stars of the sky and sand of the sea

Factual Questions
1

In the Bible, a blessing is given to Abraham that his descendants will be as numerous as the “stars of the heavens and the sand on the seashore”. (Genesis 22:17)

Here are a few questions:

a) Approximately how many stars are there, and how many grains of sand are there on the “seashore” - worldwide?

b) Assuming that there are more grains of sand (I’m not sure that’s true, but hopefully some wise poster will soon inform me), what is the area of seashore needed to include as many grains of sand as there are stars?

2

There are undoubtedly more grains of sand on a single beach than there are visible stars (visible to the unaided eye, that is, but I strongly suspect that the number of stars in the universe far outnumber the grains of sand on this planet.

Perhaps it would be useful to have some sort of yardstick; could someone who is well versed in astronomy and physics tell us; if you took a number of (say, silicon) atoms that was equivalent to the estimated number of stars in the universe, how big a pile of silicon would you have? (I won’t be surprised to learn that it outweighs the earth.

3

As an aside, I think what is behind the Bible quote is God saying to Abraham; “Think of an unimaginably large number”

4

There are surprisingly few stars visible to the naked eye from earth, somewhere around 6,000 IIRC. As a very rough estimate of the number of stars in the universe, consider there are roughly 100 billion stars in our Galaxy and roughly 100 billion galaxies in the universe, for a very rough estimate of 10[sup]22[/sup] stars in the universe.

5

Arguably there might have been a few more stars visible to the naked eye under normal conditions in Abraham’s day than there are under normal conditions today; I’m thinking pollution (chemical and light).

6

There were certainly more stars visible to Abraham than to a modern observer: In addition to the difference in light pollution (chemical pollution isn’t too relevant here), he also had the advantage of living in a dry climate, which is good for astronomy, and close to the Equator, so he could see a larger percentage of the sky over the course of the year. bibliophage’s figure of 6000 is presuming ideal conditions, so that’s already taken into account.

The figure of a hundred billion galaxies is probably a bit low; that was the standard figure tossed around before the Hubble Deep Field, but the HDF showed many more galaxies than were expected. In addition, that’s just for the visible Universe, and the Universe is almost certainly larger than that and quite possibly infinite. If we use bibliophage’s number, though, then one silicon atom per star would only be about half a gram of silicon.

On the third hand, though, why are we restricting the sand to the Earth’s beaches? Many stars have planets, and many of those planets must have liquid water and dry land, and where liquid water and dry land meet, you’re likely to find beaches, so sand grains probably outnumber stars by a considerable margin, in the Universe as a whole.

7

I’m going to start with bibliophage’s figure of:

10,000,000,000,000,000,000,000 stars (#a)

(that’s 10 to the power of 22 - if anyone can tell me how to superscript in this forum, i’d be appreciative).

Now, i want to work backwards from this number. First, i’m going to make an assumption that i believe is conservative, and say that 1 cubic centimetre contains 1,000 grains of sand.

This means that #a grains of sand will take up

10,000,000,000,000,000,000 cc (#b)

With 1,000,000 cc per cubic metre, that gives us:

10,000,000,000,000 cubic metres (#c)

which in turn, at 1,000,000,000 cubic metres per cubic km, gives:

10,000 cubic kilometres, or in other words a box of dimensions:

10km x 10km x 100km, or approximately

6.21m x 6.21m x 62.1m.

So, if you believe that all the sand in the world would overflow a box this big, then there is more sand than there are stars. On the other hand, if the sand would come up short, then there are more stars.

Caveat: if, as i believe, my estimate of 1,000 grains of sand per cc is conservative, then the box would be smaller and the likelihood of stars winning would increase proportionally.

michael.

PS. let me know if i’ve stuffed up the mathematics.

8

Ask and ye shall receive.

In general, About This Message Board is a good place for new folks [sub]like yourself[/sub] to find this kind of stuff. Or you can do quote and see what people did in their posts. Welcome aboard!

[sup]Gotta run, Simpsons is on you know…[/sup]

9

many thanks :slight_smile:

10

This site seems to give an estimate:

http://www.hawaii.edu/suremath/jsand.html

(I’d quote it, but I don’t know if the vB code could handle the math.)

It comes to the conclusion that there are approximately
7.5 x 10[sup]18[/sup] grains of sand on all the beaches of the earth.

11

And this site:
http://webug.physics.uiuc.edu/courses/phys150/fall97/slides/lect24/sld006.htm

comes up with 10[sup]23[/sup], which is remarkably close to the number of stars!

12

Curwin said:

If you are using the earlier figure of 10[sup]22[/sup] stars, the number of sand grains given at your linked site is actually 10x that. Not really that close!

13

I’m saying remarkably close since both numbers are estimations, and I assume either could be off by that much.

14

Possibly a low estimate. I’ve seen estimates ranging from 100-1,000 billion stars in the Milky Way (but usually cited in the range of 100-400 billion).

15

more stars than sand…
http://itss.raytheon.com/cafe/qadir/q2865.html

close call…
http://newton.dep.anl.gov/askasci/ast99/ast99215.htm (bibliophage will like this link)

16

I don’t know about that. In every astronomy course I’ve taken the professors have joked that anything within three orders of magnitude could be considered a correct answer. :smiley:

Semi-hijack: In college, our profs called these kinds of questions where you estimate some huge number from a few estimated figures (# of bricks in New York City, leaves in the Amazon, grains of sand on Earth) ‘Fermi problems’. Is this the typical name? And if so, was Enrico Fermi well known for doing this sort of thing?

–sublight.

17

I take your point.

18

semi-hijack followup:
Fermi is credited for the archetypal ‘back of envelope’ calculation. According to legend, at the first atomic test blast, he ripped up a paper (or was it an envelope? :slight_smile: and threw it in the air just before the shockwave hit. He observed how far the confetti was carried and got a quick estimate of the energy of the blast. His estimate turned out to be fairly close to the readings of more exact sensors.

19

I’ve always heard them referred to as Fermi problems, too, and the final answer isn’t necessarily a large number. The classic example is “How many professional piano tuners are there in Chicago?”.