Starry Eyed Dimensions

By The Metric Maven

Bulldog Edition

My friend Dr Sunshine is very good at expressing and interpreting numbers. He has a favorite example from Star Trek IV: The Voyage Home (1986) that he uses to illustrate numerical importance:

Spock: [in response to Kirk pawning his antique spectacles from Wrath of Khan] Excuse me, Admiral. But weren’t those a birthday gift from Dr. McCoy?

Kirk: And they will be again, that’s the beauty of it.

[to Antique Store Owner]

Kirk: How much?

Antique Store Owner: Well, they’d be worth more if the lenses were intact. I’ll give you one hundred dollars for them.

Kirk: …Is that a lot?

Recently the farthest star ever viewed by a telescope was sighted. Phil Plait, Bad Astronomer, and worse metric user, attempted to impress his audience by saying:

This is incredible: Due to a quirk of cosmic geometry, astronomers have detected the light from the farthest individual star ever seen. How far away is it?

Over nine billion light-years away.

Yes, you read that right. Nine. Billion. Light-years.

A single star, from that distance. Holy yikes. Seriously, when I read about this the hairs on the back of my neck stood up. This is seriously amazing, so much so that for a moment I couldn’t believe it was real. Then I read the paper, played with the math a little, and, sure enough, this appears legit.

I was immediately uncertain just how far away this star is. A billion light years?—is that a lot? In my essay Long Distance Voyager, I use metric prefixes to categorize different astronomical items:

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I define nearby stars as those measured in Petameters (1015), and far away when measured with Exameters (1018). Long ago it stuck in my brain that the observable universe has a dimension that is in Yottameters (1024). So just how big is 9 billion light years? Well, knowing that a light-year is 9.4607 Petameters we multiply this by 9 billion (Giga-) and obtain 85 Yottameters! Wow, that is big. The farthest detected galaxy is about 126 Yottameters, and the diameter of the observable universe is about 880 Yottameters! This is one serious Yottasurprise. We can see two metric triads farther than the metric definition of far away stars! How on Earth, or actually how in the universe, did this happen?

Well, it is an interesting coincidence that allowed it. The star would normally be too faint to see, but a cluster of galaxies between the star and ourselves acts as a gravitational lens, which concentrates the light from that star enough for us to see it. Not only can we see it, the star has been identified as a blue supergiant, which is one of the brightest type of stars known. Rigel in the Orion constellation (lower right star) is a blue supergiant, but is at a distance of only about 8 Exameters from us. Deneb is 24 Exameters from us. One of the farthest stars ever seen is UDF 2457, which is 558 Exameters away; whereas the just discovered Lensed Star 1 (LS1) is 85 000 000 Exameters distant. The human eye can only detect a minute number of stars which are only about 10 Exameters from us, beyond that, individual stars fade into the blackness, hidden from our unaided gaze. Galileo was amazed at the number of normally invisible stars that his telescope allowed him to suddenly see. Keep in mind that our Galaxy is only about 1000 Exameters across, all the stars you see with your eyes are essentially local.

Einstein asserted that a large mass literally warps space. The closer one is to the large mass, the larger the amount of warping. On May 29, 1919, a group led by Arthur Eddington (1882-1944) and Frank Dyson (1868-1939) took a photograph during a total solar eclipse. Stars near the Sun changed their position with respect to stars further away. When images of the stars, taken when the Sun was absent, was placed over one taken by Eddington’s group during the eclipse, stars near the Sun were seen to be in a different position than those radially further away, and therefore less influenced by the Sun’s gravity. This bending of light has important uses in astronomy. When searching for planets that might have been ejected from their home solar systems into space, astronomers watch for a light-warped signature that a planet produces when passing in front of a star. In the case of LS1, lensing distortion occurs as it orbits around the center of the galaxy where it resides. The location of the individual galaxies that make up the “lensing cluster” are not homogeneous which also introduce undesired aberration.

The cluster of galaxies happen to be located in positions that add together (most of the time) in a way to capture and concentrate the light from this single star, and allow us to see an extra two metric triads (1 000 000) further in distance than is normally possible. Is that alot?—YES!

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Postscript: On 2017-08-24 Bad Astronomy posted an essay titled: A 500 TRILLION KM LONG STREAMER OF AMMONIA IN ORION. Is that a lot? Well, 500 Trillion Km is 500 Petameters, or a length that encompasses a distance to nearby stars in our own galaxy. When one uses Ye Olde English Prefixes with metric, it’s not even pigfish, it’s just fishy.

Context and Units

By The Metric Maven

Bulldog Edition

The late Isaac Asimov once pointed out that people often use units alone to imply the magnitude of a dimension. A certain store is only minutes from your house, or a car missed another by inches and so on. Of course if the two cars were separated by 63 360 inches, they then also missed each other “by a mile.” The statement that two cars were separated by only inches as they passed each other is true, but they were not in any danger of colliding.  Using a unit without any numerical magnitude leaves one to comfortably assume a magnitude,  and trust that the person offering said unit is using it appropriately.

Years ago my father sent away for a set of cookware. The price was too good to be true, and the items that arrived were all about 25% of their expected size. I watched a consumer  advocate expose this rip-off on television. The advocate showed that using the cookware was not feasible and in one case the handle would become so hot it would burn anyone who simply used it to boil water. Many moons ago, it was apocryphally claimed that a raffle was held where the winner would get a sports car, such as a Corvette, as a prize. The winner did indeed receive a Corvette, but it was a  scale model worth only a few tens of dollars.

When really large numbers are expressed, such as those in astronomy, one generally ends up with concatenated pigfish such as billions of Kilometers. There are many examples of people who decide to use these large Olde English prefixes with incredibly small “everyday” units, in an attempt, I assume, to make the number something to which the average Jane and Joe can “relate.” As I’ve said before, large numbers are almost impossible to visualize, but with the metric system, their magnitudes can be categorized and metric worlds imagined.

I might ask, as a bit of a trivia question, if the Starship Enterprise, in the original Star Trek series, ever made a voyage that was more than a Zettameter? The answer is, probably yes, but not by much. The maximum extent of the Milky Way Galaxy is about 1000 Exameters or 1 Zettameter. TOS episode #51, titled By Any Other Name, has the Enterprise taken over by beings from the Andromeda Galaxy. The aliens were in the Milky Way looking for planets worth taking over or conquering. Their ship was destroyed and so the aliens duped the Enterprise crew into stopping by and then took over their ship. The alien beings, called Kelvans, modify the Enterprise so that it will only take 300 years to reach their place of origin. The distance to Andromeda is given in Wikipedia as about 2.5 million light-years. The use of light-years is bad enough, but using a Ye Olde English prefix modifier really helps to obscure the distance value. The distance, when written out, is 2 500 000 light-years which does not really help that much. We can calculate the Kelvans would be traveling about 8333 times the speed of light to reach Andromeda in “only” years—ok—300 years. How far is Andromeda from us? Well, in metric it’s about 23.7 Zettameters. The Andromeda Galaxy is about 220 000 light-years across, or about 2.1 Zettameters (2081 Exameters).

With our galaxy about 1 Zettameter in extent, we immediately see that Andromeda is about twice the size of our galaxy. The distance from us to Andromeda is about 24 times the extent of our Galaxy. Now that is rather close—and it’s getting closer—in fact it’s going to “collide” with The Milky Way in the future. But it’s only coming at us at the anemic rate of 600 Gigameters per hour. The distance from the Sun to Jupiter is 778 Gm. At this rate, it will “crash into us”  in about 4.5 billion years. Andromeda’s yearly rate of encroachment is a mere 5.25 Petameters, or 525 Petameters per century. A “light-year” is 9.46 Petameters, and therefore Andromeda is about 23 650 000 Petameters distant.  Andromeda is definitely taking its time getting here at its 5250 Petameters per 1000 year rate. When we use Zettameters  for galactic dimensions (or we could use Exameters and drop the decimal points) it is intuitive how far the two galaxies are separated, and their overall extent. Other appropriate prefixes provide clear context for a reader. Milliards and Milliards doesn’t cut it for astronomy.

We can never voyage more than 1000 Exameters (1 Zettameter) and remain within our galaxy. One could argue that when the Enterprise is on an imaginary voyage only Petameters in distance, it’s a nearby journey, and a voyage measured in Exameters, is a far away journey. Beyond 1000 Exameters, we are outside of our “Island Universe.”  Once again, we could be faced with a lack of magnitude causing confusion. If we accept as proper practice, that one does not go beyond 1000 for each metric prefix, when informally discussing magnitudes, we would expect that a 1 000 000 Petameter journey, would not be considered a “Petameter Voyage.” If we discovered otherwise, we would consider this an exaggeration, or in some cases even fraud.

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Zettameters and Exameters are not just for galaxies, there are other instances in astronomy where they can effectively be used. The May 2016 issue of Astronomy has an article[1] that discusses hourglass shaped lobes that extend for 25 000 light-years either side of our galaxy. Well, just how big are these lobes? A light year is 9.46 Petameters, and they extend about 240 Exameters above and below our galactic disc, with a maximum extent of about 500 Exameters (approximately half the maximum length of our galaxy). These structures are currently known as Fermi Bubbles. They could possibly be jets of material ejected by supermassive black holes found at the center of many galaxies, including our own. The Exameter sized bubble is composed of silicon and carbon atoms.

Recently, Astronomers have located unusual radio bursts “from beyond our galaxy.” These signals are called Fast Radio Bursts (FRB), and one of them, FRB 121102 is located in dwarf galaxy, dimmer than our own, over three billion light years away. But just how far is that?  It’s about 28 Yottameters! Remember our Universe has a diameter
of about 880 Yottameters. 28 Ym is a long way from Kansas.

The metric system is so well-suited for taming and categorizing astronomical distances, it’s a shame Astronomers refuse to use it in their work without Ye Olde English
prefixes, and generally after a light-year value has been alternatively presented. Perhaps Grade School and High School teachers could adopt the use of metric when expressing astronomical distances, and their students in turn might eventually become astronomers, and question why an infinitesimal yardstick the size of a light-year is used to measure the entire Universe. If you are an instructor, and have read this essay, please consider doing so.

[1] Kruesi, Liz “What’s Blowing Bubbles in The Milky Way?” Astronomy May 2016, pp 44-49.

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Related essays:

Long Distance Voyager

The “Best Possible Unit Bar None”