Friday, May 10, 2019

About Surface Brightness

About Surface Brightness

                                                                   Martin Lewicki

First published in the Bulletin of the Astronomical Society of South Australia
May 2005


Astronomers use a brightness scale called magnitude to indicate how bright a star appears to the eye. The magnitude scale has been in use since the time of Hipparchus (about 130 BCE). The brightest stars were binned as “magnitude 1” with progressively fainter stars binned down in stages to naked eye limit at “magnitude 6”. After the invention of the telescope stars fainter than naked-eye limit were further scaled down beyond magnitude 6 to as faint as modern telescopes can detect at around magnitude 30!  Put simply, a brighter magnitude was a smaller number than a fainter magnitude with a lager number. To make astronomical object listings more complete astronomers also determined magnitudes for non-stellar objects such as nebulae and clusters. When a deep sky object is given a “magnitude” it means that if its light were concentrated to a stellar point it would shine with the same brightness as a star of that same magnitude. This is known as its integrated magnitude. It would then seem reasonable to assume that deep sky objects with brighter magnitudes should consistently be easier to visually detect than those with fainter magnitudes. Yet even a novice soon discovers that many deep sky objects of the same magnitude do not always look the same brightness. Furthermore, sometimes an object of the same magnitude as another may not even be visible while the other still is! What’s happening here?

The discrepancy arises due to the varying sizes of deep sky objects in the sky. For stars, their light is always concentrated into a point so that there is a direct relationship between a star’s brightness and the magnitude scale. But deep sky objects vary in size so their light may be spread more or less over different size areas making them more or less visible for a given magnitude. Their visibility depends therefore on their surface brightness rather than their total brightness or integrated magnitude. You can see surface brightness in action when you aim a torch-light at a surface and move it inward then outwards. While the surface brightness of the circle of light dims as it enlarges and brightens when it contracts, the total amount of light remains constant.

Surface brightness of an object is measured as magnitude per square arc minute. For example the galaxy NGC 55 at magnitude 8 spreads its light over about 180 square arc minutes. This gives it a surface brightness of about magnitude 13 per square arc minute. The planetary nebula NGC 3132 in Vela is also at magnitude 8 but has its light concentrated into a much smaller area about 1.3 square arc minutes. This results in a surface brightness just under magnitude 8 per square arc minute — almost the same as its “stellar” magnitude. This makes NGC 3132 much easier visually detect than NGC 55.
                              

Another example is the “Silver Coin Galaxy” NGC 253 in Sculptor at magnitude 7.6. The Silver Coin is easily picked up with pair of binoculars when near zenith whereas under the same circumstances the enigmatic galaxy Centaurus A at a much brighter magnitude 6.7 is somewhat more difficult. The reason again is surface brightness. NGC 253 has its light concentrated in 160 square arc minutes giving it a surface brightness of magnitude 12.7 per square arc minute, while the light of Centaurus A is thinly spread out over a much larger 550 square arc minutes giving it a surface brightness of magnitude 13.5 per square arc minute. No wonder the Silver Coin is easier to visually detect! Using surface brightness magnitude therefore is a more practical way to estimate the degree of visibility of extended deep sky objects than using integrated magnitude.







 NGC 253 The “Silver Coin Galaxy” ( left) at magnitude 7.6 is paradoxically easier to visually
 detect than the “brighter” Centaurus A right) at magnitude 6.7
Images: Paul Haese


Most deep sky objects however vary their light distribution across their surfaces and produce variations in visibility for a given surface brightness whereas listed surface brightness magnitudes are the average brightness across the object. Surface brightness is therefore an approximate guide to visibility. For example, galaxies with bright cores will be easier to visually detect than the same size and surface brightness galaxies with a more even light distribution.  The Seyfert galaxy M77 in Cetus is a good example. Its 8.9 magnitudes is spread out to a surface brightness of 12.8 magnitude per square arcminute. But it has a bright nucleus that concentrates more of its light making it more star like and more easily visible.

While catalogues also give surface brightness for open star clusters too they are not often that useful. Stars in open clusters vary greatly in distribution, number and brightness of stars and the eye tends to focus on individual stars than the overall light distribution. IC 2602, the bright  “Southern Pleiades” for example has a listed surface brightness of magnitude 11.6, hardly an indication of its true visibility! Here IC 2602 has several bright stars ranging from magnitude 2.7 to 5 spread over 7,800 square degrees — plenty of room to dilute its 1.9 magnitudes. Surface brightness is more useful for globular clusters and for open clusters if they are distant and begin to resemble nebulae. 


Most planetarium software now include surface brightness magnitudes as well as the integrated magnitudes in their deep sky listings. Other listings such as those in the Bright Star Atlas 2000 (Tirion) provide only integrated magnitudes and object sizes in arc minutes. But these two factors will enable you to calculate surface brightness yourself (see side-box). Serious deep sky observers may use other criteria such as surface brightness per square arc second to determine visibility especially when using large apertures and high magnifications.

Armed with surface brightness listings I have found that with my Meade ETX90 (Maksutov 90mm), I can on a good night from my suburban backyard pick up deep sky objects to as faint as a surface brightness magnitude 13.5 per square arc minute. Of course this appears to fly in the face of the magnitude limit for a 90mm telescope (magnitude 11.0 for stars at my observing site). But then, when you are looking at an extended deep sky object in the eyepiece the eye is recording photons over a larger area of the retina and your amazing brain software is capable of integrating these hits to inform you that “there is something there”.

***
 

 

Calculating Surface Brightness
 
Get the magnitude and dimensions in arc minutes of the object from a catalogue. Calculate its area in square arc minutes

Circular object
A=pi*r*r (where r is radius)

Elliptical object
A=pi*(a/2*b/2) where a & b are the major and minor axes of the ellipse
Rectangular object

A=a*b  (where a & b are length and breadth).

Example: Omega Centauri mag 3.7 dimension 36’
A=3.142*17*17 = 907.9
SB= mag+2.5*log10(A) = 11.1
Surface brightness = mag 11.1 /sq arcmin



Thursday, May 26, 2016



The “Sam Brown” Pipe Mount – A Telescope Mount For All Seasons

First Published in the Astronomical Society of South Australia Bulletin
 March 2006 (www.assa.org.au)

Martin Lewicki
Home-made Classic 6-inch Newtonian Reflector



Way back in 1974 I decided it was time to build a decent telescope. Until then I observed mainly with a pair of 10x50 binoculars and prior to this a home made simple lens 30mm telescope made from whatever was lying about at the time. My new project was to grind and polish a mirror to make a 6-inch Newtonian reflecting telescope.

As I frequently visited my brother’s bookshop in Adelaide it was just a short walk around the corner to Chesser Street to seek advice from John Cole from Cole Precision Optics. John supplied the Pyrex mirror blank and plate glass tool along with the abrasives and polishing formula along with patient advice on what I would be up against in making my first mirror. He also supplied me with a singular book by Sam Brown, the classic All About Telescopes published by Edmund Scientific. Its profusely illustrated pages had all the instructions on making telescopes of all kinds from simple to complex. The instructions covered mirror grinding and polishing, telescope math, mounts, photography and optical theory.

I was so excited and driven that the next weekend, in the space of 48 hours, and virtually no sleep, I had ground and polished the mirror and tested it with a rhonchi set-up in my shed. The following day I handed it over to John Cole for examination. He declared it a “good mirror” — at least for a first timer, and we decided to go ahead with the coating. The optical performance subsequently turned out to be rather good showing diffraction disks and airy rings on stars on nights with steady seeing.

In the mean time I had to think about what kind of mount I would choose for my 6-inch reflector. This is before the days of John Dobson and his famous utilitarian dobsonian telescope mount, which I’m sure I would have chosen had it been contemporary. I perused through Brown’s book at the copious choices of mounts that could be made from all manner of materials. While I would have liked to have gone for one of equatorial roller bearing mounts I felt this was a bit too advanced for me. I was instead taken by a simple mount that could be made from plumbing pipes. The illustrations showed how I could use a 45-degree elbow joint and a T-section to make a hand-push turn-on-threads German equatorial mount.

Cover and sample pages of Sam Brown's All About Telescopes. The equatorial at right is the inspiration for the mount.

The 45-degree elbow joint would serve to angle the upper part of the mount to point roughly at the south celestial pole at mid latitudes and rotate on its screw thread in right ascension. The T-section would hold a cradle with telescope and rotate on its thread in declination. All this is balanced by an opposing counter-weight. I went for 2-inch pipe for sturdiness and to possibly handle a future 8 or 10-inch scope.

After a few trips to the hardware store to buy the joints and 2-inch pipe cut to length for the pedestal I followed Browns instructions. While the 45-degree elbow would have been quite suitable for a rough polar alignment near 45 degrees latitude, for Adelaide at 35 degrees this is too far out for comfortable equatorial tracking. It would require too many frequent corrections in declination to keep an object in the field of view as I tracked the scope. So I decide to combine 45-degree, 90-degree and T-elbows that enabled me to twist the first two into a position so that the “polar-shaft” could be set at 35 degrees. I had a friend drill and tap three holes in the lower elbow to insert bolts to lock the polar elevation in place.

The lock bolts could also be loosened to adjust for a different latitude if required. The top of the mount was fitted with a timber cradle for the tube and mated to one end of the T-pipe with a flange to turn in declination. An azimuth-lock bolt was also added to the elbow mated to the pedestal pipe to facilitate aligning the “polar shaft” to south.

Modified pipe arrangement for 35° latitude

The turning screw threads for the right ascension and declination axes were lapped (fine ground) with wet 600-grit carborundum powder left over from the mirror making process. Several twists of the mated threads smoothed their contacts. They were washed then lubricated with a layer of grease, re-mated and finally assembled on to the pipe pedestal which had three legs made of meranti timber bolted to the base.

While a mount that turns on plumbing pipe threads appears to be crude in comparison to a precision roller bearing mount the pipes turned out to work remarkably well. Once the telescope tube was mounted and balanced with a counter weight the movement on the axes was surprisingly smooth. I found the natural clutch action of the 2-inch threads had very little backlash when fine aiming by hand. In fact it is much smoother than any 6-inch dobsonian that I have ever tried!

In addition, when the mount is rough-aligned with the celestial pole within a degree or two I can gently hand push (or pull, depending on which side of the meridian the telescope is pointed) in just the one right ascension axis to track an object for 10 to 20 minutes at low magnification before a declination tweak is required. You give it a gentle push, let go, and it stays put. Even inexperienced visitors get the hang of tracking a planet very quickly by this method because it avoids the more tedious and sometimes confusing step-wise actions required to track an object as with a dobsonian mount.

An important advantage of an equatorial mount is its ability to easily tack an object through zenith where sky transparency and seeing conditions are optimal. The alt-azimuth configuration of a dobsonian however hits a mechanical dead spot as it becomes ungainly to point along its azimuth axis aimed at zenith requiring awkward manipulation of the tube to acquire and track an object. A similar dead spot exists for the equatorial mount when the telescope is aimed at the celestial pole. But here only a small circular section of the sky is involved that is rarely targeted by telescope users.

A German equatorial mount necessarily has a protruding counter weight shaft and the eyepiece will rotate to different orientations depending on where the telescope is pointed. This may require a raised footstep for some people to reach the eyepiece in some viewing orientations. And of course the counterweight adds a necessary, but a dead weight to the entire assembly.

My mount plus pedestal weighs in at 15 kg compared to the wood mass of an equivalent dobsonian at about 12kg. Also my mount has several parts that need to be assembled and disassembled in the event of having to load in a car for transportation. Assembly and disassembly can take 10 or more minutes. This might be a disadvantage for those used to a dob mount. However I find the smooth push-aiming action and simple equatorial tracking of the Sam Brown pipe mount a sufficient compensation for the drawbacks.

Over the years my pipe mount has served me well. The galvanized iron parts are so sturdy and robust that at the end of an observing session I bring only the telescope tube indoors for storage and permanently leave the mount out in the backyard — exposed to the elements! This saves me a lot of assembly-disassembly and carrying weight. It has survived 32 winters, summers, and seasons in between and has been subjected to all manner of weather onslaught in that time with no loss of performance!

The only regular servicing is cleaning and re-greasing the threads on the turning axes every two years or so and changing the iron lock bolts when they begin to rust. Though in future I intend to use brass bolts for more permanent solution. The timber cradle and tripod base with several coats of outdoor clear enamel lasted most of those 32 years though in the last couple of years had become so weather beaten that I finally replaced them with fresh timbers.

Casual visitors often comment on the “contraption” standing sentinel (minus tube) in my backyard and sometimes venture a guess as to its purpose. Among other things it has been taken for an attempt at postmodern sculpture and a device for stringing up tennis rackets. Others have correctly guessed its purpose and one tradesperson, a plumber, and owner of a 4-inch commercially made equatorial reflector especially commented on the simple design and smooth motion of the axes. Meanwhile my astronomy friends have dubbed it the “plumber-scope”.

Over the years I did consider making a dobsonian mount to replace the pipe mount for my 6-inch reflector for the quick set-up that it affords. But the Sam Brown pipe mount has a quaint elegance about it that I find difficult to relinquish. While these days the cost of making an equatorial pipe mount would exceed that of making a dobsonian mount, a telescope that is polar aligned brings it in line with the way the diurnal sky rotates and has a natural feel as you track a celestial object. My indelible pipe mount as it stands in my backyard and weathers yet another round of seasons reminds me of the continuity of a life of observing. I tip my hat to Sam Brown. ***

Friday, June 20, 2014

Backyard Astronomy with a 17th Century Telescope

First published in the Bulletin of the Astronomical Society of South Australia,
 August 2014.  Expanded version
 (www.assa.org.au)
 by Martin Lewicki



Telescope users are usually well aware of the benefits of advanced optics available in their instruments today. Compared to the primitive optics that astronomers contended with in the early days of telescopic astronomy, today's high precision optics yield sharp, high contrast views that we now take for granted.

Prior to the invention of achromatic lens in 1733 early astronomers had to contend with views plagued by chromatic aberration, often referred to as “false colour”. Chromatic aberration and to a lesser extent spherical aberration are natural image defects of simple lenses. They produce views of celestial objects surrounded with unwanted colour fringing due to the inability of a simple lens to bring all colours of an image to the same focus. This results in lower image contrast and washed out colours.  Yet these telescopes opened up a new universe that included the revolutionary discoveries of Galileo with his small 15mm (1/2-inch) aperture lens. Later larger versions up to 200mm (8-inch) objective lenses were built by Huygens, Cassini and Hevelius. These telescope makers realised that extremely long focal ratios were required to diminish the chromatic aberration suffered by these simple objective lenses. They discovered that if aperture was doubled then focal length had to be squared, (or four times longer) to keep the chromatic aberration in check! As a consequence of desiring larger apertures their telescopes correspondingly grew to unwieldy lengths, up to 46 meters such as Hevelius' “150-foot telescope”!

Hevelius' 150-foot (46m) 8-inch (200mm) Telescope 1673
In order to get the feel of what it may have been like to use a non-achromatic telescope of the day I decided to build a small long focus refractor with only simple lenses like what would have been available in the early 17th century. I felt a 30mm (1.2-inch) objective diameter of 1000mm (“three-foot”) focal length would be a good start. Thus my telescope while smaller than that used by serious observers of the time might have been about the size owned by a well to do dilettante with astronomical interests.

I purchased a surplus 30mm plano-convex lens over the internet for a few dollars. After a trip to Spotlight for some spent cardboard material tubes of the right diameter I made a cardboard cell for the objective lens, fitted it to one end of a cut-to-length “three-foot” tube and inserted a smaller diameter draw tube for the eyepieces in the other end. The flat side of the plano-convex objective faces inward. The plano-convex lens is preferred as it has less spherical aberration than the more common double convex lenses. Indeed, two of Galileo's surviving telescopes have plano-convex and plano-concave for the objective and eyepiece respectively, though this may have been to simplify fabrication by fashioning one instead of two curves on each glass.



The eyepieces I use are old Tasco of the Huygens design in keeping with the type used in the 17th century invented by Christiaan Huygens himself. The Huygens eyepiece comprises of two short focus plano-convex lenses appropriately spaced with flat sides facing the eye to give a wider field of view than a single lens. My eyepieces are focal lengths of 38mm, 23mm and 12.5mm giving 26x, 43x and 80x. Finally a light baffle was placed in the tube to reduce internal light scatter. In all, the optics of my three-foot telescope use simple lenses; no achromatics, no coated lenses, in keeping with the 17th century theme.

It was time to try my scope out on objects in the celestial firmament. First targets were stars. I was surprised to find they could be focused sharply enough so that the airy disk (sometimes known as the diffraction disk) was apparent. Savvy telescope users know this is a sign of good optical performance. Point sources like stars will focus at best to a small disk thanks to the wave-like properties of light. Only a slight amount of false colour was evident surrounding the stars. Brighter stars and higher magnifications show more false colour but the airy disk was still clearly evident.


Snapshot of moon at 26x with camera at eyepiece. Some colour fringing is evident around the lunar limb and craters.






 Next was the Moon. Again, surprisingly good with only slight false colour fringing around the lunar limb and shadowed craters. I felt the view at 26x was quite acceptable with sufficient contrast revealing a wealth of detail in craters and mountains. Saturn was next. At 26x its ball and ring were easily evident and at 43x the ring was distinctly separated from the ball. But one could understand how Galileo was perplexed by the 'handles' of Saturn. If I had not known that they were rings my first impression would have been rather like that of Galileo. Some false colour fringing was seen as a blue and red halo around the edges of the planet and its ring which increased at higher magnifications. Later in the year Jupiter was visible. The four Galilean moons at 26x were crisp points and the disk of Jupiter itself just barely hinted at the equatorial belts. Like Saturn, Jupiter showed a certain amount of false colour around its bright disk.

Snapshot of Venus 26x







Venus also graced the evening sky. I was able to trace its phases in my telescope over the closing months of 2013 toward its inferior conjunction. The planet's brilliance however exacerbated the false colour so that it was surround by glorious halos of red, yellow, blue and purple. It was with Venus that it was plainly evident the telescope was not corrected for chromatic aberration! Like many observers I found Venus easier to appreciate in a daytime sky where contrast is lower. Mars however at it's current apparent diameter of 14” (late 2013) shows little more than a orange disk at all magnifications.


However my biggest surprise was how well this simple-lens telescope performs on “close” binary stars. Stars are limited to those with a separation of 3.9 arcseconds - the so-called Dawes limit for a 30mm aperture. My first target was Alpha Centauri. The two components are now 4.5 arcseconds apart (2013). My telescope revealed their duplicity. At 43x they appeared as two airy discs of unequal size almost touching surrounded by several airy rings. The Alpha Crucis pair was even more intriguing. At 43x and 80x the two components at 4 arcseconds apart sat close together with a thin line separating their two airy disks.

Sketch Alpha Centauri and Crucis at 80x
The pretty binary Alberio did not disappoint. The two components showed their delightful orange and blue-white colours due to their spectral types K3 and B8. At 26x false colour hardly interfered with their appearance. A selection of other binaries such as the orange dwarfs 61Cygni, the wonderful Theta Eridani pair (8.3”), Beta Tucanae (30”) and the Beta Monocerotis (7.2”) gave pleasing views.

Next were deep sky objects. Under light polluted urban skies they were pale versions of themselves due to the small aperture. But away from light polluted skies at 26x the Orion Nebula showed a diffuse mist with its characteristic structure but with only three of the four trapezium stars apparent. Clusters such as such as M7 and M41 look like a fine sprinkling of stars with no hint of false colour. Eta Carina nebula clearly revealed its “L-shaped” misty form and the Jewelbox its “A” shaped asterism. In December 2014 Comet Lovejoy (C/2014 Q2) graced the evening sky. From my light polluted suburban location I was pleased to pick the comet at 26x shining at magnitude 7.5 drifting through the constellation Puppis. The sketch reveals stars down to magnitude 8 (labelled without the decimal point). An advantage of long focal ratio telescopes is that the background sky darkens more than a star making fainter stars more visible than otherwise. 

Comet C/2014 Q2 Lovejoy with field stars to magnitude 8
Finally, in order to get the best sharpness out of my 17th century telescope I attached a modern photography-grade deep orange filter to the eyepiece. These filters were not available to 17th century observers. But the filter made an immediate difference. The light through the filter is now nearly monochromatic and can be sharply focused. The Moon looks perfectly sharp with virtually no trace of false colour! The outlines of Jupiter and Saturn snapped into sharpness along with brilliant Venus showing clean views of its phases with little false colour. However for such a small aperture the orange filter blocks more than half of the light so it is next to useless for faint stars and deep sky objects. Had 17th century astronomers been able to make precision optical glass flats I imagine they would have benefited with “stained glass” versions as filters to sharpen the views through their much larger light-capturing apertures.

An orange filter dramatically improves sharpness.
Clearly these 17th century telescopes were capable of revealing detail in planets and stars that paved the way for new discoveries. Essentially, a simple lens telescope will perform to the same resolution and almost same contrast as an achromatic lens of the same aperture - if the focal ratio is long enough. This enabled 17th century astronomers to make significant discoveries with their simple glasses at the end of their long tubes. Discoveries of Saturn's moons Titan, Tethys, Dione and Rhea, the ice caps of Mars and Cassini's division in Saturn's rings were made with these pre achromatic telescopes. These telescopes were used by the likes of Edmund Halley, and Robert Hooke who discovered Jupiter's Great Red Spot and William Gascoigne who invented the filar micrometer in 1633 and used it to prove the Moon's orbit is elliptical. Even when the colour-corrected achromatic lens finally became widely available in the 1750's the long telescope persisted for some years because flint glass, one of the components of the achromatic lens, was difficult to manufacture with consistent quality to make large aperture objectives.




My long skinny telescope attracts attention when I bring it to star parties. Many viewers comment on the clarity of the moon, planets and stars seen through the three-footer and were surprised to learn learn that it cost about $25 to make mostly from recycled and second-hand materials. For convenience especially for star parties I added a 45 degree mirror diagonal for comfortable viewing. I also added a small finder to help with aiming. To complete my range of eyepieces I also made a second draw tube fitted with a single plano-concave lens of minus 70mm focal length. When inserted in the eyepiece end it becomes a Galilean Telescope producing a 14x upright image that is optically similar to Galileo’s early telescopes. It allows viewers for example to appreciate how Galileo saw the Moon and Jupiter with its satellites in its very narrow field of view. The telescope thus proved to perform rather better than I and most people would have expected. Visitors and in particular children are often intrigued with the views possible through this simple-lens home-made astronomical telescope. ***



Snapshot of Sun through eyepiece.


Pencil sketch of Moon at 26x with orange filter





Notes:
  1. Objective lens obtained from Surplusshed http://www.surplusshed.com/
  2. Hevelius telescope image - Wikipedia
    To see this simple lens act as a 1000mm telephoto lens see: 
    https://sites.google.com/site/simplelenstelephoto/



    What's Next?
    A test rig with 2-inch (50mm) planoconvex lens objective x focal length 2500mm
    working at f50
    (update 9 February 2016) 
    Two 1000x50mm PVC tubes joined by a 50mm collar making a 2m tube. Cardboard focus tube slides in at right to make a 2.5m telescope. The join is braced by a u-bolt tightened by wing nuts to keep tube (near) perfectly straight.


    Materials from hardware shop and piece of timber from garage. Total cost is about AU$20 for tube assembly.

    The 50x2500mm planoconvex objective from OptoSigma US$49.50. They have 50mm up to 5m focal length!
    Hand-held views of the moon and some bright stars look promising. Now to make a mount!

    _________________________________________________________________________


    References


    Sky and Telescope
    Astronomy’s Neglected Child- The Long refractor – R. Berry,  Feb 1976
    A
    Telescope of the 17th Century - A Binder, Apr 1992
     

    Books
    Stargazer - Fred Watson
    Seeing and Believing – Richard Panek
    All About telescopes – Sam Brown 1975 (Edmund)
     

    Telescope/Optics links 
    http://www.telescope-optics.net
    Wikipedia sources
    Articles

    Could Jean-Dominique Cassini see the famous
    division in Saturn’s rings? arXiv:1309.1711v1
     

    Software
    http://www.atmos-software.it/Atmos.html
    http://www.lambdares.com/oslo
     

    Optical Suppliers
    http://www.surplusshed.com/
    including various sources of miscellaneous lens 
    http://galileotelescope.org/Galileo_telescope/ (for Huygens eyepieces. Search eBay too)
     

Thursday, May 2, 2013

How Long to Alpha Centauri?

Martin Lewicki

Astronomy Educator, Adelaide Planetarium, University of South Australia
 First published in the Astronomical society of South Australia Bulletin May 2013

The famous Alpha Centauri binary star system is our nearest stellar neighbour at a distance of 4.4 light years. This binary sun-like star system features in many science fiction stories and has been the subject of imagined futuristic colonizing journeys. In spite of Alpha Centauri's relative nearness to us, its distance of 45 trillion kilometers poses a formidable challenge in terms of travel time with current space craft propulsion technology. Articles written about travel time to the Alpha Centauri system attempt to illustrate how long would it take a conventional current day space craft to get there traveling at its typical escape velocities out of the solar system.

Most state that a space craft traveling at the current record breaking speed of Voyager 1 at 65,000 km/h or 17 km/sec aimed at Alpha Centauri would take about 80,000 years to arrive. (Voyager 1 itself is not actually aimed at Alpha Centauri). I have heard this figure repeated many times in web articles, in lectures and in planetariums. While the calculation is correct in theory, in practice it is the wrong strategy because it incorrectly assumes that Alpha Centauri remains permanently the same 4.4 light years from us. Alpha Centauri like all stars has a relative space motion to us. It is the reason why after several thousand years the space motions of stars in our sky will begin to deform the familiar shapes of many constellations. This motion as it appears on the sky is easily looked up in any star catalog and is known as proper motion and radial velocity.

Proper motion is the transverse (apparent sideways) motion of the star on the sky and is expressed as arc-seconds per year in right ascension and declination. Radial velocity is the star's apparent velocity toward or away from us in the line of sight. With this information and some trigonometry it is possible to calculate the true space motion and velocity of the star relative to us and work out where it will be in the future or past. This is a crucial factor to be accounted for when aiming a space craft for a long journey to a star.

In the case of Alpha Centauri its proper motion is -3.678 arc seconds in right ascension and +0.482 arc seconds in declination and a radial velocity of 21.7 km/sec in approach. Combining these figures we get a space velocity of Alpha Centauri approximately toward our direction at 32 km/sec at an approach angle of 47 degrees.

At this velocity and approach angle, Alpha Centauri will pass at its closest to us in 27,700 years at a distance of 3.2 light years and in a direction 43 degrees away in the sky from where it is now in Centaurus. At it closest approach it will be among the stars at the border of Antlia and Hydra shining at a brighter magnitude of -1.0 At this time Alpha Centauri's radial velocity will be zero (neither moving toward or away) and its transverse proper motion (sideways) will greatest. From this point on it will begin to recede from us and head out in the direction of Hydra.

A direct shot at Alpha Centauri will ensure a complete miss as shown by the 80,000-year gray trajectory line (red X). Alpha Centauri will by then have moved to lower left (dashed line). The most efficient trajectory is the 27,700 year trip along the blue line, but at twice the speed of the fastest escaping space craft – Voyager 1.  Illustration by Martin Lewicki


In 80,000 years from now Alpha Centauri will be 7.4 light years away in southern Cancer dimmed to magnitude 0.8 and 100 degrees away across the sky from where it is now in Centaurus. This means if you aim a Voyager 1 class space craft at where Alpha Centauri is NOW the space craft will find nothing there when it gets there in 80,000 years. If instead we aim the Voyager 1 space craft in the direction of Alpha Centauri's nearest approach in Antlia/Hydra in the anticipation of intercepting it in 27,700 years, we would fail yet again. Alpha Centauri's space velocity of 32 km/secs would out-run the slower 17 km/sec rate of the space craft, leaving it behind, never catching up! So none of the current escaping interplanetary space craft such as the Pioneers, Voyagers or New Horizons can ever get to Alpha Centauri - even if they were pointed right at it. Alpha Centauri would simply out-run them all!


Alpha Centauri's trajectory during an 80,000-year trek across the sky. Many familiar constellations also become distorted due to the space motions of their stars in the intervening time.  Adapted from Stellarium by Martin Lewicki

And The Answer Is?
Clearly the minimum space velocity of a Voyager 1 class space craft will need to be greater to intercept Alpha Centauri when it is nearest to us in 27,700 years. If we launched now it will need to attain a velocity of 34 km/sec - about twice the current velocity of Voyager 1 to make the rendezvous in time. This is the minimum speed required to ever catch Alpha Centauri! Any slower just would not make it. Only one other space craft out-speeds Voyager 1. Helios-2 launched in 1976 to study the space environment within 0.3 and 1AU of the Sun can attain a speed of 67 km/sec when at perihelion. While it is not actually escaping the solar system if this motion was translated to a gravitational slingshot toward Alpha Centauri it would intercept the star before its closest approach to us and would get there in about 15,600 years[1]. ***


References:


Universe Today

Calculations:


Heavens Above

[1] Helios intercept calculation by Mark Taylor.