Gravitas of Prefixes

By The Metric Maven

Recently I read the book Gravitational Waves by Brian Clegg in conjunction with attending a talk on the subject. Both were quite interesting and had their method of numerical presentation in common. During the presentation it was revealed that the distance of the source of the first gravitational wave detected was 1.8 Billion light years. “Is this a lot?”—as my friend Dr. Sunshine likes to ask when putting numbers in context. I immediately wanted to know the distance with a metric prefix. If it is in Exameters, then it would be inside of our galaxy. Our galaxy is about 1000 Exameters or a Zettameter. I did not stop to estimate the values as I wanted to listen to the presentation.

First we have an Olde English prefix with a ersatz “unit” called the light year. 1.8 billion of them is 1.8 Giga units, and the light year unit is 9.4607 Petameters. We end up with  1.8 * 9.4 x 109 * 1015 = 16.92 x 1024  or about 17 Yottameters. Wow! the observable universe is about 880 Yottameters, can this possibly be right? It seems very large, just based on the metric prefix. I go to Wikipedia to see if I can verify this number. They currently quote it as 1.4 +/- 0.6 billion light years. It’s a bit less, but same magnitude. They also state it is 440 Megaparsecs. A parsec is about 31 Petameters, so we have 440*31 x 106 * 1015  or 13.64 Yottameters! I’m immediately able to  grasp the size of this number in metric, and it seems astonishing.

Assuming I haven’t made a mistake, what are the detection distances in ascending order of the gravitational wave observations to date?

GW170817 2017-08-17         1.24 Ym

GW170608 2017-06-08       10.54 Ym

GW150914 2015-09-14       13.64 Ym

GW151226 2015-12-26       13.64 Ym

GW170814 2017-08-14       16.74 Ym

GW170104 2017-01-04        27.28 Ym

This is a rather amazing list to me. They are all further out than I would have expected gravitational waves to be detected. There is an unconfirmed observation that occurred at 31 Ym. This gives me some idea of the approximate detection limit for the current version of LIGO. This list gives you metric units that allow you to compare the distances to the size of the observable universe. As our Milky Way Galaxy is about 1 Zettameter across, we could write the list in a way that allows us to use our galaxy as a measurement touchstone:

GW170817 2017-08-17        1 240 Zm

GW170608 2017-06-08       10 540 Zm

GW150914 2015-09-14       13 640 Zm

GW151226 2015-12-26       13 640 Zm

GW170814 2017-08-14       16 740 Zm

GW170104 2017-01-04       27 280 Zm

That is a lot of galactic lengths from us. According to Brian Clegg, it is expected that around 2020 a LIGO upgrade has the potential to increase the detection distance by about a factor of three. If my estimate is right, this will be about 75 Yottameters. The detection volume will increase by 30 %. A set of enhancements scheduled for implementation from now to 2026 (LIGO A+) are expected to double the sensitivity distance again. So if my estimate is good, it would be out to 150 Yottameters! With this sensitivity, several black hole mergers per hour are expected to be detected.

There are discussions of a 40 Kilometer long LIGO receiver in space called the Cosmic Explorer. This is expected to increase the volume of sensitivity to black hole merger detection to cover the entire 880 Yottameter extent of the visible Universe. That would be amazing.

Why stop there? Brian Clegg discusses a concept known as LISA (Laser Interferometer Space Antenna). The arms of the interferometer would be formed between three satellites in a triangular configuration with 2.5 Gigameter sides!  LISA would orbit the Sun following along Earth’s orbit at a distance of about 50 to 65 Gigameters! Wow that seems just really big. Below is an animated GIF of the LISA satellite array orbit.

LISA Motion — Wikimedia Commons

In Brian Clegg’s words:

Unlike a ground-based observatory such as LIGO, LISA would have the chance to take in the whole of the sky. Rather than orbit the Earth as most satellites do, LISA is planned to be  in an orbit around the Sun, following the Earth’s path at a distance of between 50 and 65 million kilometres, about a quarter again the distance at which the Moon orbits. (pg 142)

Did I compute this distance wrong? 65 * 106 * 103 meters = 65 Gigameters. The distance from the Earth to Venus is about 42 Gm unless I’m mistaken. The length of the arc the Earth travels around the Sun is about 940 Gm. This is about one-fifteenth the distance arc length of the orbit. The animated gif above seems consistent with this value.

The distance from the Earth to the Moon is 384 402 Km or 384 Megameters. 1.25 multiplied by this number is 480 Megameters. The number is not even in the right metric prefix “area code.” The Olde English prefixes when used with metric are a pigfish disaster. They provide no real magnitude distinction when concatenated with metric prefixes. I’m still concerned I’ve made a conversion error or misinterpreted Glegg’s prose.  He seems to be conflating a distance in Gigameters with one in Megameters. Perhaps the Megameter distance is the closest approach of each satellite.

Clegg discusses the history of LISA on Page 142-143:

LISA was originally a joint venture between the European Space Agency (ESA) and NASA, but in 2011, suffering severe funding restrictions, NASA pulled out. Initially, ESA looked likely to go for a scaled-down version, known as the New Gravitational Wave Observatory, but with a renewed interest in gravitational waves after the LIGO discoveries, in early 2017 a revamped version of LISA, now featuring 2.5-million-kilometre beams, was proposed at the time, was proposed and at the time of writing has just been accepted for funding. This followed the test launch in 2015 of the LISA Pathfinder, as single satellite with tiny 38-centimetre (15 inch) interferometer arms……

He uses the pseudo-inch known as the centimeter with conversion to barleycorn inches next to it to express the tiny arm length. Would writing 380 mm arms killed him?

I don’t want my readers to get the wrong impression. I like Brian Clegg’s book. It is well worth reading if you are interested in gravitational waves. (I recommended it to the audience at the talk I attended) Its pigfish metric usage is common in science writing. He is doing what essentially all other contemporary science writers do. Astronomers only offer the same manner of visceral push-back at using metric units that citizens of the US exhibit. For those of you who might be interested in metric astronomy, I recommend my essay Long Distance Voyager.

On page 58-59 Clegg explains the density of a neutron star thus:

But a neutron star consists only of neutrons. With no electrical charge to repel each other, these particles can be pulled closer and closer by gravity until the exclusion principle kicks in when they’re practically on top of one another, enabling that great mass to be squeezed into a ridiculously small space. The result is that a teaspoonful of neutron star material would weigh about 100 million tonnes.

Once again an Olde English prefix (million) and a retro Olde English “metric” value tonne serve to obscure as much as impress. When the Olde English prefix is converted to metric and the tonne converted to metric we have a MegaMegagram or Teragram! Wow 100 Teragrams! The total mass of humanity is about 423 Teragrams, so about 65 mL of neutron star would contain the mass of all the humans on Earth. If you cup both of your hands together side-by-side, they would easily contain all of humanity at this density.

The future of gravitational wave astronomy is bright, it would be brighter if it was expressed exclusively with the metric system.

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The Ephemeral Search for The Real Planet 9

By The Metric Maven

This last Summer I visited Lowell Observatory in Flagstaff Arizona. I saw the telescope where Percival Lowell (1855-1916) convinced himself he saw canals on Mars. In science one can easily fall in love with a hypothesis and begin to see what you expect to see. After the Martian canals had been vanquished, and Perceval Lowell had passed away, a young Astronomer by the name of Clyde Tombaugh (1906-1997) took up his search for a ninth planet. Tombaugh painstakingly photographed the night sky and miraculously discovered a new planet (expected to be at least Earth-sized) in the expected area of the sky predicted in February of 1930. The amazing part, is how lucky Tombaugh had been. Pluto has a 17 degree tilt upward from the ecliptic, which means its not in the plane of the other planets—where one would expect to find it. Pluto was in a location where it was very close to the ecliptic—a rare occurrence. With an orbital period of 280 years, if Pluto had been in its farthest part of its orbit, Tombaugh would have gazed into empty space. In many ways he won a cosmic lottery ticket. The new planet  became known as Pluto and as PL is also the initials of Percival Lowell, it was greeted with open arms at Lowell Observatory. All was fine until a team, lead by Mike Brown (1965- ) at Cal Tech, located Eris which is much farther out from the Sun than Pluto, and appeared to be larger than Pluto, was, for a while, considered Planet 10, with Pluto still designated as Planet 9.

Better measurements slowly reduced the mass, size and mathematical need for Pluto to provide an explanation of the now nonexistent gravitational perturbations. As we all know now, Pluto is at best considered a dwarf planet in the Kuiper Belt. After Pluto’s change in categorization, it stopped being the last planet discovered, and became the first Kuiper Belt object discovered. Planet 9 then vanished in an organizational puff of smoke. The description of our solar system from the Sun to the hypothetical Ort Cloud looked quite fixed at that point. In 2010, astronomer Mike Brown wrote a book titled How I killed Pluto and Why It Had It Coming. He had been at the forefront of Pluto’s nomenclatureral demise. Then in January of 2016, he and Konstantin Batygin (1986- ),  would ironically propose the existence of a new planet, based on orbital perturbations,  the same type of evidence that began the search for Pluto by Tombaugh.

The new non-Pluto Planet 9 begins its theoretical existence with a large mass of 60 000 Yottagrams, and an orbital distance that varies from 30 000 Gigameters to 180 000 Gigameters. It has a semi-major axis of about 105 000 Gigameters. Gigameter is the natural  metric unit for describing the distances of planets in a solar system. Planet 9 is estimated to take about 10 000 to 20 000 years for a single orbit around the sun. Uranus, at 87 000 Yottagrams, is slightly more massive than the hypothetical Planet 9.

In June of 2017, Kat Volk, and Renu Malhotra, both from the University of Arizona, announced that computations they undertook indicate that a 10th planet exists. They estimate it is about 9000 Gigameters from the Sun and possesses a mass about that of Mars. Again, unexpected gravitational perturbations led researchers to suspect the existence of another planet, other than Planet 9.

In order to compare the two newly hypothesized planets, with our existing list of Planets, Kuiper Belt objects, and human created spacecraft; I have updated a table given in my essay Long Distance Voyager (about metric distances and the universe) which is presented below:

The first change I noticed is that if Planet 9 exists, Voyager 1 and Voyager 2 would no longer be “outside our solar system.” So are the Voyager Spacecraft still in interstellar space, or do we redefine them as inside our solar system? Categorization can be a difficult objective for astronomy, but where the Voyager spacecraft are, will probably not stir up the controversy that Pluto did when Eris was discovered. Eris is appropriately named for the Greek goddess of Strife and discord. The other categorization problem is that Planet 10 is well inside the orbit of Planet 9, so one would think they should swap numbers so Planet 10 is the furthest out and Planet 9 the next planet toward the Sun. Planet 10 also finds itself outside of the Kuiper Belt, and is probably a Trans-Neptunian planet, although how meaningful this designation would be remains to be seen. Planet 10 is between Pluto and Eris, and Planet 9 is the farthest hypothetical planet out by about an order of magnitude compared to Planet 10.

In many cases, astronomical masses outstrip the metric system, and one must resort to scientific notation, but in the case of our solar system, it might be useful to express the values using a large metric prefix. We will use Yottagrams, as that is the last magnifying metric prefix. Below is a table of Planetary Mass for selected objects in our solar system.

It is clear that Jupiter dominates the mass total of our solar system. One can estimate immediately that Jupiter is somewhere on the order of three times the mass of
the next most massive planet Saturn. Mercury, the smallest planet, is well over an order of magnitude more massive than Pluto or Eris. Pluto and Eris are an order of magnitude larger than Ceres the largest asteroid in the Asteroid Belt. It is clear that Jupiter, Saturn, Uranus, and Neptune form a Gas Giant mass class that is separate, and dominates all the other planets. The new Planet 9, should it exist, would be the runt member of this fraternity–unless it is not a Gas Giant, we then might need to implement a new designation from boxing and call them the Heavymass planets. The new Planet 10 would currently be grouped with the current Rocky planets, but from a distance perspective it would be the only member of this designation outside of the classical distance grouping of the inner and outer planets that are bounded on either side by the Asteroid Belt. Perhaps the less massive rocky planets could be called the Lightmass rocky planets, unless Planet 10 is gaseous? Whatever the Astronomical Union decides, the metric system is there for them, whether they use it, or not.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page.

Related Essays:

Long Distance Voyager

The Expanding Universe

 


The Metric Maven has published a book titled The Dimensions of The Cosmos. It examines the basic quantities of the world from yocto to Yotta with a mixture of scientific anecdotes and may be purchased here.

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