Cassiopeia’s Illusion

Cassiopeia, the elegant constellation which hovers year-round in the skies of the Northern Hemisphere is typically recognized by its more simple asterism shaped like a “W” with a slight tilt on one side. (An asterism is a prominent pattern or group of stars, typically having a popular name but smaller than a constellation.)

(Image of Cassiopeia is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.)
Stars of Cassiopeia

The constellation represents the queen of Aethiopia*, the mother of Andromeda in Greek mythology. It’s interesting to note that the Andromeda constellation lies adjacent to Cassiopeia in the night sky. Cassiopeia as a constellation has been known for a long time, as it was listed as one of the 48 original constellations in the 2nd century by Greek astronomer, Ptolemy. Today that list has been extended to 88 official constellations by the International Astronomical Union (IAU).

(*Aethiopia were ancient lands in the area of the upper Nile, not to be confused with modern day Ethiopia.)

The asterism is made up of five stars that can be seen in the illustration below, which shows their distance from Earth and their apparent and absolute magnitudes.

Cassiopeia in 3-D (Click on the picture to see a larger image.)

The table below lists the stars that make up the asterism, arranged in order of their distance from Earth:

What makes Cassiopeia’s asterism remarkable is that four of the five stars appear to be very close in brightness with their apparent magnitudes varying about 1.5 times from the dimmest, Ruchbah (2.68), to the brightest, Navi (2.15). The fifth star, Segin, is notably dimmer than the rest (3.35) but still is fairly bright. (Remember, the more positive the number, the dimmer the star.) This uniformity in brightness gives the impression that the stars are all the same size and distance from Earth.

Being about the same brightness is, in itself, not all that noteworthy until you look at their absolute magnitudes, their distances from Earth and how they work together to create the constellation we see and give us Cassiopeia’s illusion.

To understand what’s happening one has to remember that light has a property that its intensity diminishes by one over the distance squared (1/d2). A candle two feet from you is ¼ the brightness it is one foot away. So one naturally expects to see the stars get dimmer the further away they are. But, that’s not what we see with Cassiopeia.

Starting with the closest star, Caph, 54 light-years from Earth, and moving further out we see that each successive star’s absolute magnitude is more negative (i.e. brighter) than the preceding one:

  • Ruchbah is twice as far as Caph, and it’s 3.7 times as bright – almost 4 times. “If” Caph and Ruchbah had the same absolute magnitude, and Ruchbah was at twice the distance of Caph, we would expect its apparent magnitude to be ¼ that of Caph’s, but that’s not what we see. Ruchbah is almost 4 times brighter. Its intrinsic brightness is such that it compensates for being twice as far away. So it appears to us to be about as bright as Caph.
  • Likewise, Schedar is 4.2 times further and 18 times brighter. If we take the square of the distance – (4.2 x 4.2 = 17.6) – almost 18. Schedar’s intrinsic brightness compensates for the distance, again making it appear to be as bright as Caph to us.
  • Navi is 10 times further but 115 times brighter – that’s pretty close to 10 x 10 = 100 – the square of the distance. Again Navi’s brightness compensates for the greater distance.
  • Segin doesn’t follow this pattern and is dimmer than the rest. If it had an absolute magnitude of -3.1 instead of -2.16, it would be about 50 times brighter than Caph and at its distance from Earth it would have about the same apparent magnitude.

So, through random chance of the stars’ distance and intrinsic brightness, the stars of Cassiopeia very closely compensate for the 1/d2 reduction in the intensity of light over distance. So we see them to be all about the same brightness from here on Earth.

(Note that intervening dust and gas along our line of sight can cause the star to appear dimmer and therefore perceived to be further away than it really is. This is one of the many sources of error that astronomers have to take into account when measuring the brightness and distance of stars.)

So how do these stars make up for their distance?

The other stars in the asterism are hotter and bigger than Caph, especially the more distant stars. Caph is a yellow subgiant, about as hot as our Sun but 28 times more luminous. Navi and Segin are very hot blue stars with luminosities of 161 and 57 times Caph’s luminosity, respectively. Schedar, although a cooler orange-red giant star, is 32 times more luminous than Caph. Even Ruchbah, a more typical main sequence star, is 2.3 times more luminous than Caph.

So, how bright a star appears to be in the night sky is determined not only by its distance and the dust and gas that might lay between it and the observer, but it also its intrinsic brightness. This is a property of the star which depends on how big and how hot it is. So Mother Nature’s distribution of stars in the cosmos can conspire to present us with the illusion, at least for Cassiopeia, that all these stars are the same size and distance from us.

Till next time,

RC Davison


Navi information:

Stellar Systems in Orion

As we head into summer, Orion has departed the northern nighttime skies and will reappear in the chill evenings of autumn. Looking at this distinctive constellation, we are dazzled by the bright stars that define its form: Betelgeuse, the red supergiant of Orion’s left shoulder; Rigel, the blue supergiant that marks his right leg; Saiph, the blue giant for his left leg; Bellatrix, another blue giant that marks his right shoulder and the blue giant and supergiant belt stars, Alnitak, Alnilam and Mintaka.

Orion“, plate 29 in Urania’s Mirror, a set of celestial cards accompanied by
A familiar treatise on astronomy …by Jehoshaphat Aspin. London. (Sidney Hall, Public domain, via Wikimedia Commons)

As impressive as these stars are, there is more to three of them than meets the human eye. What we see as single stars with the naked eye are in reality multiple star systems containing from three to as many as six stars doing a celestial dance together that is governed by the laws of physics.

In the illustration below we can see that Rigel, Mintaka and Alnitak, plus an additional star system, Sigma Orionis, which lies in a cluster of stars just below the left-most belt-star, Alnitak, are multiple star systems. The Orion Nebula itself is a literal star factory containing over 3000 stars with more than 700 of them in various stages of development. There are over 150 stars in this region that have protoplanetary disks – dusty regions around the stars where planets may be forming.

Stellar systems of Orion. Click on image for larger view.

Note that in the illustration the stellar orbits are not to scale, and the orientation of the orbits do not reflect the actual orientation relative to Earth, but the size of the stars displayed are to scale with the Sun’s size shown for reference. One can easily see that the Sun is dwarfed by even the smallest of these stars, which in turn are minuscule relative to the supergiant, Rigel, which is 79 times the size of our star and has 21 times the mass.

The Alnitak and Rigel systems contain pairs of stars that orbit too close together to be resolved (seen as separate stars) using the current state-of-the-art optical telescopes we have available today. These binary systems were discovered by looking at the spectrum of the stars’ light and how it shifts over time. Check out this great article on how spectral binary stars are identified.

Rigel has the most complex system in Orion with four stars. The spectra pair, Ba/Bb, orbit each other every 9.9 days and they orbit about a common center with Rigel C every 63 years. This trinary system obits about Rigel with a period of 24,000 years.

The Mintaka system has five stars in two systems: a binary consisting of Mintaka C/B, which may or may not be gravitationally part of the trinary system made up of the pair, Aa1/Aa2, with a period of 5.7 days, and Mintaka Ab, which orbits around the pair with a period of 350 years.

Alnitak’s spectra binary system, Aa/Ab, has a longer period of 7.3 years. Aa, a supergiant, is 20 times the size of our sun and has 33 times the mass. The smaller partner, Ab is 7 times the size of the sun. This pair is in orbit with a third star, B, and has an orbital period of just over 1500 years. Some references mention the possibility of another star in the group, but as of yet it has not been proven to be gravitationally bound to the system.

A less prominent star, Sigma Orionis, found within the Orion constellation contains a close binary pair Aa/Ab, which is made up of stars very similar in size and mass. (About 5 times the size of the sun.) They orbit each other every 143 days and the pair orbits another star, also similarly sized, with an orbital period of 160 years. These stars cast light on the famous Horsehead nebula of Orion.

σ Orionis (lower right) and the Horsehead nebula. The brighter stars are Alnitak and Alnilam. (Credit: ESO and Digitized Sky Survey 2. Acknowledgment: Davide De Martin)

The Orion Nebula is a vast stellar nursery filled with gas and dust which constantly feeds the growing stars. Some of these stars or protostars are cultivating disks of dust and gas that will eventually coalesce into planets. The two images below show Orion in visible light on the left and in infrared light on the right. The longer wavelengths of the infrared light pass through the dusty veil of the nebula giving us a clearer picture of what’s going on inside. Over the millennia to come, there may be many more stellar systems evolving and becoming visible as the nebular dissipates.

Orion Nebula in optical light (Wikimedia Commons:
Orion Nebula in Infrared light. (ESO/H. Drass et al.)

The cosmos contains so many wonders and we, with our limited senses, have barely scratched the surface to see and understand what is out there!

Till next time,

RC Davison







Chandra article on Mintaka:

Sigma Orionis:

Orion Nebula

Orion In 3D Revisited

With the red giant, Betelgeuse, popping up in the media, I thought it would be a good time to take another look at Orion and the stars that make up this iconic constellation.  Consider this an update to my earlier post “The Multidimensional Constellation, Orion” way back in 2014 – when Orion was behaving himself. (Check the post for more detail on the constellation and its stars.)  In the fall of 2019 Betelgeuse began to dim dramatically, leading many to wonder if it was the time for Betelgeuse to exit stage right in a blazing supernova.

Orion Constellation and Nebulae. Rogelio Bernal Andreo / CC BY-SA (

So Betelgeuse didn’t fade away to oblivion nor did it flash into a supernova, but after losing two-thirds of its brightness it began to recover its luster in February of 2020. Studies just released indicate that the supergiant may have ejected a large mass of hot gas in our general direction that coalesced into dust grains as it cooled and began to block the light from the star. Is this a precursor to the star going supernova? We don’t know. The star will eventually meet that fate, but it could be tomorrow or in the next 100,000 years. Stay tuned!

While reviewing the seven major stars that make up Orion I came across a revised estimate for the stars’ distances from Earth and updated the illustration of Orion in 3-D to reflect this new data. The new data adjusts the distance to most of the stars, mostly closer, but Alnilam, the central star in Orion’s belt, shifted from 1359 light years (ly) to 1976 ly.









Original Distance (ly)








Revised Distance (ly)








Orion’s stars in 3D with new distances based on new Hipparcos reduction. (Click on image for larger version.)

The fact that Alnilam may be 617 ly further away and that its brightness did not change, means that this star is a lot bigger and a lot brighter than previously thought. Alnilam went from being about 375,000 times as bright as our Sun to 832,000 times brighter at this new distance! Also, because of this extra distance the star’s diameter must be larger, changing from 24 times the radius of the Sun to 42 times.

It’s difficult for us to grasp these numbers but there is a way to compare the brightness of these stars and that is to use their ‘absolute magnitude’ as opposed to their apparent magnitude. The apparent magnitude of a star is the brightness of the star as we see it normally in the night sky. Absolute magnitude is the magnitude, or brightness if you will, of the star if it were at a fixed distance from the Earth. The distance that is used is 10 parsecs, where a parsec is 3.26 ly, so the star would be placed at 32.6 ly from Earth and its magnitude recalculated at this new distance.

The apparent magnitude of our Sun is -26.7 (Note, the more negative the number for magnitude, the brighter the object.) if it were moved to 10 parsecs its absolute magnitude would be, +4.83. At +4.83 the Sun would be difficult to see at night with the naked eye, especially with the light pollution we have in cities and towns.  Note that Venus is typically between -2 and -4 when it is visible in the evening, substantially brighter than our Sun would be at 10 parsecs.

Below is table that shows the apparent and absolute magnitude for the stars of Orion.









Apparent Mag








Absolute Mag








One can see that Alnilam is the brightest star in the constellation, surpassing Rigel. So how bright is this?

If Orion’s stars were all at 10 parsecs from Earth, most of the stars would be visible during the day! The illustration below shows an approximation of what one might see. The average magnitude of the brightness of the midday sky is about -4, so all of these stars, except Bellatrix, would be brighter than the sky. Saiph and Mintaka would just barely be visible in the sky, but Rigel and especially Alnilam would stand out prominently. At 10 parsecs, Orion would be amazingly bright constellation at night; out-shining everything but the full moon!

The constellation of Orion would be visible during the day if all of its stars were moved to a distance of 10 parsecs. (Click on image for larger version.)

There is one thing to keep in mind with these numbers, and that is that they are estimates with inherent errors due to the difficulties in determining the exact distance of the stars from Earth.  That uncertainty affects all other calculated values, so you may see the distance, diameter, mass and magnitude values for these stars and others vary from source to source depending on how the data was used.  It doesn’t mean they are wrong; just that we don’t have the technology to absolutely determine their distance.  With each new terrestrial telescope we built, and each new telescope we put into space we refine our measurements and advance our knowledge of the celestial objects that make up the cosmos.

Orion will be rising in the evening in the Northern Hemisphere towards the end of October, so it will be a good time to take a look at this wonderful constellation in person, and keep an eye on Betelgeuse. If you are inclined to do a bit more that just observe with the naked eye and would like to photograph Orion in all its splendor, check out this informative guide to astrophotography.

Till next time,

RC Davison


The HGY Database:

Validation of the New Hipparcos Reduction:

Alnilam, The Brightest Gem in Orion’s Belt:

**Apologies for the barrage of old posts


I didn’t realize that my attempt to stop the plague of bogus posts and ping-backs to the blog site would result in all of the previous post being resent!!

Because each post had to be updated to stop the ping-backs, WordPress happily resent them all, thinking that there was new content!   🙁

My sincere apologies for the unintended barrage of past posts!

RC Davison






It’s been a long while since I’ve posted anything, but with all that’s going on around our planet today I thought it would be a good time to make ORBITAL MANEUVERS free to everyone to help pass the time.  This promotion goes until the 20th of April.

Part of the reason to do this is to remind everyone that things could be a lot worse!  Being confined to one’s home is tedious and challenging, but imagine it with no electricity, no water, no food or fighting just to survive.  Jump into the world of OM and I think you’ll be happy that the coronavirus is all we must contend with.

Also, this is a good time to let you know that the sequel to OM is in the final stages of publication!  ORBITAL RENDEZVOUS will be out sometime later this summer – hopefully!  Stay tuned!

Here’s the link for the free download.  Please feel free to share this.

Be safe, be considerate of others and yourself and follow the guidelines put out by your local health officials.  Understand that this will pass -don’t panic.  Let us all hope that as a global population we will come out of this more united and humbled by how fragile we really are!  We are stronger together than we will ever be apart.

Till next time,

RC Davison

Bridge to a Galaxy Far

Two new images are available in the gallery:

Bridge to a Galaxy Far:

Globular clusters orbit around the center of a galaxy, (Our Milky Way Galaxy has about 150 of them.) and in this image the inhabitants of a planet in one cluster have the pleasure of seeing their parent galaxy rise in all it’s glory every night. As they watch the galaxy rise, there’s more than one set of eyes in the galaxy admiring the globular cluster rising in their night sky.

Bridge to a Galaxy Far


A follow-up to “Bridge to a Galaxy Far”: Morning comes with the rising of the parent gas giant and sister moon as the nearby galaxy that dominated the night sky sets.

Bridge to a Galaxy Far – Morning


Till next time,

RC Davison


Voyagers to the Stars

Voyager: One who takes a long and sometimes dangerous journey involving travel by sea…or in space.

Forty years ago two intrepid spacecraft, aptly named Voyager 1 and 2, set off on a remarkable journey dubbed the “Grand Tour” to visit the gas giants in the outer solar system. Launching Voyager 2 on August 2 and Voyager 1 on September 5, 1977, NASA took advantage of an alignment of the outer planets that made it possible (economically and energy-wise) to visit at least Jupiter and Saturn and potentially Uranus and Neptune. This alignment wouldn’t occur again for 176 years.

Voyager (Image courtesy of NASA)

Although Voyager 1 launched after Voyager 2 it took a faster path and arrived at Jupiter ahead of Voyager 2. Voyager 1 flew by Jupiter and used the gas giant’s gravity to boost its speed and change direction to head off toward Saturn, retracing Pioneer 11’s journey to Jupiter and Saturn earlier in the decade. The trajectory Voyager 1 had as it approached the ringed giant dictated that it was destined to head out of the solar system above (or north of) the ecliptic, the imaginary plane in which the planets orbit the sun.

NASA had to make a decision with regard to Voyager 2: If Voyager 1 did not successfully complete its pass by Saturn, gathering data on the planet’s largest moon, Titan, Voyager 2’s trajectory would be adjusted to make up for its twin’s shortcomings, otherwise it would encounter the ringed planet and slingshot out to Uranus. To all our benefit, Voyager 1 completed its mission and Voyager 2 went on to visit the ice giants, Uranus and Neptune.

Uranus as seen by Voyager 2. (Image courtesy of NASA/JPL)

Neptune as seen by Voyager 2 (Image courtesy of NASA/JPL)

The probe was not designed from the start to encounter the last two distant planets, but it was designed to be reprogrammed on the fly. So NASA engineers rewrote Voyager 2’s programming to account for the much lower light levels at these greater distances from the sun, allowing the probe to capture the first closeup images of Uranus and Neptune. In 1989, after its encounter with Neptune, Voyager 2 took a southerly path below the ecliptic plane and off toward interstellar space.

Today, both probes are still transmitting data from a half dozen or so instruments, their optical cameras and infrared sensors have long since been shut down to conserve power. Notably, Voyager 1 has passed the boundary between the sun’s influence in our solar system and interstellar space known as the heliopause. We find Voyager 1, the most distant object man has ever sent into space, moving beyond 21 billion kilometers (12.9 billion miles) moving at a speed of 61,000 kph (38,000 mph). It takes almost 19.5 hours for a data transmission to reach Earth from Voyager 1 moving at the speed of light. Voyager 2 is a bit closer at 17 billion kilometers (10.5 billion miles) and is moving slower at about 56,500 kph (35,000 mph) with a transmission time of almost 16 hours.

The radio that the probes carry only transmits at 23 watts. That’s about 5 times a typical cell phone’s transmission power we carry around with us. Since the strength of the signal is reduced by the square of the transmission distance, the signal that we receive from Voyager 1 is really, really small: a tenth of a billionth of a trillionth of a watt. That’s .0000000000000000000001 watts. A very small number! To try to put this is some sort of perspective (and even this is hard to grasp!):

If you dropped a grain of salt from the tabletop to the floor, the energy contained in that grain of salt is 10 x 1 million x 1 billion times larger than the energy contained in Voyager’s signal for one second!

As amazing as it is that these spacecraft have been in space for 40 years and are at these extreme distance, to me, it’s even more amazing that we can detect these signals. We use a network of radio telescopes called the Deep Space Network (DSN) that are superbly designed to pick up these astonishingly small signals. There are three sites across the globe that contain multiple radio telescopes to maintain communication with the distant probes in space. The are located in Canberra Australia, Madrid, Spain and Barstow, California (Goldstone). The facility in Canberra is the only site that has a view of Voyager 2 as it exits the solar system to the south, consequently Canberra had to have its antenna dish increased in diameter in 1987 from 64 meters to 70 meters to be able to track Voyager 2’s diminishing signal.

Radio Telescope, Canberra Au. (Image courtesy of NASA)

The Voyagers will eventually stop transmitting around 2030 as their radioisotope thermoelectric generators (RTGs) finally are depleted. The probes will continue on their respective journeys unimpeded. They will not slow down and will not change direction unless something, or someone interferes with them. They may survive for tens of millions of years – a calling card with a Golden Record carrying representations of the inhabitants from a nondescript little water-planet orbiting a very run-of-the-mill star in an arm of the Milky Way Galaxy.


  1. Check on the latest status of Voyager 1 and 2:
  2. Indepth review of Voyager 2’s mission:
  3. A nice review of the Voyager missions:

Till next time,

RC Davison


Hollywood has introduced us to many extraterrestrials, most of them hell-bent on either eating us or conquering and enslaving us.  But, what will first contact really be like.  What will they look like?  What will they smell like?  How will they talk and communicate with us?  Will this contact be amicable or deadly?  So many questions and none of them will be answered until that very first moment we discover that we are not alone in the cosmos.  “Contact” depicts our first literal contact with an alien species.

Wallpaper - Contact

Contact – between two species.


Till next time,

RC Davison

Mountain Mists

Water, water everywhere.  With the prevalence of water all around us (cosmically speaking), it’s not hard to imagine worlds with oceans, lakes, rivers and flowing waterfalls.  It would be very interesting to know if the beings populating these planets and moons appreciate water in it’s many dynamical forms as much as we do.

Relax and enjoy Mountain Mists!

Wallpaper - Mountain Mists

Mountain Mists

Till next time,

RC Davison