake, I remind that Newton seemed a bit on his high 
horse to claim his gravity theory was universal. Yet in his day, late 
1600s, the only place where gravity was known to exert itself was 
within the solar system. The stars beyond were truly fixed points. 
    When by the end of the 1700s binary stars were discovered, the 
Newton theory was applied to them. The first gravity-based orbits were 
worked up n the early 1800s after enough observations were accumulated 
for a good arc of motion. Since binary stars are disposed thruout the 
profundity of space to indefinitely remote distances from Earth, the 
universality of the Newton theory was first demonstrated. 
Source for specs 
    When an orbit of record exists, you can compute the specs of the 
star for a given date and use it to evaluate the aspect of the star. 
This is good if the orbit is well established, as by having a short 
period and strong observation record. 
    This is hardly the normal situation. Because double stars can have 
long periods, their history spans several lifetimes. I mean not only 
human lifes but the lifes of an observatory. Its mission and purpose 
may shift, leaving the star un observed for many decades. The orbit of 
record could be based on too short an observed arc. Specs generated 
from it for a current date can be well off of the mark. 
    Believe it or not, this was the case with gamma Virginis! As late 
as 2005, when the stars were obviously closing together month by 
month, there were still in circulation old orbits that put off the 
periastron for a few more years! This is for a very important star, 
the very first one to witnessed thru a periastron back in 1838. 
    The location of the secondary could also be nn observed spec, 
measured by photographs or micrometer. This is both a good practice 
and not. It's good in that it adds to the history of the star. When 
combined with other measures, the orbit is ever better defined over 
the years. 
    Its not so good if the observation is in isolation and then quoted 
as a precise parameter in observing guides. Some authors try to update 
their books by hunting for recent observations of the star. Doing so 
for the sake of capturing the latest, rather than the best fit trend, 
leads to erratic specs for the star. 
    You may look in double star records and see how the observations 
whack around so badly. Errors up to 1/3 of the instant radius of the 
orbit are annoyingly common. If you look up in an observatory journal 
for the one newest report you don't know where it sits on the fitted 
orbit and you may then cite a reckless specification. 
    The miserable harm is that almost never is the source of the spec 
given in observing guides. Is it computed form a such-&-such orbit? Is 
it merely an entry in some laboratory's observing logbook? 
Selecting double stars 
    Because the prime factor in seeing a star as double is the 
separation, many guides select stars wider apart than a certain number 
of arcseconds. The author explains that he wants to offer stars within 
range of certain instruments assumed for the reader. Such reasoning is 
consistent with that for picking out only the brighter star clusters 
or deeper range of variable star. 
    With the mutation of a double star's specs, the roster may be 
inaccurate because the author used, often by ignorance, ediurnate 
specs. He can include stars that were once wide enough to qualify for 
his list but are now too close together. Conversely, stars falling 
short of the author's qualification may actually meet them because 
they are now wider apart. 
    This is why you can not beat up an author with 'the such-&-such 
book has a star that should be in your list'. While there can be 
honest omission by mistake of a good specimen, you better make the 
inquiry about your suggested entry. You could be reading ediurnate 
    Note well that you can not be clued by the issue date of the book! 
The author may copy data from older material. A new work can still 
have out of date information about a double star. 
    There aere many attemtps to screen pairs for the prospect of being 
real binaries. None work well. The problem is that a candidate star 
will call for years and decades of further examination, so a simple 
quick screen would be deeply welcome. 
    One common method is a formula with star magnitudes and separation 
as input. If the formula value excedes, or decedes, a decalred limit, 
the star is a a possible binary. There are as many such formulae as 
astronomers who propose them, with the outcome for a given star being 
at the mercy of each. 
    Other methods include orbital motion, proper motion, and radial 
velocity. If the star has a short period, comparing measurements of 
over years could reveal one component to orbit the other. This is in 
fact how binary stars were discovered in the late 1700s. Before than 
it was assumed the pairs were all chance alignments. 
    If the star has a long period, orbital motion may not yet be 
evidenced. The two components will travel thru space together as a 
unit, sharing the same proper motion. Comparing proper motion measures 
can uncover such pairs. In some double star catalogs these stars are 
tagged 'cpm' for 'common proper motion'. 
    The radial velocity, or Doppler, method is not as secure a test 
but a clue. If the suspected pair has the same radial velocity, within 
some dispersion limits, it could be a binary. The dispersion comes 
from the one star running in its orbit to or from us relative to the 
other. Taking Doppler meassurements over many years or decades will 
receal, like orbital motion, the binary. 
    The real difficulty comes in selecting perspective, line-of-sight, 
doubles. With no physical attachment between the components there is 
coordianted study of them. 
    There is no positive way to hunt for them or cull them from 
catalogs. You make do with anecdote: ' There's a star just north of 
the nebula with a timy adjacent companion in a pretty field'. It could 
be a binary or a perspective double. There could be other cnadidates 
in the vicinity that chnaced to be overlooked. 
    All in all, there simply is no uniform consistent catalog of 
double -- binaries or line-of-sight pairs -- for the home astronomer 
to enjoy. There are hundreds of well known stars that turn up again 
and again in observing guides. Among these the selection is erratic, 
some stars in one are missed form an other bu some, often unknown, 
author's judgement. 
    There arises from time to time a fetish for the resolving power of 
a telescope. This was a major source of good arguments when double 
stars were a larger part of home astronomy, It persists today for 
discerning details ob planets and even on the moons of other planets. 
    The common sense of resolution is that you must positively tell if 
two point sources are really two or are blended into one. The most 
conservative criterion is that in the instrument the two stars must be 
clearly tangent to each other. A nudge farther apart will collapse the 
notch between them into a clean break. That its, they must be 
separated by the sum of their radii. 
    Points do got radii. A 'point' of a star's image is really a tiny 
dot of finite diameter. This is the Airy disc and is a result of the 
wave nature of light. Without going into the theory, this disc is only 
a very few seconds across so under low power it does look pretty like 
a pinpoint. 
    The formation of optical images from a point source into a finite 
dot is one example of how Nature avoids the singularity problem. If 
the image was in fact a true point, the energy density there would be 
infinite: (energy flux)/(area of image) --> (infinity). Since this 
constitutes a singularity, Nature forces the image to occupy a finite 
area so the ratio is a finite value, not infinity. 
    If the stars are about of equal brightness their Airy discs are of 
equal diameter, so it is often noted that resolution is achieved if 
the stars are apart by one diameter (two equal radii) of their Airy 
    Opticly the Airy discs are of equal size, but blooming in the 
eye's perception cna make the brighter star appear to have a bigger 
disc. Some light from its disc splashes over to adjacent cells on the 
retina to excite them into vision. This is how a double star of very 
mismatched brightness can be a lot harder to resolve than one of more 
equal brightness. 
    A less stringent rule is that the stars must stand only one radius 
apart. In this case the discs overlap with a notch along the sides 
halfway between the ends of the elongated image. You can demonstrate 
this with two coins or other discs. When overlapping, the common 
figure is a sort of dimpled ellipse. 
    It is by interpretation, knowing that there should be two round 
dots, that allows you to claim there are two stars. Without such prior 
expectation you could be looking at a funny-shaped sharp-edged nebula. 
If by some chance, the object really is a single odd-shaped thing, you 
would be fooled. 
    Staying with stars in proximity, the optical theory allows that 
resolution is achieved if the separation of the stars is greater than
    (resolution in arcsec) =  (120) / (aperture in mm) 
This is rounded from the theoretical formula and is a lot easier to 
mentally do the math for the common apertures among telescopes. 
    A 60mm aperture of scope should by this formula resolve double 
stars as close as 2 seconds apart. A 250mm scope should split stars of 
only 1/2 sec separation. And so on. 
    From the ground, the atmosphere is hardly so stable and still to 
allow perfect optical images. The ideal Airy disc is more likely to be 
a wretched spot of a couple seconds diameter. Thus it is common to 
experience when among many different telescopes that none penetrate 
deeper in resolution than, say, 3 seconds on a given night. Such is 
the case at starparties where there are impromptu competitions among 
    For telescopes outside of the atmosphere, things are vastly 
better. The ideal limit for resolution based on aperture is achieved. 
That's why as example Hubble can see such amazing detail that a 
similar size of scope on the ground can not see. 
    Hubble can resolve to about 5/100 arcsecond, allowing for huge 
enlargement of its images while keeping its star images as neat round 
dots. The equal and greater size of ground scope can hardly achieve 
3/10 -- one sixth of Hubble -- under the best of atmosphere above it. 
    This is based on the skills and arts of telescope building when 
Hubble was under design in the 1970s. Today with adaptive optics, 
ground scopes equal and excede Hubble. 
    For photography when the camera shutter was open to incoming light 
for many minutes or hours, the movement of the air made the star image 
/wander over the film. The result was a blotch a coup;e arcsecond 
across. This so severely limited the detail in pictures that the 
traditional rubric was that the eye can always capture, in the instant 
of still air, much finer texture than a photograph can ever get. 
    For home astronomers, the practical limit from most observing 
sites is one arcsecond. This is based on long experience with many 
scopes and sites and is rounded for simplicity sake. If a double star 
is closer than that, even for larger scopes, it congeals into a single 
image with no definite evidence of duplicity. 
    I know there can be chance moments when the air calms dowm to let 
a better image be formed, For this instant the combined blurry dot 
condenses into two points, but that demands lots of patience and a 
quick eye. Unless you are favored by a site with exceptionally stable 
air, you may pass up double stars of separation less than one second. 
    Achieving the ideal resolution, as limited by your air, calls for 
optics that in fact render a point source, the star, as an ideal Airy 
disc. This is a function of both the quality of the optics and your 
maintenance of them. The former used to be an issue among commercial 
telescopes. thru the mid 20th century, the lack of affordbale good 
quality optics was one motivation for building your own scope. Today, 
however, commercial scopes typcily have theoreticly perfect optics for 
affordable prices. 
    Where many scope fail down is the observer's maintenance. The 
instrument must be clean, collimated, free of damage. Altho it is easy 
to avoid damage and to keep the optics clean, it is a real chore to 
keep collimation within specs. 
    Most home astronomers do not have the tools, test rigs, skill, 
patience to look after colimmation. Yet loss of collimation is among 
the most common defects in home telescopes. The usual situation is 
that the optics creep slowly over years without the observer noticing 
a deterioration of the images they produce. Only when he views thru a 
scope known to be well aligned does he realize his own instrument is 
out of spec. 
    A scope out of collimation will not send all the incoming rays 
from a point into an ideal Airy disc. Some will spray outside of it. 
Those within it may form a oval or irregular disc. Such behavior 
degrades the image and resolving power. Double stars can not be split 
so closely because, perhaps unknown to the observer, the image is 
swollen beyond the diameter of the ideal Airy disc. 
    In spite of the necessity to keep collimation, there are so few 
really simple and reliable ways to do so. In some telescopes, there is 
no way to adjust the optics, like screws, spring bolts, shims. In many 
cases the instrument is sealed against tampering. If you eventually 
discover loss of collimation, chances are the scope must be sent to the 
manufacturer for adjustment and, by the way, its warranty expired. 
    Serious and detailed inspection of double stars requires really 
good optics, both by design and construction, maintenace under your 
care. A shortfall in optics will ruin double star observing. 
Highest power 
    Can't you separate a pair of stars, how ever closely spaced, just 
by applying a high enough magnification on the telescope? No. As noted 
above the image of points in space are finite dots. It is only in 
geometric, ray tracing, Gauss optics that points in space map into 
points in the image. 
    When you magnify this image, you enlarge the dots. If the dots 
overlap, you see only bigger overlapping dots. Think of a regular 
photograph. It contains a certain depth of texture. If you do a 
photographic enlargement of this picture you do not acquire more 
texture. The existing texture is made bigger with no new information 
    In fact, you can apply too much magnification. The texture in the 
image can be so enlarged that its smallest feature occupies a sizable 
angular extent before your eye. It occupies several retina cells. At 
this point the image is blurred, grainy, diffuse, and unattractive and 
unappealing. You have to step down to a lower power to obtain a more 
pleasing, smaller, view. 
    The highest magnification is usually capped by the state of the 
air, which governs the size of the star images. Turbulent air yields 
larger dot images, forcing you to be content with lower power. Good 
and stable air approaches the ideal image formation, permitting higher 
powers before the view turns lousy. 
    There is no determinist figure for the highest feasible power of a 
telescope because the evaluation of the image is subjective by each 
observer. The general rule is that highest magnification you can 
expect to apply is
    (highestt power) =  (2) * (aperture in mm) 
A 200mm scope has a highest power of 400. This rule assumes good 
optics, a reasonable assumption with modern telescope manufacture, and 
good collimation, not nearly so good an assumption for many scopes. 
    This does not mean you must not excede this limit. There will be 
occasions when a higher power can be usefully employed. Please have in 
your observing kit one or two high power eyepieces. 
    The essential point to appreciate is that the property of a 
telescope often hawked is its magnification, as if this was the prime 
purpose of the instrument. That's why low-end scopes banner their 
highest power. You will soon find that it about never can you usefully 
enjoy that high power on this scope. 
    Because double stars can have close separations, high power may be 
needed to resolve them. Resolution comes only when the optical image 
of that star in fact consists tf two distinct dots tangent or with 
empty space between them. Else you will obtain only a larger, more 
blurred and diffuse, single elongated spot. 
Lowest power
    There is a LOWEST magnification limit for double stars. Recall 
that by eye a certain star looks single and it becomes double under 
telesocpic  resolution and magnification. The eye alone has too little 
power to resolve the star. 
    The situation here is in the retina, composed of cells of light 
reception. These cells have a finite size, about 10 micron diameter in 
normal eyes. If the image on the retina spans several cells, you see 
texture in the image, a bit from each cell. 
    If the image, however finely textured, sits entirely on one cell, 
you get only a blended dot for its visual impression. In the normal 
eye, the daytime resolution is about one arcminute. Targets in space 
angularly smaller than that register in the brain as a dot with no 
internal detail. 
    Since we observe double stars as night, we are viewing with the 
night vision cells of the eye, the rods, which are larger and less 
numerous than the day cells, the cones. For the normal eye the cell 
size of rod cells is about 30 microns, resulting in a night resolution 
of about 3 minutes. 
    If even in the telescope the images of two stars fall within 3 
minutes of each other before your eye, you see only one star. The two 
images are exciting only one rod and send a single combined signal to 
the brain. 
    By applying some magnification, the two images are made to sit on 
their own cells and produce two impressions in the brain. Thus, there 
actually is a lowest power below which the double star remains 
    There are several ways to determine this minimum power but the one 
I use is useful and simple. It asks:'What power is needed to put a 
double star's image on the retina at least 3 minutes apart'? The 
resolution of a telescope, to create two distinct Airy dots in the 
image is (120)/(aperture in mm) in arcseconds. 3 arcminutes is 180 
asrcseconds, so we have (180)/((120)/(aperture)) = 
(180)*(aperture)/(120) = (1.5)*(aperture). Thus
    (lowest power) = (1.5) * (aperture in mm) 
    This resolution-based minimum power is a different parameter fro 
an other lowest power based on aperture. This works on capturing the 
outcoming beam of light from the eyepiece. In astronomy every photon 
counts. You want to get as many of the ones entering the telescope to 
then enter your eye. The eye's own aperture of about 5mm at night for 
a normal adult. 
    The diameter of the exit beam of light from the eyepiece is 
(aperture ub nn)/(magnification). To make sure the exit beam is no 
larger than 5mm, else you spill photons over the edge of your pupil, 
you must apply a minimum power of (aperturein mm)/(5mm). A 150mm scope 
has a lowest power of 30. Less than that and you spill some of the 
photons collected by the instrument. They miss your eye by falling 
betond the edge of the eye pupil. 
    Note well that this aperture-based power will not exploit the full 
resolution of the scope! The 150mm scope needs 225 power to split the 
closest pairs. For wider pairs, lower power may be used to improve the 
pleasure of the view. This is particularly the case if the star is in 
a pretty field of other stars. 
    For some targets there is an abundance of light like the Moon. 
Some targets need a wide field of view like an open cluster, large 
comet, or the spread of Jupiter's moons. Powers less than the minimum 
limit are handy to have in your kit for these targets. 
Visual magnitude 
    Human vision, appearing so real and physical, is really a response 
to the stimulus of radiation impinging on the eye. Without eyes in the 
form we do have there is no vision, even tho the incoming radiation 
still exists. This fact causes severe angst among those studying life 
on other worlds. It is also a primne factor in anthropic cosmology.  
    The failure to realize that light is not a physical construct built 
up an edifice of misleading, erroneous, and at times ridiculous lore 
about human vision. Here I discuss only a couple aspects relating to 
double stars. 
      The 'magnitude' system by which we rank the apparent brightness 
of stars, is speficily defined only within the wavelength range of 
human eye sensitivity. Because that sensitivity varies widely among 
observers, a standard curve of response to radiation was adopted for 
photometric and illumination work. Your individual eye may diverge 
severely from this standard model. You likely know a person claiming a 
lamp is too dim while you assert it's a too bright for comfort. 
    Valiant attempts are made to build devices that emulate the eye 
and record star magnitudes automaticly. With lots of sweat and tears 
these do work but there is yet to arrive a unit that you point at a 
star and get a reading 'magnitude '+7.54' directly. You get an 
electric current, electron count, sensor value that you must interpret 
as a magnitude for the star that excited the device. 
    That's why photometry in astronomy is so prevalently differential, 
not absolute. You box in the target star between other stars of known 
or declared magnitude. You then trend the device readings on a graph 
and pick off the target's magnitude. Altho this chore can be performed 
automaticly, there must still be the standards to calibrate the plot. 
    Observing guides are inconsistent with magnitudes. Some give the 
primary's brightness as the combined brightness of the two stars while 
others give the individual magnitude. The former is likely for stars 
intended for naked eye view where the double remains single. You do 
get the combined illumination from the two stars. The individual 
magnitudes are common for stars both listed in a photometric catalog. 
    Be careful when a guide gives a magnitude for the primary and a 
DIFFERENCE of magnitude for the secondary. The observer took the 
primary's magnitude from some source and estimated how much fainter 
the comes is; 'Hmmm, it looks 2.5 magnitude dimmer.' 
    A gurther variation is to offer the RATIO (illumination, not 
magnitude) between the two stars. The secondatu is a certain frction, 
decimal, of the primary. 
    As an example suppose a double star consists of two stars of 4.0 
an 4.7 magnitude. We can read in the various guides: 
        1st  2nd  meaning 
    --  ---  ---  ----------------------------
    #1  4.0  4.7  each star with own magnitude 
    #2  4.0  0.7  1st with own magnitude, 2nd is offset from it 
    #3  3.3  4.7  1st is combined magnitude, 2nd is own magnitude 
    #4  3.3  4.0  1st is combined, 2nd is magnitude of primary 
    #5  3.3  0.5  ist is combined magnitude, 2nd is ratio (2nd/1st) 
    The correct meaning may be buried in the letterpress or left for 
the the reader to guess. 
    The magnitude can be deliberately approximate. It usually isn't 
all that important what the separate brightnesses are. What counts is 
the dispersion of the two. It is a lot easier to see the pair if the 
stars are about equally bright than if they are deeply different. The 
brighter star may overshine the fainter, even tho they may be 
separated enough to resolve in your scope. 
    The human eye needs a certain minimum influx of radiant energy to 
trigger perception. In astronomy this is expressed by saying the 
threshold brightness of star for the normal eye is 6th or perhaps 6-
1/2 magnitude. A star chart that reaches this faintness is a 'naked-
eye' chart and you're supposed to perceive all stars on it, within 
constraints of altitude, latitude, and sky darkness. Falling short of 
doing so marks you as somehow imperfect. 
    Human sensitivity varies all over the map. Some people genuinely 
can see 8th magnitude stars in the zenith from a darksky site while 
others barely make out 5th magnitude from the same place. The lower, 
deeper, limit is rare, but among many hundreds of observers at a large 
starparty there can be a couple who achieve it. For them the Sky Atlas 
2000 is their naked-eye chart! 
    As an observer ages his eye sensitivity declines. The falloff is 
extremely gentle. The astronomer assigns it to deteriorating sky 
conditions over his site. There is increasing suspicion that reports 
of worsening sky transparency, judged by the raising of the threshold 
limit of star magnitude by long time residents, may be the result of 
the observer's own aging. 
    Adding to the perceptin of worsening skies is the lack, since the 
mid 20th century, of new, keen-eyed, astronomers into the progfssion. 
On the whole, the profession is aging and the threshold magnitude 
becomes brighter. This phaenomenon can seriously compromise the 
tracking of luminous graffiti, routinely monitored by assessing the 
threshold star magnitude. 
    The situation feeds on itself. With brighter limiting magnitude, 
observing become more infrequent as many nights are passed up. When 
the night is taken, fewer challenge targets are tried. The astronomer 
sticks to the easier ones under the 'brighter' skies. 
    There sets in a discouragement from attracting new astronomers to 
the 'vanishing' opportunities fo stargazing. Clubs shrink, astronomy 
readership dwindles. public awareness and support for the profession 
evaporates. Some pessimists fear that home astronomy by the mid 21st 
century may resemble the ghost seas of Mars. 
    Altho double stars are quite resistant against bright skies, the 
constricted selection of targets infects them as well. Fainter double 
stars, still quite visible with satisfaction, are skipped. 
Eye care 
    The size and density of cells on the retina ranges widely thru the 
human population. You surely know of heard of a person having extra 
keen sight to read newsprint at 30 meters (in daylight, please) while 
others must bring the print to within one meter to begin reading it.  
    At night some observers can see double stars, opticly resolved 
ones, with lower power than other observers. Their smaller denser rods 
allow the image to span two or more cells and impress in their brain 
as distinct points. The astronomer with less dense rods must use 
higher power to push the two images onto separate cells. 
    If the loss of acuity is disease-induced degeneration of the 
retina, relief could come from medical treatment or delicate surgery. 
These methods so far can only slow or stop the progress, not reverse 
it back to good vision. Such a situation requires entering into 
continuous ophthalmic care. 
    A corollary condition is clarity, the ability to see stars close 
together without hazing, misting, glaring from each other. It depends 
on the eye being truly transparent, with no nebulous obstruction. 
    Young eyes tend to be really clear, to the point of revealing the 
Moons of Jupiter when near elongation from the planet. 
    Older eyes tend to be clouded, tho not so much as to impede 
ordinary life. While a person can still function by day with a 
moderate loss of clarity, it takes but the merest defect of clarity to 
punch holes in the view of the night sky! Even for nonastronomy 
functions, it is common to know someone who has only a 'daytime' 
automobile licence or complains about uncertain goings about at night. 
    The archetypical cause of clouded vision is cataracts. The lens 
inside the eye gets milky. This causes a mist around bright lights 
(stars and street lights), veiling of darker objects near bright ones, 
whiting out the scene in the face of sunlight or headlights, obscuring 
signs and print, diffusing colors, impeding navigation in the dark. 
The effect is like looking thru a dusty window. 
    The remedy is surgery. The defective lens is bodily removed and 
replaced by an artificial one that is mechanicly attached inside the 
eye. If you wear eyeglasses or contacts, the correction can be molded 
into the new lens. The prescription is now INSIDE your eyeball! You 
discard the exterior glasses after the surgery. 
    In double star work, a faint comes may be veiled, perhaps at first 
unnoticeably so, by a mist around the primary. The sky isn't really 
black, but gray with the comes buried behind it. You lose the pleasure 
offered by the star's colors, seeing see only a drab pair of dots.. 
    As you examine double stars, you'll be astounded, maybe scared, to 
learn that your eye has a patch work of sensitivity, clairty, acuity 
over the retina! In day vision you don't notice this but at night with 
only points of light hitting the eye in a dark background, vision 
defects show up harshly. 
    In fact, one instrument used in ophthamic tests looks like a 
planetarium! You sit in front of a dark titled dome. Over its surface 
are lamps that blink on and off in a random pattern. You click a 
button when you see a blink, keeping your head still on a chin rest. 
The record of clicks and blinks maps out your visual field. 
    There are other causes for loss of clarity that only a proper 
ophthalmic examination can determine. Good astronomers do an eye check 
once or twice each year. Many health insurances cover these exams as 
part of prevemtive care. Please inquire after this feature. 
Night vision 
    There is a yin-yang about vision at night. For ordinary tasks, the 
eye shifts from day vision to night vision during nautical twilight, 
roughly 1/2 to 1 hour after sunset. The shift is reersed an equal time 
before sunrise. This is away from artificial nighttime illumination 
like within a town. 
    The smaller, color-sensing, close-packed cone cells shut off and 
the larger, looser-packed color-dull rod cells take over. The rods are 
far more sensitive to dim light at the cost of losing resolution, and 
color perception. The scene is grayscale at night and texture issigns 
harder to interpret. 
    In addition, the rods at the edges of the retina are even more 
sensitive to low lighting, making the center seem 'blind'. The trick 
of averted vision to see extra faint objects in the telescope exploits 
this feature of night vision. 
    For earthly tasks, some persons have a gtadation of night vision 
from center to edge that can be positively dangerous. The dullness of 
sight in the center impedes confident view of the scene. Such perople 
may miss, or hit!, curbs, steps, poles, walls, furntiure, trees, 
fences, cliff edges, cuts and pits, standing water, pipes and chains, 
and more. 
    For astronomy thry may have trouble reading maps and markings, 
working dials and knobs, finding dropped items, checking around for 
cleanup, aiming a telescope, looking thru a narrow field eyepiece. 
    For double stars, the situation can be seriously obstructive. It 
is real hard to concentrate on a target set off to the edge of the 
visual field. But when centered it is too dim for comfort or is 
vanished completely. 
    Using a high power eyepiece, that typicly also has a narrow field 
of view, the double star may be missed, making the astronomer think he 
isn't aiming at it. There follows a spell of frustration as he tries 
again and again to acquire the star. 
Night color
    If night vision is grayscale vision, how can you see distinguish 
colors in stars? Allowing for the dispersion of the claimed color seen 
by different observers, why is any color noticed at all? Most 
observing litterature is silent on this fact. They have a chapter on 
night vision, like the section above, and then procede without a blink 
to assert the colors present in double stars. 
    Stars have colors but only weak tints like pastel. Even the 
brighter stars do not have vivid hues, altho you read that Arcturus is 
an 'orange' star. To me it does look sort of orange but hardly so deep 
a hue as a traffic cone, the fruit itself, or anything else that's 
orange in sunlight. 
    Before astrophysics there was no known cause for the colors of 
stars. One early thought was that the color came from the Doppler 
shift of their rest color due to recession or accession. Such an idea 
sounds idiotic today but long before the nature of light was 
understood, the Crazy-Eddie speeds worked out for such immense Doppler 
shifts seemed plausible. 
    In the mid to late 19th century there was a flap to carefully 
assess the colors of stars and keep records of them. One thing found 
soon was that red stars are prevalently variable stars. We know now 
that this is a result of the location of red stars in the HR diagram. 
Since we can only see the more luminous red stars by eye or small 
scope, the red stars are among the giants and supergiants on the  
chart. Such stars are indeed prevalently variable by the energy 
processes associated with this part of the HR diagram. 
    It is true that there is little color in night vision because the 
light level is below the trigger threshold for the color-sensitive 
cone cells. This applies to the general field of view where overall 
the retina suffers too low an influx of radiation. Cone vision 
switches to rod vision. 
    If a PARTICULAR spot on the retina has enough illumination for day 
vision, THAT spot switches to cone vision and you discern color in the 
illumination! This happens when in an otherwise dark field of view 
there are singular points of light hitting the eye. Each point strikes 
the retina under its image and could, if bright enough, cause it to 
hand the vision function to the cones. 
    A sky at night, by direct view or thru a telescope, is exacta 
mente such a field of view. The spot on the retina lighted by a star 
could be illuminated enough to excite the cones into action and pick 
up a color in the star. The retina nearby, still in darkness, remains 
under rod vision. Under a general night vision you see colors in 
    The effect is momentary. Soonest you move the star away the rods 
come back into play and cones under the new location of the star's 
image act up. There still is the absolute trigger influx that 
restricts color perception to the brighter images. Faint stars in the 
field remain grayscale. 
Color clash
    Altho the physiology of color perception under night vision is 
still loosely known, one fascinating effect is well documented. When 
two points of color are close together, on adjacent or almost adjacent 
retina cells, their colors amplify. A resolved double star, with sky 
between the stars, sits on at least three cells (star A, empty sky, 
star B). By some physiological mechanism the color of each intensifies 
into vivid hues. 
    Because most celestial targets are grayscale or have only weak 
tints, a double star attracts attention by what sure as hell looks 
like fiery hues. In some cases the effect is so lovely that vocabulary 
to describe it can be awfully, erm, colorful. 
    With no generally credible way to quantify color for home 
astronomy, there arose a broad diversity in double star description. 
Authors tried to find regular words to define precisely what color a 
double star presented to his sight. Or he copied the description from 
some authority or more experience observer. 
     It is impossible, unless there comes a way to link up brains 
between two persons, to know what an other person sees compared to 
your impression. The other astronomer can not 'show' you his color 
rendition to compare with yours. 
    The honest truth is that each and every person has his unique 
color perception. This is part of the natural diversity of spectral 
sensitivity and rendition from person to person. You can not be taught 
to see a certain color. No amount of training or practice will let you 
confidently see a prescribed hue. 
    Even if you somehow manage to call certain samples of color 
correctly, this technique can not be applied to new, not previously 
exercised, examples. You will fail to call them properly. The color 
you see IS the true color for you and that's that. 
    The lurid terms used to specify double star colors are actually 
useless for a given observer. What can happen is that when a new 
astronomer fails to see what is supposed to be seen, like the color 
stated by an experienced observer, he feels failed as an observer. 
    The bottom line is that the crazy words to portray double star 
colors are really silly and may be discarded from your expectations.      
Schematic color 
    My own practice is to cite the schematic colors according to the 
spectral class of the two stars. This is artificial in that these 
colors are themselfs not what you 'should' or 'must' see in a star of 
a given spectral type. When I say Arcturus is an orange star I mean 
that is has a K type spectrum, whose schematic color is orange. Or, to 
invert the sense, an 'orange' star is a k type of star. 
    The colors scheme is listed below 
        spec | color        | temp 
          O  | blue         | hotest 
          B  | blue-white   |    | 
          A  | white        |    | 
          F  | yellow-white |   \|/ 
          G  | yellow       | solar-type 
          K  | orange       |   \|/ 
          M  | red          | coldest 
    These colors are commonlyy used to tint stars in a chart or lamps 
in a projection planetarium. The color gradation is conitnuous thru 
the spectral classes, but binned. Any finer distinction would be 
beyond normal people to pick out the colors. 
    This would be a very fair and consistent manner of specifying 
double star colors but for one major hitch. The spectra of double 
stars are not well cataloged. Usually only that for the primary or a 
blend of the two is stated. 
    Individual spectra are on the books for both components of only 
the brighter double stars, Unless there was a pointed interest in the 
individual spectra for dimmer pairs, chances are they were never 
captured and cataloged. 
    Stars in a binary system have different spectral types because the 
two stars are of different mass. While formed together, so they are of 
the same age, they are generally of different mass. Heavier stars sit 
on higher points of the main sequence in the HR diagram and go thru 
their life cycle faster. The most massive stars evolved into the red 
giant phase of life, leaving their less massive companion still on the 
main sequence. 
    For this reason, among the more important uses of double stars is 
astrophysics. Since the two stars were formed together, the age factor 
is eliminated from the cause of divergent spectral types. Also 
eliminated is chemistry, being that the two stars came from the same 
nebula of a single composition. Eventually it was learned that mass 
was the dominant factor in dispersing spectral types within a binary 
    Because it can take some concentration to inspect a double star, 
it helps immensely if your telescope tracks the star. Traditionally 
this required a conventional equatorial mount, but modern scopes can 
follow the star with a computer controlled altazimuth mount. Having 
the star sit still in the field, or at worse drift only slowly, is a 
huge facilitation for inspecting the double star. 
    Any distraction, like to twiddle axis knobs or press motor 
buttons, upsets your concentration. This is specially true if your 
hoping for a brief instant of still air on a turbulent night.
    Tracking also helps in perceiving color. By holding the star still 
in the eyepiece field you can hunt around your eye's field of vision, 
placing the image here and there on the retina, to find the overall 
best view.
    Other distractions must be banushed. Things like street noise, 
wind and rafts, ground vibration, other people walking around, 
headache, muscle stiffness, thirst and hunger will chip away at your 
observing comfort and concentration. 
    In deed, the best of serious observing is done alone or with 
highly cooperative partners. At a starparty or public viewing it is 
just about impossible. 
    Double stars were and can still be a substantial part of the home 
astronomer's stargazing. There are so many in all sectors of the sky 
that there is always an ample selection when and where ever you 
observe. There are specimina for all size of telescope, even for 
binoculars, allowing enjoyment under just about all circumstances of 
being outdoors at night. 
    The main obstacles for confidently selecting targets is the 
ediurnation of published parameters. These, due to orbital motion of 
the stars, can be so baldy wrong after a few decades that many stars 
now are out of range of the instrument to hand. Other stars omitted 
from old lists could be widened into good targets. 
    Double stars present intriguing insight to human vision. They may 
help you understand your own vision regime and seek appropriate eye 
care. They also point out some of the misapprehensions of vision that 
still circulates thru astronomy. 
    In spite of it all, double stars are a most rewarding and 
enjoyable target, offering beauty and color wanting from most other 
celestial objects.