# Scale of the universe if a star was a grain of sand

by pelooyen
Tags: grain, sand, scale, star, universe
 P: 1 As a teacher, I am trying to help students understand the scale of the universe. Using the analogy of sand as stars, and based on the average size of sand as .5mm across, I worked out... 1. The number of stars is greater than the grains of sand on all the beaches of the world (allowing for the fact that that actual length of coastline is variable depending on how you measure it) 2. The number of stars in our galaxy is about 100 billion stars, and so, in terms of sand, that is about 500 tonne and would fill approx 320 cubic meters, so three large rooms worth. That's considerably smaller than all the beaches of the earth. 3. However, if an average star is about the size of a grain of sand... - our solar system would be 3.5 m across (give or take where your think the boundary is) - our galaxy would be still 340,000 km across My question is: Am I roughly correct in my estimation? I'd hate to think I am out by many orders of magnitude :D Paul Looyen
 P: 3,099 This interactive video might help with showing the scale of things: http://htwins.net/scale2/ and then there's the classic Powers of Ten video by Charles Eames: https://www.youtube.com/watch?v=38ti9BJiyvs
P: 2,953
 Quote by pelooyen As a teacher, I am trying to help students understand the scale of the universe. Using the analogy of sand as stars, and based on the average size of sand as .5mm across, I worked out... 1. The number of stars is greater than the grains of sand on all the beaches of the world (allowing for the fact that that actual length of coastline is variable depending on how you measure it) 2. The number of stars in our galaxy is about 100 billion stars, and so, in terms of sand, that is about 500 tonne and would fill approx 320 cubic meters, so three large rooms worth. That's considerably smaller than all the beaches of the earth. 3. However, if an average star is about the size of a grain of sand... - our solar system would be 3.5 m across (give or take where your think the boundary is) - our galaxy would be still 340,000 km across My question is: Am I roughly correct in my estimation? I'd hate to think I am out by many orders of magnitude :D Paul Looyen
Let's take your word that sand is .5mm across (pretty fine sand it seems), and do some order of magnitude, back of the envelope calculations then! .5mm across means .25mm in radius. We assume sand is a sphere.

1) There are about 100 billion (dwarf galaxies have fewer) to 1 trillion stars per galaxy (only for the largest elliptical galaxies), and about 200 billion galaxies in our observable universe. Let's just take each galaxy to have approximately 200 billion stars (roughly size of the Milky way). That's 2*10^11 stars per galaxy, and 2*10^11 galaxies for a total of 4*10^22 stars.

Next we have to estimate how much sand is on all the beaches of the world. Certainly not an easy task. The CIA world fact book states that there is about 400,000km of coastline in the World. Now, of course, not all of that coastline is comprised of beaches. But we can use it as an upper bound. If each beach is roughly 50 meters in length, and 10 meters deep (just my personal guesses, if you want to use others, you can do so as well), then that's roughly 4*10^8m*50m*10m=10^11 cubic meters in volume. Looking at problem 2) (I did that one earlier since it's easier) we see that 10 cubic meters of sand contains roughly 10^11 grains, or 1 cubic meter contains 10^10 grains.

As such, 10^11 cubic meters of sand contains roughly 10^11*10^10=10^21 grains of sand. This is comparable to the number of stars within the observable universe, being only 1 order of magnitude lower. We can't conclude for certain, then either way, because we may certainly be off by an order of magnitude or two in either direction. This is probably the most uncertain calculation.

2) I've heard the estimate 200 billion for our Milky way galaxy, but let's use 100 billion here. We said sand was .25mm in radius, that means it's volume is 4/3*pi*(1/4 mm)^3~4*(1/64 mm^3)~1/16 mm^3. Call that 10^-1 mm^3. 10^-1 mm^3 times 10^11 stars equal 10^10 mm^3 which is 10 cubic meters. So we are off from each other by 2 orders of magnitude here. Similarly, I think our mass estimates will be also off from each other. I don't see an error in my calculation, perhaps you can spot one?

3) Our solar system's size is very very variable depending on what you define to be our solar system. If you define our solar system to be to the orbit of Neptune, then the size is ~60AU across. If you define our system to include the Kuiper belt, then the size is ~100AU across (the Heliopause is a bit farther, at 120AU or so). If you include the oort cloud, then the size is ~100,000AU (across).

Stars of course, also vary by size quite a bit, in terms of size. The Sun is ~700,000km in radius, while the largest red giants may have a radius that can be >1AU. Let's just use 1 million km for our calculations, and neglect the massive stars. This is good because there are not all that many massive stars compared with the very tiny ones (the massive stars die very quickly!). So 10^6 km = .25mm. That means 1AU ~150 million km = 150*.25mm~300mm (30 centimeters).

This means the the orbit of Neptune is ~20 meters across, the Kuiper belt and Heliopause makes the solar system ~40 meters across, and the oort cloud makes it a ridiculous 30,000 meters (30 km) across!

Similar concerns happen with our Galaxy. Usually one uses the dimensions of ~50,000 light years in radius, but the halo of stars surrounding our galaxy extends far beyond that. The dark matter distribution extends probably much much farther still. Still, let's take the conventional 10^5 light years across scenario. 10^5 light years, with one light year ~300,000AU means that the galaxy is roughly 3*10^10 AU ~ 10^10 meters (10 million km) across!

It seems here we are off again by a couple of orders of magnitude.

Of course I may be wrong, or off by a couple of orders of magnitude. I did not double/triple check my results.

PF Gold
P: 2,741
Scale of the universe if a star was a grain of sand

hi ya Paul

welcome to PF

you can add a lot more to your count, here's info from one site and it roughly matches others that I quickly looked at

 According to astronomers, our Milky Way is an average-sized barred spiral galaxy measuring up to 120,000 light-years across. Our Sun is located about 27,000 light-years from the galactic core in the Orion arm. Astronomers estimate that the Milky Way contains up to 400 billion stars of various sizes and brightness. A few are supergiants, like Betelgeuse or Rigel. Many more are average-sized stars like our Sun. The vast majority of stars in the Milky Way are red dwarf stars; dim, low mass, with a fraction of the brightness of our Sun. As we peer through our telescopes, we can see fuzzy patches in the sky which astronomers now know are other galaxies like our Milky Way. These massive structures can contain more or less stars than our own Milky Way. Elliptical galaxy ESO 325-G004. ESO Elliptical galaxy ESO 325-G004. ESO There are spiral galaxies out there with more than a trillion stars, and giant elliptical galaxies with 100 trillion stars. And there are tiny dwarf galaxies with a fraction of our number of stars. So how many galaxies are there? According to astronomers, there are probably more than 170 billion galaxies in the observable Universe, stretching out into a region of space 13.8 billion light-years away from us in all directions. Read more: http://www.universetoday.com/102630/...#ixzz391PkP6Hw
one quote I saw some long time ago was " there's more stars in the universe than ALL the grains of sand on earth's beaches and deserts

Dave
 P: 102 The Anthropic Cosmological Principle Hardcover – March 6, 1986 by John D. Barrow (Author), Frank J. Tipler (Author), & 1 more ISBN-13: 978-0198519492 ISBN-10: 0198519494 Would be a good read for you.
 P: 1 Randall Munroe has tackled the sand:star analogy in his What-If series: http://what-if.xkcd.com/83/ 1) Only for the Milky Way, but a good basis for your average galaxy. 2) "Sand" works for the majority of stars, but the volume of star "gravel" and star "boulders" would dwarf our star beach!

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