Because I could
In a recent article on slashdot, the subject came up as to why this was a story, since the 300 million year old spiders were only the size of a 50p piece. Someone commented that due to inflation, they'd actually be the size of some pretty big boulders of gold. In the name of science, I decided to work out exactly how big.
Price of gold = £9.80/g, density of gold = 19.3g/cm^3, atomic weight of gold = 196.97g/mol. So 50p of gold has a mass of 0.5/9.8 = 0.051g, a size of 0.051/19.3 = 2.64x10^-3cm^3 or 2.64x10^-9m^3, this lump of gold has 0.051/196.96xL = 1.56x10^20 atoms (L is Avogadro's constant).
Now, how much inflation to use? 5% per year for 300 million years overflows GNU Octave, so let's go for a smaller amount. How about 0.0001%? 300 million years of (pretty rubbish) inflation at 0.0001% is an increase by a factor of 1.000001^(3x10^8) = 1.942x10^130. So the 50p piece of gold is now 5.134x10^121 m^3, and contains 3.030x10^150 atoms.
The universe is estimated to have a diameter of 7.8x10^10 light years, and about 10^80 atoms. So the lump of gold has 3.030x10^70 times as many atoms as the universe. Of course space is pretty sparse, so let's work out how big this boulder is going to be.
Let's assume the gold hasn't collapsed in on itself, but has instead formed a gold ball. It will have a diameter of 2*(.75/pi*5.134x10^121)^(1/3) = 4.611x10^40m, or 4.874x10^24 light years. This is 6.249x10^13 times or 62.5 trillion (that's 62.5 billion in traditional maths) times the size of the universe. That's how big our prehistoric spiders were.
At this point a physicist can take over and tell me exactly what happens when you have a boulder of gold 6.25x10^13 times the size of the universe floating around in space.
Just to reassure people, if the inflation was only 0.000001% per year, then the spiders would only be 20 times the size.
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P.S. What's this new LJ guests thing that just popped up. Should I be worried?
Price of gold = £9.80/g, density of gold = 19.3g/cm^3, atomic weight of gold = 196.97g/mol. So 50p of gold has a mass of 0.5/9.8 = 0.051g, a size of 0.051/19.3 = 2.64x10^-3cm^3 or 2.64x10^-9m^3, this lump of gold has 0.051/196.96xL = 1.56x10^20 atoms (L is Avogadro's constant).
Now, how much inflation to use? 5% per year for 300 million years overflows GNU Octave, so let's go for a smaller amount. How about 0.0001%? 300 million years of (pretty rubbish) inflation at 0.0001% is an increase by a factor of 1.000001^(3x10^8) = 1.942x10^130. So the 50p piece of gold is now 5.134x10^121 m^3, and contains 3.030x10^150 atoms.
The universe is estimated to have a diameter of 7.8x10^10 light years, and about 10^80 atoms. So the lump of gold has 3.030x10^70 times as many atoms as the universe. Of course space is pretty sparse, so let's work out how big this boulder is going to be.
Let's assume the gold hasn't collapsed in on itself, but has instead formed a gold ball. It will have a diameter of 2*(.75/pi*5.134x10^121)^(1/3) = 4.611x10^40m, or 4.874x10^24 light years. This is 6.249x10^13 times or 62.5 trillion (that's 62.5 billion in traditional maths) times the size of the universe. That's how big our prehistoric spiders were.
At this point a physicist can take over and tell me exactly what happens when you have a boulder of gold 6.25x10^13 times the size of the universe floating around in space.
Just to reassure people, if the inflation was only 0.000001% per year, then the spiders would only be 20 times the size.
--
P.S. What's this new LJ guests thing that just popped up. Should I be worried?