# I Math doesn't add up: stars + planets < particles in universe?

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1. Apr 16, 2017

### Travois

I see they finally counted all the particles in the universe, it's10 to power of 80

They also counted all the planets: 10 to power of 24
and also counted all the stars: 10 to power of 24
and also counted all the atoms in the Earth: 1.3 x 10 power of 50

Good work everyone!

Now, I'm trying my hand at some of this math: multiplying atoms on Earth (10^50) * number of planets (10^24) * number of stars (10^24) which is 1 x 10^98.....So I'm out by a tiny bit.....please help me figure out where my math is wrong, or, why the discrepancy, or, maybe I've calculated an even more accurate number of particles in the universe!???

Cheers and thanks!

2. Apr 16, 2017

### davenn

care to share the "reliable" source for this info ?

3. Apr 16, 2017

### Travois

4. Apr 16, 2017

### dkotschessaa

Surely you got the information from somewhere. Usually if somebody asks for your sources it's polite to give them the sources rather than to ask them to google it.

It's not really a bad problem you propose, but lets find some place where we can get some decent numbers or find out where your other sources may have gone wrong.

5. Apr 16, 2017

### jbriggs444

If you want the number of atoms in planets throughout the [observable] universe then you should not multiply by the number of stars.

Based on the figures given, the average number of planets per star is one.

6. Apr 16, 2017

### Travois

--------Isn't that interesting that the estimate for planets and stars in the universe is a 1:1 ratio?

Ah, thanks, jrbriggs444, I was multiplying total particles of stars and planets instead of adding them. Here's my revised math, for curiosity's sake. I arrived at the right answer, or at least close enough, thanks for your correction.

All the numbers I'm listing are actually estimates, and the wording in my original question is also (attempting to be) humorous given the nature of trying to consider this sort of calculation. Sorry for any confusion there. Also note this is based on the finite or observable universe.

The main number I find fascinating to consider is the estimated number of particles in universe, 1x10^80 (http://www.physicsoftheuniverse.com/numbers.html). Also:

"The commonly accepted answer for the number of particles in the observable universe is 10^80. This number would include the total of the number of protons, neutrons and electrons." Frank Heile, P.h.D. Physics, Stanford University. In Quora (https://www.quora.com/How-many-particles-are-there-in-the-universe)​

Compare that to the number of molecules in a drop of water, which is 10^23. (https://www.thenakedscientists.com/.../drop-water-contains-one-molecule-litre-water-eart...)

I'll open up / rephrase the original question again:

When I add up all the estimates for particles in the planets and stars in the observable universe, I get a lower number than the given estimate for total number of particles in the universe. Why is this? Where is my math wrong, or what adjustments are being made in arriving at this figure? Is it in mixing up terms in atoms vs particles?

Thanks for the correction jbriggs444. I was multiplying stars and planets instead of adding.

First:
Add together total particles in planets and stars:
Particles in Earth: 10^49
Number of planets in universe: 10^24
Particles in Sun: 10^57
Stars in Universe: 10^24

(particles making up a planet * number of planets ) + (particles making up a sun * number of stars)
(10^49 * 10^24) plus (10^57 * 10^24)
10^73 plus 10^81
which is still basically 10^81 (i.e. 1.0000001 x 10^81)

That's a little bit greater than the estimate. I'm close enough for immediate needs.

I've also seen 10^89 proposed, using photons in the estimate, I'm not sure how to explain that one.

7. Apr 16, 2017

### phyzguy

There are ~10^9 photons in the universe for each baryon. That's where this estimate comes from. You can arrive at this number by counting the photons in the CMB radiation and comparing to your estimate of number of baryons.

8. Apr 16, 2017

### Chalnoth

It's not the number of planets times the number of stars. There aren't $10^{24}$ planets per star, but close to $10^{24}$ planets in the entire universe.

So a (somewhat) more reasonable calculation would be:
Atoms on Earth ($10^{50}$) * (number of planets ($10^{24}$) + number of stars ($10^{24}$)) $\approx 10^{74}$.

However, there's another error in your calculation: stars don't have the same number of atoms as planets. Our own Sun, for example, has on the order of a million times as many atoms as the Earth. Since most stars are low-mass stars, let's assume that stars typically have 100,000 times as many atoms as the Earth. With this, we can completely ignore the number of atoms in planets, and just write:

Atoms on Earth ($10^{50}$) * star/planet ratio ($10^5$) * Number of stars ($10^{24}$) $\approx 10^{79}$.

This gets us about as close as we could expect to be with this kind of very rough calculation. But there's also the fact that most of the matter in the universe has never collapsed into stars or planets, so that there's a fair amount more than $10^{79}$ atoms in total.

All that said, it's not hard to calculate the approximate number of atoms in the observable universe if you just make use of the CMB data to determine the matter density and from that calculate the approximate number density (to a very good approximation, the matter in the universe is 75% hydrogen and 25% helium), then multiply by the volume of the observable universe.

9. Apr 17, 2017

### newjerseyrunner

Correct me if I'm wrong, but isn't the mass of the [baryonic] interstellar medium fairly significant? I can't find an actual number for how much it is, but googling gives me a range from ISM being 5% the mass of the galaxy to it being the majority.

10. Apr 17, 2017

### phyzguy

This is what Chalnoth means when he says, "But there's also the fact that most of the matter in the universe has never collapsed into stars or planets...". Adding in the ISM will bring the 10^79 up to 10^80 or so, which is the "accepted" number. These are just order of magnitude estimates after all.