Monday, 14 November 2011

Golden Planets -- Final Result

For those of you following the story of the 200 million golden planets, I have added an Addendum to the post When This Old Hat Was New (posted on 10/11/2011).

To save you the trouble, here is the quote that sparked the enquiry:
A few years before Franklin drafted his will, philosopher Richard Price rhapsodized in a sober treatise on the national debt, “One penny, put out at our Savior’s birth to 5 percent compound interest, would, in the present year 1781, have increased to a greater sum than would be contained in two hundred millions of earths, all solid gold. But, if put out to simple interest, it would, in the same time, have amounted to no more than seven shillings and sixpence.”
My challenge was this: "That's surely the 18th century equivalent of Hunter S. Thompson-esque 'gonzo journalism' -- too much coffee and snuff, probably. Can anyone out there do the maths?"

Well, here is the answer, provided by old friend Andy S., a.k.a. Science Man:

1d invested for 1780 years at 5% would yield 1 x 1.05^1780 = 5.2 x 10^37 d

Price of gold was fixed by Isaac Newton in 1717 at £4 8s 9d per Troy ounce (it stayed this way for about 200 years)

1 Troy ounce = 31.03g

Therefore price of gold = 4x240 + 8x12 + 9 d/Troy ounce = 1065 d/Troy Ounce

1065d/31.103g = 34.32d/g = 34,320d/kg

Therefore 5.2 x 10^37d could buy (5.2 x 10^37)/(34320) kg of gold = 1.52 x 10^33 kg

The Mass of the Earth is about 5.978 x 10^24 kg (OU Science Data Book 1978)

Therefore 1.52 x 10^33 represents (1.52 x10^33)/(5.978 x 10^24) Earth Masses = 2.54 x 10^8 Earth Masses

i.e. about 250 million Earth Masses (at 1780 Gold Prices)

How about that? Thanks, Science Man! Seems it wasn't the snuff talking, after all.

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