If you don't like the math ... just scroll down to the results of the calculations at the bottom.
From the 4000 km diameter and the equation for the volume of a sphere, (4/3)(pi)r^3, I calculate the following for the volume of the chunk of diamond:
(4/3) x 3.14 x (4000km/2)^3 = 3.3 e 10 km^3
From Wikipedia I get the density of diamond, 3.5 g/cm^3
Getting the volume of the chunk of diamond into cubic centimeters and then using the density to determine the mass in grams I get:
3.3 e 10 km^3 x (1000 m / 1 km)^3 x (100 cm / 1 m)^3 = 3.3 e 25 cm^3
3.3 e 25 cm^3 x (3.5 g/cm^3) = 1.2 e 26 g (mass of chunk of diamond in grams)
1 carat is equal to 0.2 g:
1.2 e 26 g x (1 carat / 0.2 g) = 5.8 e 26 carats
So “Lucy in the Sky” is 5.8 e 26 carats or
580,000,000,000,000,000,000,000,000 carats
I was unable to find current values for uncut diamonds so just for the sake of argument, let’s say diamond goes for $5000 US per carat. That would mean, Lucy would be worth approximately
$2,900,000,000,000,000,000,000,000,000,000
post edited by quantumeffect - 2010/09/14 22:53:04