Size Scales of the Universe at Home

In the Hayden Planetarium at the American Museum of Natural History in New York City is an exhibit called Scales of the Universe. The exhibit consists of a series of models that, combined with the "Hayden Sphere" that contains the planetarium theatre and dominates the room, show the relative sizes of objects of all sizes. For example, in this picture a model of the Hayden Sphere reflects how small it would have to be if Meteor Crater in Arizona were reduced to the size of the real Hayden Sphere (which is out of view to the right):

Hayden Sphere relative to Meteor Crater

"If the Hayden Sphere is the size of Meteor Crater,

then this model is the relative size of the Hayden Sphere."

To the left you can see a small scale model of Meteor Crater, and behind it, a model of Saturn's moon Janus. The Meteor Crater model shows how small Meteor Crater would be if Janus were the size of the Hayden Sphere; the Janus model shows how small Janus would be if the Earth were the size of the Hayden Sphere; and so on.

I like these sorts of things and decided it would be great to make a set of models of my own.

My models clearly had to be smaller than those in the public exhibit, for ease of construction as well as for storage. I also wanted to avoid having to find a huge object to use in place of the Hayden Sphere, so I decided to use the room itself as a substitute for the Hayden Sphere. This provides three advantages:

• The "exhibit" can be moved to any room of nearly the same size, and still work.

• No need to transport, assemble and/or inflate a large object.

• The viewer can hold the small model in the center of the room, to easily visualize its relative position within the larger object represented by the size of the room. This is particularly relevant for the astronomical scales, such as the place of the inner Solar System in relation to the Scatted Disc.

The room I used for this project is a bedroom in a three-family home in Cambridge, MA. It is a square room of about 11 feet, which is a fairly typical size for rooms found in most homes and apartments in the United States. The ceiling is far too low for the room to be a cube — although that would improve the exhibit a bit, it is not essential.

In the Hayden exhibit, most of the models are about 100 to 200 times smaller than the Hayden Sphere (about 25 to 50 cm). The models represent a sequence of objects of progressively smaller size: observable universe, Virgo supercluster, our Local Group of galaxies, Milky Way Galaxy (or its halo), the solar neighborhood of stars (250 LY across), the Oort Cloud, the Kuiper belt, Rigel (a supergiant star), the Sun, the Earth, Saturn's moon Janus, Meteor Crater in Arizona, Hayden sphere, a human brain, a raindrop, a red blood cell, a rhinovirus, a hydrogen atom, a proton, and a quark or electron.

I could have used the same sequence of steps for my models. Because my room is about 1/8 the size of the Hayden Sphere, all the models would be of a managable size to build. However, I made several changes which I consider to be improvements, as explained in the table:

Observable Universe

It is unknown how large the entire universe is in comparison to the observable universe.

There are different definitions of "observable universe". Generally it has the straightforward meaning "everything that can be observed" — which implies that distant objects are being seen in the past. By this definition, the "observable universe" would include an object like Q0906+6930, which appears to be 12.7 billion light years away, and which is therefore being seen as it existed 12.7 billion years ago. Q0906+6930 is moving away very fast, and so (with the tacit assumption that it still exists) it is now considerably further away.

If the (estimated) present position of all such objects is used, combined withour knowledge of the rate at which the universe's expansion is increasing, the present size of the observable universe works out to about 46.5 billion light-years in every direction, or 93 billion light-years "across".

It is known that there is much more to the universe beyond what is observed. In particular, the "cosmic background radiation" (radio waves left over from a very early point in the formation of the universe) are very uniform (have the same brightness everywhere in the sky). From this and other similar observations it is possible to show that an an earlier point in the Universe's history, Spacetime grew faster than light for a brief period, and this growth was so great that the entire universe is at least 10²³ times larger than the observable universe — and probably much larger even than that. For example, in [2] (page 12), Guth implies that "each second the number of universes that exist is multiplied" by approximately e¹⁰³⁷. If this has been happening for the entire 13.7-billion-year history of our universe, then there is 10¹⁰⁵⁴ times as much space beyond the limit of our visibility, also populated with matter, energy, galaxies, stars and planets.

Virgo supercluster

At a scale of 1/2.6×10²⁶, the Observable Universe would be the size of this room, and the Virgo supercluster would be the size of this model.

Local group of galaxies

At a scale of 1/5.78×10²³, the Virgo supercluster would be the size of this room, and the Local Group of galaxies would be the size of this model.

The Local Group includes everything that can be seen by the naked eye. The Andromeda galaxy is usually the farthest thing that can be seen with the naked eye. The Triangulum galaxy (M33, NGC 598) is a little further away and can also be seen by most observers, and with considerable effort M81 (at a distance of 12 million light years) can be seen by experts.

Small Magellanic Cloud

At a scale of 1/1.45×10²², the Local Group of galaxies would be the size of this room, and the Small Magellanic Cloud would be the size of this model.

The Small Magellanic Cloud is a nearby galaxy clearly visible to the naked eye to observers in the southern hemisphere. To the same scale, the Milky Way galaxy would be about 6.5 cm across.

Human radio bubble

At a scale of 1/2.83×10¹⁹, the Small Magellanic Cloud would be the size of this room, and the Human radio bubble would be the size of this model.

As depicted in the movie Contact (1997), there are radio broadcasts traveling away from Earth at the speed of light, which can (in theory) be detected by an extraterrestrial civilization. Earlier signals have had more time to travel, and form a spherical "shell" emanating from our solar system.

Although radio transmissions go back to around 1900, the size of the radio bubble used here is based on the beginning of regularly-scheduled high-power television broadcasts in the late 1940's.

Oort cloud

At a scale of 1/3.55×10¹⁷, the Human radio bubble would be the size of this room, and the Oort cloud would be the size of this model.

We know of the existence of the Oort cloud through deductive logic and observation of comets. Comets like Halley's only "last" a limited amount of time, before using up all their volatile material (ice) and becoming small asteroids. In order for there to be any comets now, "new" (unheated) ones must be coming in from some place.

The origin of the Oort cloud is explained by the Nice model, a computer model that also explains most of the other features of the Solar system. In this model, Neptune began in an orbit between Saturn and Uranus, and there were a much larger number of Pluto-like objects beyond Uranus. These objects gradually acquired elliptical orbits like that of Halley's comet through gravitational interactions with the large planets, causing the latter to drift outward in their orbits. When interacting with Jupiter, the small bodies were put into orbits that take them out to a very large aphelion (in the area called the Oort cloud) and remain there because their interaction with the other large planets cause the aphelion to grow as well.

Trough this process Jupiter srifted inward slightly, while the other three large planets drifted outwards, and Uranus and Neptune switched places.

Scattered disc and Kuiper belt

At a scale of 1/4.34×10¹⁵, the Oort cloud would be the size of this room, and the Scattered disc would be the size of this model.

The Scattered disc and Kuiper belt are only partly explained by the Nice model (described above under "Oort cloud"). In particular, the origin of the "cold" Kuiper objects (which have redder surfaces and were formed further from the Sun) is still poorly understood.

Two other classes of objects are explained by the Nice model: the "hot" Kuiper objects (which have grayer surfaces like the asteroids) probably formed at a distance near that of Jupiter and were pushed outwards. The scattered disc objects reached their current location by being in an orbital resonance with Neptune and gradually shifting outwards as Neptune drifted outwards.

The star Enif (in Pegasus)

At a scale of 1/8.67×10¹², the Scattered disc would be the size of this room, and the star Enif would be the size of this model.

The Sun

At a scale of 1/6.07×10¹⁰, Enif would be the size of this room, and the Sun would be the size of this model.

The Earth

At a scale of 1/4.02×10⁸, the Sun would be the size of this room, and the Earth would be the size of this model.

Metis (moon of Jupiter)

At a scale of 1/2,300,000, the Earth would be the size of this room, and Jupiter's moon Metis would be the size of this model.

The Vehicle Assembly Building

At a scale of 1/12,400, Metis would be the size of this room, and the Vehicle Assembly Building would be the size of this model.

This Room

At a scale of 1/51.2, the Vehicle Assembly Building would be the size of this room, and this room would be the size of this model.

A human pituitary gland

At a scale of 1 to 1, this room is its actual size, and a human pituitary gland is the size of this model.

A human egg cell, zygote, or morula

At a scale of 314×, a pituitary gland would be the size of this room, and a human egg cell would be the size of this model.

A staphylococcus bacterium

At a scale of 34,600×, a human egg cell would be the size of this room, and a staphylococcus bacterium would be the size of this model.

A hemoglobin molecule

At a scale of 5,770,000×, a staphylococcus bacterium would be the size of this room, and a hemoglobin molecule would be the size of this model.

A Hydrogen atom

At a scale of 577,000,000×, a hemoglobin molecule would be the size of this room, and a Hydrogen atom would be the size of this model.

A muonic Hydrogen atom

At a scale of 1.08×10¹¹×, a Hydrogen atom would be the size of this room, and a muonic Hydrogen atom would be the size of this model.

Muons are the most numerous cosmic-ray particles at sea level. Every minute, about 10⁴ muons arrive at every square meter of the Earth's surface. Typically the muon will penetrate a distance of over 1 kg/cm² (about 10 meters through water, less through denser material) before interacting with an atomic nucleus. Depending on your size, a muon interacts with an atom in your body about 500 to 1300 times per minute.

When the muon interacts with a nucleus, it begins to "orbit" the nucleus just as an electron would. Because of the muon's higher mass, its wavefunction (charge distribution) is correspondingly smaller. The muon thus spends nearly all its time at a distance about 200 times closer than an electron in the innermost "shell" of the atom. One of the atom's electrons is displaced by this process.

If the nucleus happens to be a Hydrogen nucleus, the result is a muonic Hydrogen atom, an atom that behaves just like a Hydrogen atom but is 207 times smaller. This atom lasts until the muon decays (its half-life of 2.2 microseconds) after which the muon produces a normal electron and two neutrinos. The two neutrinos leave without interacting with anything, and the atom returns to normal.

Given that your body is 10% Hydrogen by mass, there are about 50 to 130 times per minute when a muonic Hydrogen atom exists within your body.

A proton

At a scale of 2.23×10¹³×, a muonic Hydrogen atom would be the size of this room, and a proton would be the size of this model.

An electron or a quark

It is unknown how small an electron or a quark is in comparison to a proton.

Footnotes

1 : C. R. Nave, Inflationary Period (part of HyperPhysics database at Georgia State University)

Bibliography

[2] Alan H. Guth, Eternal inflation and its implications, 2^nd International Conference on Quantum Theories and Renormalization Group in Gravity and Cosmology (IRGAC2006), Barcelona, Spain, 11-15 July 2006.

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