Hi Cecil,
For most of my 75 years I’ve heard that there are more stars in the universe than grains of sand on all the beaches on Earth. Perhaps so, but what are those numbers, who calculated them and how, and how widely accepted are they by the scientific community?
Aloha, Leroy Syrop
I wondered how many grains of sand there are on Earth.
A link there points to a NASA page that says there are approximately 10[sup]21[/sup] stars in the universe. Squink supposed 1.08320732 × 10[sup]30[/sup] particles if the entire Earth were broken up into 1 mm bits.
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For all my slightly fewer years I have heard no two snowflakes are alike,
Why?
Assuming it is all just water and hydrogen, how many different crystalline structures can they form?
Achimedes had an amazingly modern attempt at this sort of thing way back when. Based on several assumptions of the size of the Universe, he calculated how many grains of sand it could contain. Pretty sophisticated stuff, involving the invention of very large numbers. Just Google on “The Sand Reckoner” to read it.
Note, however, that only a minute proportion of the total Earth actually is broken up into sand-grain-sized pieces.
The OP clearly asked for grains of sand on the beach, while Johnny LA inquired about the grains of sand on earth. I am shocked at the oversight.
Volume of sand on 1 meter of coastline: Assume it’s 64 cubic meters of sand.
Number of sand grains in 64 cubic meters: 512,000,000,000
http://www.6footsix.com/my_weblog/how-many-grains-of-sand-i.html
Coastline on earth: 534,000 miles
Meters per mile: 1609 meters
5340001609 512000000000 = 439913472000000000000
or
4.39913472e20
“A link there points to a NASA page that says there are approximately 10^21 stars in the universe.”
So, yeah, I guess there are more stars than grains of sand on all the worlds beaches, by perhaps an order of magnitude or more. I geared my calculations to over-estimate the amount of sand, but I daresay there are probably more sand grains in the Sahara alone than there are stars in the universe.
You lost me. How is 4 x 10^20 an order of magnitude larger than 10^21?
The 4*10^20 is the calculation for the sand on the worlds beaches, which Measure is saying is smaller than the number of stars in the Universe.
However, there is a further guess that the grains of sand in the Sahara does exceed 10^21, due to the area being considerably larger than the area of the worlds beaches, but Measure does not provide a calculation for this.
OP leroysyrop-
Welcome to the board.
The OP asked about beaches, not sand on earth. So there are 2.5 times more stars than grains of sand.
Precisely.
At what level of detail are you measuring this meter of coastline?
I’m shocked, SHOCKED!, by the oversight of Dopers in regards to the OP! The OP clearly asked how those numbers are calculated and having answered the sand question, I hope someone can now answer how they found out there were that many stars. I’m assuming it’s more advanced work than simply some guy counting stars while staring through a telescope 
To determine the number of stars in a galaxy we use the Milky Way as a typical galaxy. We know that the galaxy consists of stars and star-like objects (white and brown dwarfs, black holes, etc. , gaseous nebulae, and a significant amount of dark matter.
However, the vast majority of the visible light produced in the galaxy comes from stars. We have a fairly good model of the distribution of different classes of stars and the amount of light produced by each type.
Knowing the total amount of light produced by the galaxy (called luminosity) and knowing the amount and distribution of (non-dark matter) mass the galaxy contains (which can be determined by measuring the galaxy’s diameter and rotation rate), we can estimate the number of stars the galaxy contains.
This is a relatively straightforward process for nearby galaxies and progressively more difficult at greater distances. At each step some assumptions must be made: the primary one being that, at large enough scales, the universe is homogeneous.
Obviously any numbers you can find are broad estimates – so a set of calculations that suggest a factor of 2.5 between the number of sand grains and the number of stars is the same as saying that, for all intents and purposes, the numbers are indistinguishable.
I’m sorry if I confused the issue with my previous question. As noted, the OP asked about sand on the beaches. I was asking about all of the sand on the planet.
Actually, the Milky Way is a bit on the large side as spiral galaxies go, and spiral galaxies are all much larger than the much more common dwarf elliptical galaxies. A better estimate would use a several typical dwarf ellipticals to get an average for them, then several spirals, then several giant ellipticals, and then take a count of each type of galaxy.
Well, I’m not going to be any help, I always fall asleep before I’m done counting…
Does the calculation of number of grains of sand allow for “packing factor.” I’d assume that could be as high as 50%, although it wouldn’t change the conclusion.
In an infinite universe, shouldn’t there be infinite stars?