# A Sense of Scale

We are going to build a scale model of the Universe, is that possible?
Tags Astronomy, Solar System, Sun, Planets, Stars, Milky Way, spiral arms, Galaxies, Local Group, Void, Filaments, Virgo Super Cluster, galaxy clusters, structure Universe, observable Universe, scale, scale model, distance, speed of light, light year,
Prerequisites
Author(s) EV
First Published May 2008
This Edition - 3.0 June 2017

## Introduction

Is there a way that we can visualise the true scale of the Universe?
In books and on the internet you can find many pictures, diagrams and even photos of groups of celestial objects.
But inevitably, these cannot be true to scale as regards both distances and size of objects.

Photo: Nicole Emanuel When we think about this problem and do some calculations, we do not only become once again impressed by the enormous size of the Universe and even small parts of it like our Solar System, but also realise that space is almost empty, because the objects are so very small in comparison with the distances between them.

In this module we attempt to give a realistic idea about the scale of the Universe and parts thereof, and will show that ultimately, a real sense of scale of the Universe is beyond our comprehension.

Many of the diagrams used in this module are obtained from the great web site Atlas of the Universe. We are very grateful for this excellent material and recommend our readers to visit that web site for much more (click logo).

## The Solar System

Remember our discussion about the scale of the Solar System? (see our EBook "Solar System").
We noticed how difficult it is to get a true sense of distances as compared to the sizes of Sun, planets and moons, and that it isn’t possible to build a scale model within a normal building that is true to scale in both distance and size.

The picture at left shows the Sun and planets to the same scale as regards size, not their distance. Is it possible to draw a picture of the Solar system where both and size and distance are at the same scale?

In our Observatory we have a wall space of about 5 metre length available to build a scale model of the Solar System. This needs to show at least the distances of the eight planets from the Sun at the true scale.

We calculated that if Neptune would have to fit within the 5 metre, the Sun would have a diameter of 1.4 mm. We used an ordinary pinhead of about that size. We realised that the Sun is the only visible object at this scale, and that Neptune, the furthest planet, is 4.5 metre away from the Sun. See the table below for details.

Scale Model Solar System
Actual (km)Scaled (mm)
ObjectDiameterDistance
from Sun
DiameterDistance
from Sun
Sun 1,392,000 - 1.4 -
Mercury 4,853 57,950,000 0.005 58
Venus 12,132 108,110,000 0.012 108
Earth 12,771 149,570,000 0.013 150
Mars 6,768 227,840,000 0.007 228
Jupiter 143,031 778,140,000 0.14 778
Saturn 120,683 1,427,000,000 0.12 1,427
Uranus 51,083 2,870,300,000 0.051 2,870
Neptune 49,550 4,499,900,000 0.050 4,500

What we have learned from this scale model?

The first four rocky planets are all very close to the Sun and the gas planets are, relatively speaking, very far away. Especially Uranus and Neptune are at a lonely distance.

The other thing that we have learned is that the planets are unimaginably small in comparison to their mutual distance. They are mere specks of dust at this scale. Just look at Neptune, a speck of only 0.05 mm orbiting a pinhead of 1.4 mm at a distance of 4.5 metre.

Hence the Solar System is a very empty place, in contrast to what is suggested on many diagrams of the Solar System.
The difficulty is to draw both distance and size to a scale so that you can see something.
You cannot build such a scale model of the Solar System inside a normal building.

The other thing we must realise is that the planets are never lined up all in a straght line away from the Sun. In reality each planet could be anywhere in the plane of the Solar System (the ecliptic). So in this scale model we have invisibly small planets that could be anywhere in a circle at the given distance from the pinhead. This really hits it home that the Solar System is a very empty place, and that pictures such as the one above are very unrealistic. In this picture Neptune would have to be at a distance of more than 400 metres from the Sun.

Actually, the Solar System extends all the way to the Oort Cloud, which is up to about half a light year from the Sun. In this scale model that is 4.7 km. So that is the real size of the Solar System at this scale, in which the Sun is the size of a pinhead.

Above we show another scale model that fits within the text area of this page. The Sun and planets are now even much smaller than in the previous model (see the details in the diagram). Even the Sun cannot be made visible at this scale,
but you can appreciate the true relative distances here.

In this EBook we are going to use this scale model in which our Sun is the size of a pinhead of 1.4 mm.
We will see how this scale model increases in size when we are leaving our Solar System, on a trip to the far reaches of the observable Universe.

## Make your own scale model of the Solar System

Maybe you have space in a hall or corridor that is much longer than the 4.5 metres we use.
Can you double that, or even more?

Alternatively, you can decide that Mercury must be e.g. 1 mm in diameter. Then calculate all the other dimensions of your scale model and see if you can fit it inside somewhere (or not). At least you will get a good idea about the true scale of the Solar System.

Use the values for size and distance in the table above.

Good luck!

## The Nearest Stars within 10 light years

When we go beyond the Solar System and continue to use the same scale model, the nearest star Prox. Centauri (together with its companions Alpha Centauri A and B), which are at a distance of 4.5 light years, is at 40 km from our pinhead.

Within a bubble of 10 light years there are about 30 neighbouring stars. This bubble in our scale model will have a radius of about 95 km. Notice that the size of our Sun is still 1.4 mm, Prox. Centauri is a lot smaller at 0.2 mm and the other stars ranging in size up to 2.8 mm (Procyon).

So in our scale model we merely have grains of sand for the stars at mutual distances in the order of 50 - 100 km. This gives an idea about how empty space really is.

How is that when we go further out?

 10 light years is 95 km in our scale model. So we have a bubble with a diameter of 190 km that contains about 30 stars at the size of a grain of sand. The average distance between these grains is about 60 km. Find a city or town at a distance of 95 km from where you are. You are in the centre of the bubble with this radius and there are only about 30 grains of sand in any direction within this bubble, representing the nearest stars. Just imagine this scale model of the immediate vicinity of our Sun.

## 250 light years

We increase the region to a radius of 250 light years. This contains the 1500 most luminous stars, most of which can be seen from Earth with the naked eye.

The total number of stars within this region is about 260,000. This region is only a tiny part of our galaxy.

In the diagram to the right individual stars have a size of about one pixel on your computer screen. If they would be plotted at the true scale of this diagram, individual stars would have a size of about one tenth of a millionth of a pixel!

 In our scale model this region has a radius of 2,370 km. In New Zealand that is the maximum North-South distance in the country, from Cape Reinga to the bottom of Stewart Island. Can you find a similar reference in your country? Note that this is only the radius of the bubble, so its diameter is twice as much. And this sphere contains about 260,000 grains of sand. These would fit in a 125 ml glass.

Photo: Alson Wong (edited)

The Hyades open cluster is about 150 light years away in the constellation Taurus. The bright red star is Aldebaran, which is a foreground star at a distance of 60 light years. In the bottom left we see the Pleiades open cluster at 440 light years, hence outside the range of the diagram above.
This is the view from the Southern Hemisphere.

## 5000 light years

We are now beginning to see some of the structure of our Milky Way galaxy. The Sun is located in the Orion Arm - a rather slim arm compared to the neighbouring Sagittarius Arm.

Several stars which are located deep within the Orion arm, are visible from Earth with the naked eye. The most notable group of stars are the main stars in the constellation of Orion. All of these stars are bright giants, thousands of times more luminous than the Sun.

There are about 600 million stars within 5000 light years from our Sun.

 This region has a radius in our scale model of 47,000 km, and it has 395 times the volume of planet Earth. The average distance between the grains of sand (stars) in this sphere is 45 km. 600 million grains of sand fit in a 300 litre bin. So far we have only covered a small part of our galaxy, but we are already far outside planet Earth with our scale model.

## The Milky Way, 100,000 light years

This map shows the full extent of the Milky Way galaxy - a spiral galaxy with at least two hundred billion stars. Our Sun is buried deep within the Orion Arm about 26,000 light years from the centre.

In our scale model the centre of the Milky Way lies at 236,000 km, which is about two-thirds on the way towards the Moon. The diameter of our galaxy is about 100,000 light years, corresponding in our scale model with a circle of 947,000 km, which is about 1.5 times the orbit of the Moon. See image below.

The size of the image to the left shows our scale model. The circle is the orbit of the Moon. The scale model of the Milky Way galaxy extends far beyond the Moon's orbit.

 So with stars at about the size of 1 mm, a scale model of the Milky Way galaxy is 1.5 times the size of the orbit of the Moon!

## Deceptive

Pictures like the ones on this page and the previous page are deceptive because it looks like the stars are densely packed in the galaxy. But note that in our scale model the stars still have the size of a grain of sand and are at a distance of about 50 km to their nearest neighbour.

These images and also photographs from galaxies (as above) do not have enough spatial (angular) resolution to show individual stars. We only see a blurred image in which one pixel of the image contains millions of stars.

## Satellite Dwarf Galaxies within 500,000 light years

There are several dwarf galaxies around the Milky Way, typically containing a few tens of millions of stars, which is not much when compared to the number of stars in the Milky Way itself.

These dwarf galaxies are all gravitationally bound to the Milky Way.

In this region with a radius of 500,000 light years, there are 13 galaxies, one large one - the Milky Way - and 12 dwarfs. The number of stars within this region is estimated at 225 billion.

 In our scale model the radius of this region corresponds to 4.7 million km. The Large Magellanic Cloud is in reality 160,000 light years away. This corresponds in our scale model with a distance of 1.5 million km. That is 5 times the distance to the Moon. What kind of scale model is that?

Photo: Akira Fujii, Sky and Telescope

The Large and Small Magellanic Clouds are visible
with the naked eye from the Southern Hemisphere.

## The Local Group, 5 million light years

What is called the Local Group extends to a region with a radius of 5 million light years. Besides the Milky Way it contains two other similar sized galaxies, the Andromeda (M31) and Triangulum (M33) galaxies. The Triangulum galaxy is also referred to as the Pinwheel Galaxy.

The Local Group also contains about 50 dwarf galaxies. There could be more, but because they are so faint several may not have been yet discovered. The number of stars within this region is estimated at 700 billion.

 5 million light years corresponds in our scale model with 47 million km, which is one third of the real distance to the Sun. The Andromeda galaxy is in our scale model almost 24 million km away.

Image: Robert Gendler, NASA POD

M31: The Andromeda Galaxy
is about 2.5 million light years away.

## The Virgo Super cluster, 100 million light years

Galaxies tend to cluster into groups. The largest nearby cluster is the Virgo cluster, a concentration of several hundred galaxies.

Other clusters in this region are the Fornax and the Eridanus clusters. These clusters are gravitationally bound together, and with many local groups within this region, they form what is called a Super Cluster.

This one is known as the Virgo Super cluster. Our galaxy with its Local Group is quite insignificant in the centre.

This region has a radius of about 100 million light years. It contains about 2,500 large galaxies and countless dwarf galaxies.

.

 This region has a radius in our scale model of 947 million km, which is more than the radius of Jupiter's orbit around the Sun.

Digitized Sky Survey, Palomar Observatory, STScI;
Source: Encyclopaedia Britannica

The central portion of the Virgo Super Cluster in an optical image taken by the Observatory on Mount Palomar in California. The galaxy in the centre is M87 (also known as the radio galaxy Virgo A).

## Walls and Filaments, 1 billion light years

On yet a larger scale we see that Super Clusters are forming vast walls and sheets with empty regions - called voids - in between.

This diagram shows many of these Super Clusters including the Virgo super cluster, quite insignificant in the centre.

In this region with a radius of 1 billion light years there are about 100 Super Clusters, some of which are named in the diagram.

 1 billion light years correspond in our scale model to a distance of 9.5 billion km, which is about twice the radius of Neptune's orbit around the Sun.

## 14 billion light years

The known visible Universe extends to 14 billion light years around us. The sheets and walls of Super Clusters give the Universe a cellular appearance.

This diagram is an impression of this entire region. The number of Super Clusters in the visible universe is estimated to 10 million.

## Dilemma

In our scale model, 14 billion light years correspond with a distance of 133 billion km or roughly the size of our Solar System, including the Oort Cloud.

Remember that the average star is 1 mm in size in this scale model. So what kind of scale model is that?

We make scale models to see the true scale of something in a small area. But if we want to see individual stars as grains of sand, like we do in our model, the scale model itself becomes larger than planet Earth, long before we can see the Milky Way galaxy.

If we limit the size of the scale model of the visible Universe (the diagram on this page) to the size of planet Earth, we have to shrink the original model by a factor of ten million. Then we end up with our Sun having a size of 1.3 x 10-7 mm or about the size of a Helium atom. These model "atoms" are then at a typical distance of 5 mm apart within a galaxy.

Can we call that a scale model? Well, that depends on what you want to see. But the bottom-line is that we cannot really say that we can comprehend distances and sizes in the Universe. We can look at the numbers and do our calculations, but we have no way of relating these to our every day experience.

We can conclude however that the Universe is very empty because there is such a large distance between neighbouring stars as compared to their size, and even more so between galaxies, clusters and super clusters.

The Universe is a very empty place.

The Astronomer
Jan Vermeer (ca. 1668)

## Time Travel

Speed of Light

Another way of looking at the scale of the Universe is to think about the speed of light, which is about 300,000 km/s. To get an idea of what this means, notice that with this speed you can go around the Earth at the equator seven and a half times in one second.

To reach the nearest star besides our Sun, you need to travel 4.5 years with this speed.

Back in Time

When we look into space, whether with the naked eye or with a telescope, we are actually looking back in time. There is no other way, because the speed with which the light that we see now has travelled, is finite compared to the huge distances of travel.

## So how far back in history do we look?

The light we see from the centre of the Milky Way galaxy, left its source about 25,000 years ago, that was when in the Upper Paleolithic the Venus of Dolní Věstonice figurine was created, one of the earliest known depictions of the human body.

Venus of Dolní Věstonice.
Source Wikipedia

The light we see from the Andromeda galaxy today, left 2.5 million years ago. That was when the Pleistocene began in the geological time scale, when on Earth the genus “Homo” appeared, from which the modern humans have evolved much later.

This skull is 1.9 million years old, discovered in Kenya in 1973. Homo habilis is arguably the first species of the Homo genus to appear.

Homo habilis
Source Wikipedia

The faintest and reddest objects in the Hubble Ultra Deep Field image are likely the oldest galaxies ever identified, having formed between only 600–900 million years after the Big Bang. More here.

These objects are at a distance of about 13 billion light years.
That light was emitted 8.4 billion years before our Solar System formed.

Photo credit: NASA/ESA/S. Beckwith(STScI) and The HUDF Team.

A sense of scale of the Universe, is that reality or just a dream?