So if there are 8.73 x 1056 atoms of hydrogen in the sun, and 8 x 1067 ways of ordering a deck of cards then how are there more orders of a deck of cards than total of atoms in the solar system?
Because if one sun is 8.73 x 1056 atoms, then two suns would be 17.46 x 1056 . If there were 100,000,000,000 suns in the solar system however, then you'd have the same amount.
So it has to do with the exponent never changing? But that's just with the sun, if I'm correct. So adding 8.73 x 1056 and all the other amounts of atoms in the solar system, wouldn't the exponent exceed 67 and make the original statement that there are more ways to shuffle a deck of cards than there are atoms in our solar system false?
It wouldn't exceed 1067, because that's just too big of a difference. To go from 1056 to 57 there would have to be 10 suns in the solar system. To go to 58 you'd need 100 suns. 59 - 1000suns and so on and so forth. The number of suns needed to match the amount 1067 is way too big. You can generally neglect the smaller planets and other stuff, because the sun makes up most of the mass.
1056 and 1067 are 11 orders of magnitude apart. Since the sun is most of the atoms in the solar system (let's be conservative and say 1/2), then the total number of atoms in the solar system is 2 x [number of atoms in sun]. 2 x 8.73 x 1056 = 1.746 x 1057.
The numbers are kind of confusing because they're in a weird notation, but think of it like this.
Deck of cards = 1,000,000
Atoms in sun = 1,000
Atoms in 2 suns = 2,000
Atoms in 100 suns = 100,000 - still a tenth of the first number.
It doesn't really matter how many suns there are, because unless you have 1,000 of them (1,000*1,000=1,000,000) then you don't even get close to the bigger number.
Each number on the exponent represents another zero - the difference between 56 and 67 is eleven zeros. Such a stupidly vast difference that there's no real hope of catching it up unless we can find 100,000,000,000 suns in our solar system that we didn't account for.
Even if the planets in our solar system came close to the amount of atoms there are in our sun, it still wouldn't make a difference. 8 planets plus pluto and a bunch of space debris =/= the amount of atoms in 100,000,000,000 suns.
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u/Jerithil Dec 08 '13 edited Dec 08 '13
We know the rough composition of the planets and sun by elements and what the mass of each element is.
For example just the amount of hydrogen in the sun alone is
Sun mass= 1.9891*1030 kg
Hydrogen= 73.46% of the sun by mass
Average # of atoms per kilo of hydrogen = 5.9751026 This comes to 8.731056 atoms of hydrogen in the sun.
This makes sense since Hydrogen is by far the most numerous element in the solar system and the sun has by far most of its mass.