John Pazmino
 NYSkies Astronomy Inc
 2005 March 28
    In April 2000 I wrote a historical piece about the star Porrima, 
or gamma Virginis. I related its discovery as a double star and the 
studies of its orbit over the centuries. I reissued it thru NYSkies in 
April 2005 as a companion article. Please read that first, 'A star on 
the move', as a prerequisite for this update here. 
    Porrima is now in the evening sky attaining a maximum altitude of 
about 49 degrees in the course of the night. It'll be with us in the 
evening sky thru late summer, when it recedes into twilight. 
    Some of us watched gamma Virginis when it was in the morning sky 
since late fall of 2004, but the bulk of NYSkiers waited until March 
for the more convenient hours of viewing. 
Amazing star 
    The 'A star on the move' piece has the detailed description of 
gamma Virginis. Here I give a brief summary. It was first noticed as a 
double star in 1689 but real study wasn't started until 1718. By 1800 
Porrima was recognized as a true binary system, not just a chance 
lineup of unrelated stars. 
    An orbit was first worked up in 1833, revealing that the two stars 
in Porrima would round periastron in 1834. Periastron is analogous to 
perigee or perihelion; it's the 'near' end of the orbit's major axis. 
This event was closely observed. The stars swang so close, angularly, 
that no telescopes of the era could resolve them. The stars appeared 
to merge into a single dot! By reverse calculation in the 20th 
century, periastron actually occurred in spring of 1836. 
Facts and figures
    Some catalog names for Porrima are 
    Aitken  ADS 8630              Bayer  gamma    
    Bonner D'g  BD-00:2601        Boss  GC 17170
    Bright Star  HR 4825, 4826    Flamsteed  29
    Draper  HD 110379, 110380     Hipparchos  HIP 61491
    Hubble  GSC 4949-1113         Smithsonian  SAO 138917
    Struve  STF 1870              P & P M  PPM 400177 
    3rd Fundamtl Kat  FK3 477     Tycho  TYC 4949-1120-2        
    Washington  WDS 12417-0127    Zodiacal  ZC 1821 
Catalogs may give data for only one component, a blend of the two, 
or each separately. 
    The celestial parameters are, for epoch 2000: 
    Right ascension 12h 41.6s   Declination  -01d 26.9m 
    Ecliptic long  190.13       Ecliptic lat +02.79 
    Galactic long  297.77       Galactic lat +61.33 
    The two stars are nearly equal in size, brilliance, diameter, and 
other properties as follows 
    diameter  2 Sun      mass  2.1 Sun 
    output  4.6 Sun      surf temp  7,100K 
    spectrum  F0         lum class  V (main seq) 
    tot app magn  +2.7   ind app magn  +3.4, +3.5 
    tot abs magn  +2.4   ind abs magn  +3.1, 3.2 
    Sun magn  +5.2       dist  38.6ly, 11.8pc 
Normal binary 
    Thruout most of the 20th century, when most of us began our 
astronomy lifes, gamma Virginis was well separated, several arcseconds 
apart, in even quite small telescopes. It was a favorite target for 
spring and summer public starviewings. 
    Porrima was for the early 2000s a favorite star for occultations 
by the Moon. It sits near the ecliptic about 60% from Denebola to 
Spica. Each component suffers its own occultation, allowing for tight 
bounds on their orientation and separation. The first such occasion so 
exploited was in 1720 for the first good measurements of the pair. 
    We just ended a season of Porrima occultations but most of the 
events were not visible from New York City. The next season begins in 
2016 with the next City event in 2017:
    UT date      event
    -----------  ----------------
    2003 Aug 03  previous occultation over NYC
    2005 Jan 03  last occultation of old season
    2016 Feb 25  first occultation of new season
    2017 Jan 18  next occultation over NYC 
    Orbits were calculated in 1908 and 1935. The latter, by Strand, is 
still in wide circulation in reference books from the mid to late 20th 
century. New orbits were issued by Heintz in 1990 and Soderhjeim in 
1999. The latter gives orbit elements as follows 
    Period = 168.9y    SMAxis = 3.68"   Inclination = 148 
    AscNode = 37       PeriT = 1836.4   Excentricity = 0.89 
    ArgPeri = 257 
From the Soderhjeim orbit comes this ephemeris of gamma:
 Year  dec dist ang  dec dist ang  dec dist ang  dec dist ang
 ----  --- ---- ---  --- ---- ---  --- ---- ---  --- ---- ---
 2003  .00 0.87 236  .25 0.82 232  .50 0.76 228  .75 0.69 222 
 2004  .00 0.63 216  .25 0.56 208  .50 0.50 198  .75 0.43 185 
 2005  .00 0.38 168  .25 0.35 147  .50 0.35 124  .75 0.38 103 
 2006  .00 0.44  86  .25 0.51  73  .50 0.58  64  .75 0.65  56  
 2007  .00 0.73  50  .25 0.80  46  .50 0.87  42  .75 0.93  38 
 2008  .00 1.00  35  .25 1.06  33  .50 1.12  30  .75 1.18  28 
 2009  .00 1.24  26  .25 1.29  24  .50 1.35  23  .75 1.40  21
 2010  .00 1.46  20  .25 1.51  19  .50 1.56  18  .75 1.61  16 
    The year is given in decimals. .00 is January 1st; .25, about 
April 1st; .50, about July 1st; .75, about Oct 1st. 'Dist' is the 
angular distance in arcseconds between the pair. 'Ang' is the direction 
from the main, primary, star and the comes. North is 0; east, 90; 
south, 180; west, 270. 
Orbital parameters 
    Altho the names of the elements look familiar, the definitions are 
quite different from the usual ones in solar system orbits. You have 
to be versed in double star work to make proper use fo these figures. 
    The semimajor axis is given in arcseconds, not linear measure. 
This is simply due to the initially uncertain or unknown remoteness of 
the star. 
    The linear separation is obtained once the distance to the star is 
known. It wasn't until the mid 1990s, quite ten years ago!, that clean 
distance measures were in hand from the HIPPARCOS spaceprobe. Porrima 
stands 38.6 lightyears, or 11.8 parsecs, away. 
    By the definition of a parsec, the linear equivalent of an angular 
extent on the sky is
    (lin sep in AU) = (ang sep in arcsec) * (dist in pc)
This gives the projected value, as if the two stars were placed flat 
against the celestial sphere. It ignores the inclination of the orbit.  
So, for Porrima at the start of 2005, we have 
    (lin sep) = (0.38 arcsec) * (11.8pc)
              = 4.13 AU
    The ascending node, argument of periastron, and inclination are 
defined on the plane of the celestial sphere. There is no common base 
plane for all binaries, such as the equatorial plane of the Milky Way. 
Thus, you can not directly compare orbits among double stars like you 
can with, say, planets or comets in the solar system. 
Orbits and orbits
    None of the orbits prove out! We can excuse the earlier 
computations, but why are there problems with a star so well and 
continuously monitored for over 250 years? The answer is partly in the 
the observations of the 1830s. Porrima's orbit is strongly elongated, 
like a long period comet. It spends most of its period near apoastron, 
where the pair moves slowly for decades. 
    Near periastron, things get weird. Despite the valiant efforts of 
the 1830s, the instruments and skills were too crude. There are no 
firm measurements in the critical years surrounding the periastron. To 
the early astronomers, the stars comgealed into one. Alas, like for a 
comet, the section of orbit close to periastron is the most sensitive 
to errors. 
    Be wary of articles still citing the Strand orbit from 1935. This 
offers a periastron in 2008! If you're not with it, you may sleep off 
the years until then and miss completely the periastron right now in 
    Even the Soderhjeim calculations are already out of spec. The 
closest separation is 0.35 arcsecond. Measurements in 2004 showed the 
stars were nearer than 0.30 arcsecond! Such a small periastron, and a  
well documented apoastron, pushes the excentricity to the Moon. The 
extant orbits posit excentricity of 0.85 or so. It looks like it may 
be as high as 0.92! 
Proximity vs periastron
    Many authors treat these two as alternate terms for the closest 
approach of the two stars. In the general case this is totally wrong. 
The dip and strike and sweep of the orbit on the celestial sphere puts 
the physical closest approach, periastron, away from the angular 
closest approach, proximity. Think of a comet in our sky. Its smallest 
angular separation from the Sun is not at all its perihelion passage. 
    We have to work with TWO orbits. The first is the apparent path on 
the sky, which is the projection of the other, true, orbit in space. 
The latter is not directly observable, unless by chance we happen to 
view it face on from its pole. 
    Elements in binary star catalogs are always for the true orbit. 
    It takes a bit of fancy maths to convert the plotted apparent 
orbit into a path in 3D space. This exercise occupied a whole weekend 
in the age before home computers and calculettes. Today, I tickle a 
handheld computer, while I type out this article, with a binary star 
orbit calculator program. A couple pecks with the stylus and I can 
play with gamma Virginis to my heart's content. 
    Due to the high excentricity of gamma Virginis and the as-yet 
still fuzzy true orbit, proximity and periastron are near together, 
within 1/10 year. The Soderhjeim orbit offers a periastron of 0.40 
arcsec on 2005.30 and a proximity of 0.35 on 2005.37. Lo here the 
    year     proxim  perias | year     proxim  perias 
    -------  ------  ------ | -------  ------  ------
    2005.28  0.3476  0.4049 | 2005.35  0.3453  0.4053 
    2005.29  0.3471  0.4048 | 2005.36  0.3452  0.4055 
    2005.30  0.3467  0.4048 | 2005.37  0.3452  0.4057 
    2005.31  0.3463  0.4048 | 2005.38  0.3452  0.4060 
    2005.32  0.3460  0.4049 | 2005.39  0.3453  0.4063 
    2005.33  0.3457  0.4050 | 2005.40  0.3454  0.4067 
    2005.34  0.3455  0.4051 | 2005.41  0.3456  0.4071 
The 2005 periastron 
    Some binary star enthusiasts, in the lack of a valid orbit, took 
to brute comparison of the 1836 experience with theirs of the 1990s and 
early 2000s. From this it appears that the periastron occurs in mid 
May 2005 with a proximity of about 0.25 arcsecond. 
    As the stars closed up in the 2000s, they fell out of range of 
ever larger home telescopes. For my own experience with a variety of 
instruments of my own and at starviewings, I followed Porrima as two 
stars thru early 2003. Then they merged in my totable scopes. By early 
2004 I lost them in almost every home telescope that crossed my path. 
Never the less, I was thrilled as the months rolled by that I could 
see for myself two suns in dynamic motion. 
    In 2003 and 2004 gamma Virginis required not only major aperture 
but also stable air and sharp eyesight. On a typical turbulent night 
it was impossible to tell that the smeared blob had two stars in it. 
    By mid 2006 the stars are receding enough for the midsize scopes 
to discern. Then year by year, the star returns to duplicity in ever 
smaller telescopes. By the New York Super Bowl, in 2010, Porrima is a 
close but resolvable star in 100mm scopes. By 2012, the New York 
Olympics, it is a trivially easy binary in the smaller scopes. There 
after, until the next periastron in 2174, gamma Virginis is a pleasing 
pair to admire, along with others in the spring sky. 
A star on the move 
    A typical binary star that is seen as two stars in home 
telescopes has a period so long that during a lifetime there is little 
motion of the components. This causes some observers to keep old 
figures for the distance and orientation thruout their astronomy life. 
The long period comes from the necessary immense linear separation of 
the stars to be seen as two in small scopes. Kepler's laws and all 
that, you know. 
    Porrima is one rare exception. Within a lifetime (provided it's 
not centered around apoastron!) real spatial motion of stars can be 
witnessed within a couple years. Near periastron the shift in position 
is discernible within months, and, now, weeks. The downside is that 
you will need some huge scope, like the largest Dobsons or a major 
    By late 2006 more and more telescopes will start seeing the return 
of the double Porrima. During this phase, the stars are still in 
revolution, so they will continuously change their orientation. Be 
sure to watch for that! 
Observing tips
    Naively the stars at periastron should be resolvable in a scope of 
480mm aperture, based on the (120)/(diam) rule. This is an ideal value 
with the stars as perfect optical images. In fact, the atmosphere 
never allows such perfect images. The stars may blur to a half to a 
full arcsecond diameter, thoroly smearing them together. 
    It may be a challenge project to capture digital videos during 
instants of good seeing and combine the best of the frames. This is 
routinely done for planet and lunar pictures, so why not try it for 
double stars? 
    When the stars start reproaching and become a pair in the 
eyepiece, inspection should be made with some particular magnification 
repeatedly to experience the widening separation at the same visual 
scale. If you use various scopes and oculars, keep within 10% of this 
nominal power. 
    The angular rotation is harder to appreciate because of field and 
optical rotation. Unless you fix the field orientation, you won't know 
which way the stars are turning. For sure, here's a star that can 
justify a permanently set up rig. 
    I haven't heard of any ongoing observations from space 
observatories. I expect at least a couple of poster or publicity shots 
by Hubble, no? Same wish with the new supersize machines in Chile with 
their adaptive optics.