To see the Universe in a Grain of Taranaki Sand

To see the Universe in a Grain of Taranaki Sand

Glen Mackie

[appeared in North and South magazine (New Zealand), May, 1999]

[... and linked to Astronomy Picture of the Day April 16, 2004, August 20, 2005, January 26, 2007, August 7, 2009.

It had worried me for a long time. I could hear his voice,

... the total number of stars in the universe is greater than all the grains of sand on all the beaches of the planet Earth.

NGC 1850 by WFPC2/HST I heard Carl Sagan repeating those words again recently when I looked along a surf beach on the Taranaki coast. Later that evening I looked up at the sky. We are fooled somewhat. Our eyes can only resolve about 5000 of the brightest stars, mostly close to our Sun, and typically within 1000 light years (1 light year is the distance light, travelling with a velocity of 300,000 kilometres per second, covers in 1 year).

From left, Alpha and Beta
Centauri, dark Coal Sack nebula, Southern Cross (Beta Crux, Alpha Crux 
(blue-ish), Gamma
Crux (orange), Delta Crux), Eta Carinae nebula (large pink blob). Our Galaxy however, is probably greater than 100,000 light years in diameter. Hence we can resolve only a very small fraction of our Galaxy with our eyes. As well, whilst our view of the brightest stars is a magnificent panorama we do not get any sense of depth or relative distances of stars. For example, the two bright stars close together, alpha and beta Centauri, (commonly called The Pointers because they guide us to the nearby Southern Cross) are at very different distances. Rigil Kentaurus and Hadar (their common names) are 4.3 and 490 light years distant, respectively. Hardly neighbours!

The faint smudge of light we call the Milky Way, easily visible on a dark night, is millions of very faint, distant stars lying in the disk of our Galaxy that our eyes cannot resolve. Dark clouds of dust (microscopic pieces of carbon and silicon) dimms the light of many more stars. Apart from a few neighbouring galaxies (including the Large and Small Magellanic Clouds visible in the southern sky), that appear as faint, fuzzy blobs of light, our naked eye perception of the universe is very myopic.

My feet stood on what seemed to be an unfathomable number of sand grains on that wide, long Taranaki beach. If sand grains were stars, a handful of sand thrown into an empty sky could easily replicate what we see. Imagine the brilliant sky you could create with a whole beach of sand! The voice returned. Carl was probably right. He would have done the calculation. Doubts remained though, and I knew it was time to put his voice to rest.

I knew some average numbers for stars and galaxies. In many astronomical studies an answer to within an order of magnitude (a factor of 10) is deemed acceptable. Since I had a funny feeling that an average beach may also be hard to describe, I decided to accept order of magnitude accuracy.

Messier 31 in Andromeda

Our Galaxy, has approximately 400 billion stars. Carl used this number in the book based on his Cosmos television series and I'll stick with it. We define a billion as 10 to the power 9, or 1 with 9 zeroes following it, ie. 1,000,000,000. Big. Is our Galaxy average? Well, it's a spiral, a little less massive than our magnificent Local Group neighbour, Messier 31 in Andromeda. As far as spirals go, it's probably close enough to average. The other galaxies that exist in the universe, large ellipticals and smaller irregular galaxies, tend to have more and less stars, respectively. I'll assume that, in terms of star numbers, our Galaxy represents the average galaxy.

What is the total number of galaxies in the universe? Sagan assumed 100 billion. Is that still valid? Recently the Hubble Space Telescope (HST) surveyed, to the faintest levels yet detected, a small area of sky. Extrapolating from the number of galaxies detected by HST to that expected over the whole sky, I calculate 130 billion galaxies, slightly larger than Sagans estimate. Then the number of stars in the universe is 400 billion x 130 billion, or about 50,000 billion billion. A billion billion. That's 1,000,000,000,000,000,000. So, grasp the concept of a billion billion, then think of 50 thousand of those. Easy!

What are the dimensions of an average, sandy beach on Earth? I was lucky. I know a Coastal Geomorphologist (doesn't everyone?) who provided some estimates. Take 360,000 kilometres of coast (the total coastline of the world is about 1 million kilometres, of which about 36 percent is sandy), mix with an average beach width of 50 metres (high to low tide lines), and add a dash of average beach depth of 4 metres.

The diameters of sand grains range from about 0.1 to 2 millimetres. We'll adopt an average diameter of 0.5 millimetres. Lets stack them simply, one on top of another (not very likely in a beach I admit), so that 8000 fit into 1 cubic centimetre. Drum roll please. The total number of sand grains on our Earth beach is then 600 billion billion. But wait!, I hear some of you remarking about sand dunes and sand below the low tide mark. To placate you worriers I'm happy to increase my initial estimate by a factor of 3. That gives me a grand total of about 2000 billion billion grains of sand on Earth.

The stars win! Carl was right, ... maybe. The excess factor (the number of stars divided by the number of grains) of 50,000/2000 or 25 is greater than an order of magnitude, but only just. My individual assumptions must be wrong at some level. Maybe the average galaxy has only 40 billion stars (faint surveys do detect many small, ``dwarf'' galaxies). As well, maybe the number of sand grains is three times greater. (In fact my Coastal Geomorphologist suggested that the average grain diameter could be smaller than 0.5 millimetres, probably allowing us to stack a factor of 3 more!). Combine these two changes and the grains win, just!

Hubble Deep Field South by NICMOS/STIS/HST

Not so fast! Any (conspired) increase in the number of sand grains is probably offset by the recent discovery of many more galaxies by HST in the near-infrared region of the electromagnetic spectrum, not previously detected in optical surveys. Observing in the infrared minimizes the absorbing effects of dust allowing us to see galaxies enshrouded in large amounts of dust present because of vigorous star formation. The odds are that there are many more than 130 billion galaxies in the universe. I'll cast my final vote in favour of the stars, and I'll admit a slight astronomical bias (see author notes).

I returned home after three days of travelling. I could now stand on a beach and not hear Carl Sagans voice. I had even warmed to the number billion. For example, whilst I was away during those three days, our Galaxy had moved another 0.2 billion kilometres towards the Virgo cluster of galaxies (located 650 billion billion kilometres away), and the population of New Zealand had experienced 1,600 billion heartbeats. Now, is that resting heartbeat? Here we go again.

Carl Sagan (1934-1996) was Director of the Laboratory for Planetary Studies and David Duncan Professor of Astronomy and Space Sciences at Cornell University. Professor Sagan was a leading popularizer of science and astronomy in particular, and presented the Cosmos television series and wrote the book (Cosmos, Random House: New York) based on the series.

Glen Mackie is Lecturer, in the Centre for Astrophysics and Supercomputing, Swinburne University of Technology, Melbourne, Australia.

Last text update February 1, 2002