Oumuamua – As Improbably Skinny as the Most Slender Human Skyscrapers

Oumuamua – As Improbably Skinny as the Most Slender Human Skyscrapers

Alien Technology?

A story on the BBC website reports that the interstellar visitor object, Oumuamua is being examined for signs of alien technology.  Billionaire Yuri Milner will be funding a project, making use of the Green Bank Radio Telescope in West Virginia, to listen for any signals (intentional or not) that would indicate a non-natural source. That might include actual attempts at communication, or radio signals that leak from the object unintentionally, say from some type of electrical machinery.  Even an unexplained heat signature would be of interest.

It seems like a real long shot, but then the term “long” is very apt for this object, as it is very unusual for its long shape, about a 10 to 1 ratio of long axis to short axis.

Estimating Oumuamua’s Size and Shape

Contrary to what one might expect based on pictures in the media, we haven’t actually been able to photograph it in the glorious detail generally shown, as above.  Those are artist renderings.  In fact we haven’t really been able to photograph it at all, as far as its shape is concerned.  From the distance at which we have observed it, it is just a speck of light, albeit a speck that varies in brightness.

Why don’t we have nice photos?  Basically, it is too small.  It is thought to be about 800 meters long, by 80 meters wide, by 80 meters deep.  A little trigonometry shows that an 0.8 km object would subtend an angle of about 0.016 arc seconds, even at the relatively close distance of 10,000,000 km. 

The telescopes and cameras that were used to photograph Oumuamua had a resolution, at best, of only about 0.1 arc seconds per pixel, so it can’t really be seen as an extended object, at the distances at which it has been observed (it was at roughly Mars-like distances when first observed, as indicated in the picture taken from the Nature paper).

The reason that the object is thought to have this shape is due to its light curve. Oumuamua varies in how bright it is by about 2.5 magnitudes over about 8 hours, which is equivalent to a brightness change of about 10 times, as explained below:

• The magnitude scale is constructed so that a difference of 5 magnitudes equals a difference of 100 time in intrinsic magnitude.  Another way of looking at that, is that each magnitude change represents about 2.5 times change in brightness.
• So, 5 magnitudes is about 2.5 raised to the fifth power, which is about 98.  A difference of 2.5 magnitudes is about 2.5 railed to the power 2.5, which is 9.88, or nearly 10.

• Note that I am making some approximations here, but they are close enough for the purpose, given the uncertainties in observational data, anyway.  

The most likely reason for this change in brightness is that it is that Oumuamua is rotating every 8 hours, with its short profile facing Earth when it is dimmest and its long profile facing Earth when it is brightest (like a North American football tumbling end over end after a kick-off, as observed from the kicker’s point of view). So, the difference of a factor of 10 in brightness would be due to the change in the amount of surface area facing the Earth, and thus the amount of reflecting surface that is reflecting sunlight back to us.

An Underestimate of the Elongation?

On interesting aspect of this explanation, is that the 10 to 1 elongation estimate might well be a significant underestimate, depending on the angle of Oumuamua’s rotation plane, as seen from the Earth.

I mocked up a model of the interstellar asteroid, with approximately the same ratio of dimensions as Oumuamua.  This was a piece of scrap wood with dimensions of about 15 inches by 1.50 inches by 1.75 inches.  That’s pretty close to the 10 to 1 elongation of Oumuamua.

I then mounted this on a tripod, using some good old duct tape.  The tripod could be rotated in all three dimensions.  That was then placed next to a wall with a light source across the room.  This was meant to very roughly model the situation of the asteroid, relative to the Earth, with the size of the shadow on the wall corresponding to the amount of area that the asteroid would present to the sun, and thereby the amount of light being reflected back to an observer on Earth.

This exercise is also a straightforward example of projecting a 3-D object onto a 2-D surface (more trigonometry), but a picture is worth a thousand words, so I thought this would be interesting an persuasive in illustrating the mathematical situation.

I have named this the “propeller” in the images below.  One can think of how a spinning propeller would look to an observer, at various angles.  Remember, though, that the propeller is rotating very slowly, about once every 8 hours, so the apparent size of it can be easily measured at various stages in the rotation.  Note also, that the pictures had to be taken at a bit of an angle, otherwise there would be no shadow to measure, since the photographer would block the light (“shades” of the observer affecting the observation).  So, the photos are a bit distorted, relative to the shadow measurements actually taken with a tape measure.  

Case 1 is the situation that is yields the maximum ratio of length to width/depth.  When the asteroid model is pointing straight up and down, relative to the observer, its shadow  measures about 17 inches long by 1.75 inches wide (the shadow is a bit longer than the model, because the light source is a non-spherical light bulb about 10 feet away, so there are some complicated penumbra effects).  When it is pointing sideways, relative to the observer, it measures about 1.75 inches long by 1.75 inches wide.  So, that yields an elongation of about 10, which is the elongation estimated for Oumuamua in the reports. 

Case 2 is the situation that is yields the minimum ratio of length to width/depth, which is to say no elongation at all.  When the asteroid model is pointing straight up and down, relative to the observer, its shadow  measures about 16 inches long by 1.75 inches wide.  When it is pointing sideways, relative to the observer, it measures about the same.  So, that yields an elongation of about 1, or no elongation at all.  So, if a long object (but relatively small) was to fly away from us, spinning like a propeller face on, we wouldn’t really know anything about its shape, as it would seem equally bright throughout its rotation.  

Case 3 is an intermediate situation, with the plane of the propeller at about 45 degrees to the observers line of sight.  When the asteroid model is pointing straight up and down, relative to the observer, its shadow measures about 16.5 inches long by 2.25 inches wide.  When it is pointing sideways, relative to the observer, it measures about 13.5 inches long by 1.75 inches wide.  So, that yields an elongation of well under 2, or not much at all, event thought we know that the dimensions of the object are actually 10 to 1.  So, for such an object oriented at an oblique angle, we would be seriously misled about its real size.  The same is true for other oblique angles – even an object inclined only 30 degrees from straight-on yields a fairly small apparent elongation, on the order of 2. 

Of course, if one followed the object for quite a long time through its orbit, its orientation relative to the Earth would constantly shift, so that would provide extra information.  But, in practice, it would become difficult to see at all, as it continued in its orbit.  Here’s a quote in the Nature discovery paper:

“The inset shows the inner solar system, with the solid line segment along ‘Oumuamua’s trajectory indicating the short window of two weeks during which it was bright enough (median magnitude of light curve V~20-24) to be studied by large telescopes on Earth.”

So, Oumuamua is a weird shaped object, at least 10 to 1 ratio of length to width, according to the light curve.  But, from this little modelling experiment, it seems likely that it is actually considerably more elongated than that, given that it is probably not at the most favorable angle to estimate elongation via the light curve.  So, that means that it probably goes from being a weird object to a very weird object, at least as far as this simple modelling experiment is concerned.

I should note that an early version of  the Astrophysical Journal paper alludes to this issue noting that the “axis ratio is a lower limit because of the effects of projection, and is extreme relative to most asteroids”.

Even a 10 to 1 ratio is surprisingly elongated.  In fact, skyscrapers with that elongation are considered to be very slender structures, as is described in the skyscraper.org website:

WHAT IS SLENDERNESS?   

"Slenderness" is an engineering definition. Structural engineers generally consider skyscrapers with a minimum 1:10 or 1:12 ratio (of the width of the building's base to its height) to be "slender." Slenderness is a proportion based on the width of the base to the height of the building.

The World Trade Center North Tower was the tallest building in the world on its completion in 1971. But at a height of 1,368 feet and with a big square floor plate, 209 feet on each side, the ratio of its base to height was less than 1:7. This image compares at the same scale the former 1 WTC and the residential tower 432 Park Avenue, now under construction. The base of the apartment building is 93 feet square, and the shaft will rise to 1,396 feet, making its slenderness ratio 1:15. To visualize a 1:12 ratio, we show a ruler 1-inch wide and set on end. The eighteen towers on our chart range from a ratio of 1:10 to an extraordinary 1:23 at 111 W. 57 Street.

 

Here’s a photo of the Empire State Building, in New York (which is not considered a slender building).  It has an elongation of perhaps 7 or 8 to 1, based on floor space, number of stories, and overall height.

It is hard to find a natural rock formation on Earth that comes anywhere near a 10 to 1 elongation.  Here’s the well-known Chimney Rock, in the U.S.A. (Nebraska).  It only looks to be about 4 to 1 elongation, on average, considering just the top spire.

So, if you observed Oumuamua from a spaceship, very close up (like the recent ESA mission to the comet), its shape might remind you of a skyscraper, and possibly an extremely skinny one (though if it looked too much like the Empire State Building, you might be running short of oxygen).  As far as we know, there is nothing like it in our solar system. 

The question is, what process made such an unusual object (see my earlier Oumuamua blog for more on that).  I guess that’s the question on Russian billionaire Yuri Milner’s mind as well.

Sources:

Nature letter

doi:10.1038/nature25020

A brief visit from a red and extremely elongated interstellar asteroid

Karen J. Meech, Robert Weryk, Marco Micheli, Jan T. Kleyna, Olivier R. Hainaut, Robert Jedicke, Richard J. Wainscoat,Kenneth C. Chambers, Jacqueline V. Keane, Andreea Petric, Larry Denneau, Eugene Magnier, Travis Berger, Mark E. Huber, Heather Flewelling, Chris Waters, Eva Schunova-Lilly & Serge Chastel

http://www.bbc.com/news/science-environment-42329244

http://skyscraper.org/EXHIBITIONS/TEN_TOPS/slender.php

http://dodecahedronbooks.blogspot.ca/2017/11/an-interstellar-oddity-oumuamua-1i2017.html

Google Images

Astrophysical Journal Letters (submitted): Interstellar Interloper 1I/2017 U1: Observations from the NOT and WIYN Telescopes, David Jewitt,Jane Luu, Jayadev Rajagopal, Ralf Kotulla, Susan Ridgway, Wilson Liu and Thomas Augusteijn

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Now that you have read about a real interstellar interloper (natural or not), you should consider reading some Science Fiction.  How about a short story, also about interstellar interlopers.  It also features one possible scenario to explain why we haven’t met ET yet (as far as we know, anyway).  Only 99 cents on Amazon.

Oh, and it has dogs.  Everyone loves dogs, don’t they?

The Zoo Hypothesis or The News of the World: A Science Fiction Story

In the field known as Astrobiology, there is a research program called SETI, The Search for Extraterrestrial Intelligence.  At the heart of SETI, there is a mystery known as The Great Silence, or The Fermi Paradox, named after the famous physicist Enrico Fermi.  Essentially, he asked “If they exist, where are they?”.

Some quite cogent arguments maintain that if there was extraterrestrial intelligence, they should have visited the Earth by now. This story, a bit tongue in cheek, gives a fictional account of one explanation for The Great Silence, known as The Zoo Hypothesis.  Are we a protected species, in a Cosmic Zoo?  If so, how did this come about?  Read on, for one possible solution to The Fermi Paradox.

The short story is about 6300 words, or about half an hour at typical reading speeds.  It will set you back 99 cents, unless it is free, which it occasionally is.

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The Constellation Cygnus Photographed with an iPhone 7

The Constellation Cygnus Photographed with an iPhone 7 – October 2017

The Summer Triangle

I took a few photos of the well-known asterism, The Summer Triangle, on a recent very clear October evening, with my iPhone 7 camera.  The Summer Triangle is easy to make out, once you are familiar with it and have a rough idea of where to look – it really does form a nice triangle of bright stars in the southern sky (as seen in the Northern Hemisphere), very prominent in the evening sky in the summer.

Constellations versus Asterisms

I did a blog on that asterism earlier – now I am focusing on a major constellation connected to The Summer Triangle, namely the constellation Cygnus, also known as The Swan.  But first, a few comments on asterisms versus constellations:

·        As many people know, the Summer Triangle is an asterism, rather than an official constellation.  An asterism is a collection of stars that paint a picture in the sky, via connecting the dots, a picture which is pretty easy for most people to recognize.  Some well-known examples of asterisms are:

• The Summer Triangle.
• The Big Dipper (in the constellation Ursa Major).
• The Northern Cross (in the constellation Cygnus).
•  The Tea Pot or Tea Kettle (in the constellation Sagittarius).  

A constellation, on the other hand, is an officially designated “piece of the sky”, as recognized by the International Astronomical Association.  It has definite boundaries, and any astronomical body can be associated with a particular constellation.  So, it is said, for example, that a star or nebula is “in” a particular constellation (e.g. Deneb is in Cygnus), if it is in the part of the sky that is assigned that constellation name.

·        That can be confusing, as there are cases where an asterism has the same name as a constellation.  For example, Leo is informally an asterism of a handful of stars that look somewhat like a lion, but it is also the name of a constellation that includes those stars, and a whole lot more.

·        Also, twelve of the constellations are also signs of the zodiac, which are familiar to people from reading horoscopes in the newspaper.  I should note that astronomy and astrology are entirely different matters, though they do share some history and content.

Cygnus the Swan - 2017 iPhone 7 photo.

So Cygnus is a constellation, which is connected to the asterism The Summer Triangle, as they share the very bright star Deneb.  Within Cygnus is another asterism, known as The Northern Cross or The Swan.

Here’s the iPhone image of Cygnus, with a little labelling and photo enhancement in GIMP. I also drew in the imaginary lines that make up the Swan or the Northern Cross,  You can imagine The Swan, with its long neck, flying down the picture, through The Summer Triangle. Alternatively, you can imagine a cross, known as The Northern Cross - whether or not to give it a religious connotation is up to you.  By the way, there is also a Southern Cross, but you have to go pretty far south to see it (it is featured on the Australian flag).

I also included a screen capture from the astronomy program Stellarium, to show how Cygnus relates to the Summer Triangle.  As you can see, the iPhone picked up most of the major stars of The Swan.  Eta seems to be somewhat out of place – it is possible that is not actually Eta – it could be a “hot pixel” that happens to be about the right brightness and position to be mistaken for Eta.

Here’s another picture, with and without the lines connecting the stars of the Swan.

Here’s an inverted image (black and white interchanged).  Sometimes that format can be easier to decipher.

Some Features of Cygnus

I will use Wiki’s article, to give a brief overview of some of the interesting facts about Cygnus:

• There are multiple occurrences of swans in Greek mythology (the source of most star lore in the western world).  The most famous is probably the subject of Yeats’ famous poem “Leda and the Swan”.  Short story – the god Zeus pretends to be a swan, who impregnates the Spartan Queen Leda, which results in the birth of the beautiful Helen, who is later kidnapped, which leads to the Trojan War.  It is not clear whether the constellation is actually connected with this story, but it is a difficult story to ignore (many constellations are definitely connected to Greek myths, though).

• The brightest star is Deneb (also known as Alpha Cygni). It is a white super giant, located some 3200 light years from Earth.  It is a huge A-class star, extremely luminous, which is why it is so easy to see from Earth even though it is a kilo-parsec distant.  Deneb means tail in Arabic – i.e. the tail of the Swan

• Gamma Cygni is a yellow super giant, also very distant at about 1500 light years.  It is also known as Sadr, which is Arabic for breast – i.e. the breast of the Swan.

• Delta and Eplison make up the wings of the Swan.  They are both fairly close to Earth, about 170 and 70 light years, respectively.

• Alberio or Beta Cigni is a beautiful binary star, with amazing colours (see below).  It is easy to see in a small to mid-sized telescope, and always a pleasing sight, with contrasting colours for the two stars, orange and blue-green.  It is a great object for newcomers to telescopes, as it is easy to find and impressively beautiful.  That system is about 380 light years from Earth.

• Cygnus X-1 is a very notable X-ray source, one of the brightest such sources in the sky.  It is the first object to be considered a black hole.

• There are scads of exoplanets in Cygnus, as the Kepler orbiting telescope focused much of its time on that constellation, during its search for extra-solar planets.

• Generally speaking, it is a region of rich star fields, as one is looking towards the center of the galaxy when looking in the direction of Cygnus.  Thus, there are many open star clusters and nebulae in Cygnus.

 

Astrophotography with an iPhone

So, why blog about astrophotography with an iPhone when there are so many great cameras and telescopes out there, suitable for amazing amateur photographs?  Several reasons, actually:

• It is easy to take pictures with an iPhone. That means it is quick and you don’t have to freeze in the cold, especially in my part of the world.

• It is fascinating to see just what a “simple” camera like an iPhone (or iPad) can do, these days, especially with a bit of post processing of the images.

• The iPhone sees pretty much what the human eye sees in the light polluted city, so it works well as an educational tool.  Long exposure astrophotography is great, but the images don’t look much like the actual sky does, for a typical viewer.

•  So, it is  a nice tool for introducing people to the brightest stars in the sky.  And, given how ignorant most modern people are of the sky, that seems like a good thing to do.

• It is good practice with Gimp or Photoshop.

• It makes for a relatively easy blog, and that is a lead-in to selling books, as you can see below.

• Though, as any blogger will tell you, the conversion rate from blog reader to book purchaser is exceedingly low.  Nonetheless, we live in hope.

Sources

• https://en.wikipedia.org/wiki/Cygnus_(constellation)

• Alberio photo: Albireo A and B (Hunter Wilson), Wikipedia

• Sky and Telescope, via Google Images

• Stellarium computer program (open source)
  

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Now that you have read some real science (astronomy and astrophysics), you should read some science fiction.  Since the blog mentioned Star Trek, here’s one with some Star Trek references (implied).

“The Zoo Hypothesis”, an Alien Invasion Story

Here’s a story giving a possible scenario for the so-called Zoo Hypothesis, known in Star Trek lore as the Prime Directive.  It’s an explanation sometimes given to account for a mystery in the Search for Intelligent Life, known as The Great Silence, or Fermi’s Paradox.

Basically, Enrico Fermi argued (quite convincingly, to many observers), that there had been ample time for an alien intelligence to colonize the galaxy since its formation, so where are they?  The Zoo Hypotheses says that they are out there, but have cordoned off the Earth from contact, until we are sufficiently evolved or culturally advanced to handle the impact of alien contact.

This story takes a humorous tongue in cheek approach to that explanation.  It also features dogs and sly references to Star Trek.  Talk about man’s Best Friend.

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