16th February 2007 - 04:20 AM
1) That's the age of the universe, not the Earth. The age of the Earth is about 5.5 billion years.
2) In SI units, the "Dark Energy Density", ρΛ, works out to be about: (0.685±0.055)×10^−26 kg/m³ (relative error = 0.09)
3) In SI units, the Age of the universe, t0, works out to be about: (4.33±0.04)×10^17 s (relative error = 0.011)
4) In SI units, the Gravitational constant, G, is about (6.6742±0.0010)×10^−11 m³/kg/s² (relative error = 0.00015)
So if t0 = k/sqrt(G×ρΛ) then k = t0×sqrt(G×ρΛ) = 0.29 with a relative error of 0.046 = 4.6%, so it's over 50 standard deviations from π.
Now it's still close because H0, the Hubble constant, is close to 1/t0 and in certain geometric units, the critical density of the universe is close to H0, and by measurement ρΛ is between 0.7 and 0.78 times this critical density, but it's nothing mystical.http://en.wikipedia.org/wiki/Lambda-CDM_modelhttp://lambda.gsfc.nasa.gov/product/map/cu...ibliography.cfmhttp://pdg.lbl.gov/2006/reviews/consrpp.pdf