The size of things

2018 November 16

David Basey

Figure 1. The relative sizes of the Sun and planets. Source Wikimedia Commons, originator NASA

Space is big, really big and in astronomy we often have to use some very large numbers indeed. So large in fact that they frequently become incomprehensible. In this tutorial we will try and bring the scale of the solar system, stars and galaxy ‘down to earth’.

What follows will be a couple of scale models in which we discuss the sizes and distances of various objects in the universe.

Figure 1 shows the relative sizes (not distances) of the Sun and planets of the Solar System. Notice in particular the wide disparity in planetary diameters and how the Sun (at the top) is so much larger than anything else.

Planetary orbits are generally not circular neither are the planets perfectly spherical. For example the distance of Mars from the Sun varies considerably as it orbits the sun and one look at the planet Jupiter will show it is much wider at the equator than it is from pole to pole. For the purposes of simplicity we will generally use mean distances and equatorial diameters but occasionally give the extremes as well in order to illustrate how non circular something is.

The figures used mostly come from NASA and unless otherwise stated, distances are measured from a body’s centre not its surface.

Earth, Moon and Sun

Let’s start in our own backyard so to speak. The planet Earth has a diameter of 12,756km. Although this in itself is quite a large number, the modern era of mass travel has made the size of our planet something most people are reasonably comfortable with.

For our purposes let’s shrink the earth down to a size of 5mm, about the size of a small pea. At this size the International Space Station orbits on average just 0.15mm above the surface of our mini-earth.

The scale size of the Moon is about 1.4mm in diameter or a little more than a quarter as large as the Earth. But how far away is it? Well the average distance from the centre of the Earth to the Moon is 384,000km so in our model the Moon is 151mm away. This is about 30 times the diameter of the Earth (Figure 2) or in terms of our scale roughly the length of a cheap ballpoint pen.

Figure 2. This picture is an approximate scale diagram of the Earth-Moon system. Source Wikimedia Commons, created by Rizzoj from NASA data.

To put the Earth-Moon distance in perspective, let’s consider how long it would take to travel there. In 1969 the Apollo 11 spacecraft reached our satellite from Earth orbit in 3 days. A modern commercial passenger jet cruising at around 900 kph would take nearly 18 days to reach the Moon assuming it could travel in space and in a straight line. A vehicle travelling steadily at the UK limit of 70mph (113 kph) would take over 4.5 months to reach our satellite and someone walking non-stop would take about 9 years!

Moving further afield, the Earth orbits the Sun at distance of 149,600,000km. In our model this equates to a little over 58.6m. As for the Sun itself, it has a diameter of 1,391,016km. That is 109 times larger than the Earth and it would have a diameter of 545mm in our model, roughly the size of a large inflatable beach ball. The mean distance from the Earth to the Sun is known as the “Astronomical Unit” (AU) and will feature again in our scale model.

The table below summarizes the position so far.

Object	Eq. Diameter (km)	Scale Diameter (mm)	Diameter Relative to Earth	Radius of Orbit (km)	Scale Orbital Radius (mm)	Orbital Radius Relative to Earth
Earth	12,756	5.0	1.0x	149,600,000	58,639	11,728x
Moon	3,475	1.4	0.27x	384,000	151	30x
Sun	1,391,016	545.2	109.1x	–	–	–

In this table the orbital data for the Earth refers to its path around the Sun and for the Moon it is for our satellite’s orbit around the Earth.

The inner solar system

Figure 3. Relative sizes of the rocky worlds of the Solar System. Adapted from Wikimedia Commons. Author: Koppelo, derived from NASA.

Now we will reposition ourselves at the centre of the Sun and travel outwards through the Solar system. For simplicity we will only give the scale diameters in millimetres and distances in metres. The tables in this section will summarize the actual sizes and distances.

The innermost planets (the so called terrestrial planets) are all rocky worlds (Figure 3) and the first planet we encounter is little Mercury with a diameter of 1.9mm, not much larger than our moon and an average distance from the Sun of around 22.7m. However, the orbit of Mercury is distinctly non-circular and the distance varies from 18.0m to 27.4m.

Figure 4. The orbits of the inner planets out to Mars. Notice how the orbits of Mercury and Mars are distinctly non-circular with the Sun off-centre.

After Mercury comes Venus with a diameter of 4.7mm not too dissimilar to that of the Earth although the conditions on Venus are wildly different to our home planet with surface temperatures of 470C and an atmospheric pressure 90 times that on the Earth’s surface (equivalent to being roughly 900m underwater in the Earth’s oceans). Venus orbits the Sun in a closely circular orbit with a scale radius of 42.4m.

Passing Venus we encounter the Earth 58.6m from the Sun before reaching the red planet Mars at a mean distance of 89.3m. However as mentioned earlier, the orbit of Mars is noticeably non-circular and varies from 80.9m to 97.7m. For comparison the Earth’s orbit is much more circular and its distance from the Sun varies by less than 2m in our scale model. Much smaller than the Earth, Mars comes in at just 2.7mm. Notice how in moving from the Earth to Mars we increased the size of the Solar System by over 50%. Figure 4 shows the relative sizes of the orbits of the inner planets.

After Mars we enter the asteroid belt. The largest of its denizens is the dwarf planet Ceres with a diameter of 0.4mm, much smaller than our moon and which orbits the Sun at a distance of 162.3m.

The table below summarizes the position so far.

Object	Eq. Diameter (km)	Scale Diameter (mm)	Size Relative to Earth	Radius of Orbit (km)	Radius of Orbit (AU)	Scale Radius of Orbit (m)
Mercury	4,879	1.9	0.38x	57,900,000	0.39	22.7
Venus	12,104	4.7	0.95x	108,200,000	0.72	42.4
Earth	12,756	5.0	1.00x	149,600,000	1.00	58.6
Mars	6,792	2.7	0.53x	227,900,000	1.52	89.3
Ceres	950	0.4	0.07x	414,000,000	2.77	162.3

The outer solar system

Figure 5. The relative sizes of the four gas giants of the solar system. Adapted from Wikimedia Commons, originator NASA.

We now leave the realm of the rocky planets and reach the region dominated by the gas giants (Figure 5) although nowadays Uranus and Neptune are often referred to as ice giants instead. First up is the solar system’s largest planet, the giant Jupiter. Jupiter is over 11 times the diameter of the Earth with a scale diameter of 56mm (roughly snooker ball size), orbiting 305m from the Sun.

Jupiter is the centre of a system of natural satellites. Of these, four are of significant size, Io, Europa, Ganymede and Callisto. These four satellites are known as the Galilean Satellites as they were discovered by Galileo and recognised as moons of Jupiter in 1610. They have scale diameters of 1.4mm, 1.2mm, 2.1mm and 1.9mm respectively. Notice that all except Europa are larger than our own Moon and that Ganymede is even larger than Mercury. Their details are in the table below along with those for Titan, Saturn’s largest satellite.

Object	Eq. Diameter (km)	Scale Diameter (mm)	Radius of Orbit around Planet (km)	Scale Radius of Orbit (mm)
Io	3,643	1.4	422,000	165
Europa	3,122	1.2	671,000	263
Ganymede	5,262	2.1	1,070,000	419
Callisto	4,821	1.9	1,883,000	738
Titan	5,150	2.0	1,222,000	139

Beyond Jupiter is the lovely ringed world of Saturn at a distance of 562m from the Sun. The globe of Saturn itself will be 47mm across and the diameter of the rings to the outer edge of the A ring (the outermost ‘obvious’ ring’) is 107mm. For more on Saturn and its rings see this tutorial by Mike Foulkes. Like Jupiter, Saturn has a large retinue of moons. Of these the largest is Titan at 2.0mm. From this we can see that not only is Titan larger than our own moon but, like Ganymede, is larger than the planet Mercury as well.

Figure 6 The orbits of the planets to scale. The arrows on each planet show the direction of its axis. Source Wikimedia Commons, originator NASA.

Moving on from Saturn we next come to Uranus, much smaller than either Jupiter or Saturn but still 4 times larger than the Earth at 20mm. Uranus too has several moons but all are relatively small. The planet orbits the Sun at a distance of well over 1km.

Next up is Neptune, slightly smaller than Uranus at 19.4mm but still a gas/ice giant in its own right orbiting at 1.76km.

Beyond Neptune we leave the realm of the giant planets and encounter what is generally known as the Kuiper belt but more properly the Kuiper-Edgeworth belt. This is a belt of cold icy worlds often in very elliptical orbits. The most famous of these is the dwarf planet Pluto. On our scale its diameter is 0.9mm (smaller than our Moon) and the orbit varies between 1.7km and 2.9km.

Figure 6 shows the relative sizes of the orbits of the outer planets with an inset for the inner planets.

The table below summarizes the position for the outer planets.

Object	Eq. Diameter (km)	Scale Diameter (mm)	Size Relative to Earth	Radius of Orbit (km)	Radius of Orbit (AU)	Scale Radius of Orbit (m)
Jupiter	142,984	56.0	11.21x	778,600,000	5.20	305.2
Saturn – Globe	120,536	47.2	9.45x	1,433,500,000	9.58	561.9
Saturn – Rings	273,560	107.2	21.45x	“	“	“
Uranus	51,118	20.0	4.01x	2,872,500,000	19.20	1,125.9
Neptune	49,528	19.4	3.88x	4,495,100,000	30.05	1,762.0
Pluto	2,374	0.9	0.19x	5,906,400,000	39.48	2,315.2

At this point we will pause briefly and just consider how large the system of planets is in comparison to the size of our home planet. Recall that we started with the Earth represented by a 5mm sphere and have now travelled around 2.3km from the Sun to reach Pluto, a factor of about 460,000.

With this in mind we can now leave the Solar System behind and venture out into deep space.

Stars and galaxies

Once we leave the Solar System, distances soon become very large indeed. The usual measure of distance is the light year, the distance light travels in one year. This is about 9,500,000,000,000km and using our scale of 5mm to the Earth’s diameter this would be about 3,725km. Bear in mind that as we travel out into the galaxy our measurement of sizes and distances becomes more difficult and the figures used represent best estimates but are subject to some uncertainty.

The nearest star to Earth after the Sun is Proxima Centauri at about 4.25 light years. This means that if we were to place our 5mm Earth in central London then Proxima would be 15,800km away, somewhere in SW Australia. Proxima is what is known as a Red Dwarf star making it both comparatively small and faint. It is nearly 202,000km in diameter, roughly 80mm on our scale or only about 50% larger than Jupiter.

Given that many stars are tens, hundreds or even thousands of light years away it is clear that with our original scale things will rapidly get out of hand. So let’s create a new scale that hopefully will give some feeling for the relationship between the sizes of the stars and the distances that separate them. This new scale will shrink the Sun down to a diameter of only 5mm. At this scale the Earth is now only 0.05mm in diameter.

With this new scale in hand let’s revisit Proxima Centauri. We now have two globes, one, the Sun, 5mm in diameter and the other, Proxima, about 0.7mm separated by over 145km. Truly, given their sizes, the stars are at immense distances from each other.

Red Dwarf stars are very common in the galaxy but because of their dimness they tend not to be very obvious. To get a feel for the sizes of the stars that we can easily see let’s look more closely at three of them that definitely are not Red Dwarfs.

Firstly, Sirius which appears as the brightest star in our sky. Sirius is 8.58 light years away which would be 293km on our new scale. It has a diameter of just less than 2.4 million kilometres which would scale down to 8.6mm, about 70% larger than our sun. Sirius is the seventh closest star system to Earth which helps explain its brightness.

Vega, the bright star visible in the summer skies of the northern hemisphere is 25 light years away (a scale distance of 854km) and over 2.8 times larger than the sun.

Lastly, another bright northern summer star, Deneb in the constellation of Cygnus the swan. Deneb is 2,600 light years distant (scale nearly 89,000km) and its diameter is about 203 times larger than our sun with an equivalent diameter of 1015mm.

So far we have just cherry picked some of the better known and brighter of the stars visible to us here on Earth. To get a better idea of the density of stars (or lack of it) consider that within a sphere of radius 10 light years (341km) there are just nine star systems. Of these, two are Brown Dwarf objects which may be thought of as “failed stars”. The table below gives details of these nearest systems.

Rank by distance	System	Distance (Ly)	Scale Distance (km)	Notes
1	Alpha Centauri	4.37	149	Multiple star, the distance given is to the main pair. Proxima is an outlying member of the group at ‘only’ 4.25 light years.
2	Barnard’s Star	5.96	204	Red dwarf
3	Luhman 16	6.59	225	Brown dwarf pair
4	Wise 0855-0714	7.27	248	Brown dwarf
5	Wolf 359	7.78	266	Red dwarf
6	Lalande 21185	8.29	283	Red dwarf
7	Sirius	8.58	293	Brightest visible star from Earth. Double with a white dwarf companion.
8	Luyten 726-8	8.73	298	Double red dwarf.
9	Ross 154	9.68	331	Red Dwarf

Figure 7. An artist’s impression of the Milky Way galaxy with the Sun below centre. Source: NASA/JPL-Caltech/ESO/R. Hurt.

Our Sun and all the stars we can see with the naked eye are only a small part of our own Milky Way Galaxy, (Figure 7) a huge assemblage of stars, gas and dust at least 100,000 light years in diameter. On our scale this would be roughly 3.4 million kilometres and our Sun is located around 26,000 light years from the centre or 888,000km on our 5mm scale.

Our Milky Way Galaxy is just one of billions and billions in the universe as a whole. If you go out on a clear night in autumn, you know where to look and the sky is dark enough you will see a small, faint patch of light in the constellation of Andromeda. This is M31, the great Andromeda galaxy. M31 is the nearest significant galaxy to our own at a distance of approximately 2.5 million light years. This would be 85.4 million kilometres on our scale.

Figure 8. The Local Group of galaxies. Source Wikimedia Commons, originator Antonio Ciccolella.

Our galaxy and M31 are the two largest members of the ‘Local Group’ (Figure 8) a collection of 50+ nearby galaxies large and small. The diameter of the Local Group is around 10 million light years or over 341 million kilometres to scale.

This in turn is part of the Virgo Supercluster with a diameter of 110 million light years scaling to 3.75 billion kilometres.

So to summarise on our GALACTIC SCALE model:

The Sun is 5mm in diameter.
The nearest star is 145km away.
From the Sun to Deneb is 89,000km.
The Sun is 888,000km from the galactic centre.
Our galaxy is 3.4 million kilometres in diameter.
The nearest major galaxy is 85.4 million kilometres distant.
The Local Group is 341.5 million kilometres across.
The Virgo Supercluster is 3.75 billion kilometres across.

In conclusion

From all of the above one thing is abundantly clear, space is primarily just that – space. The sizes of the individual planets, stars and galaxies are dwarfed by the immensity of the distances between them. The 17th century French scientist and author Blaise Pascal wrote “The eternal silences of these infinite spaces fill me with dread”. With a little contemplation it is easy to understand how he felt although perhaps nowadays the overriding emotion is wonder rather than dread.

If you are in the York area at any time and would like a practical exploration of the scale of the Solar System, the University of York has created a scale model enabling you to cycle from the Sun to Pluto.

Lastly, in 1977, IBM produced a short but very famous film on the scale of things entitled “Powers of Ten”. It is perhaps a little dated now but is still well worth watching nonetheless to gain an appreciation of both the very large and the very small. It is available on the Internet and a search will turn up many copies. If you have not seen it I would encourage you to watch it.

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