Bob the Unbeliever
Well-Known Member
So far, I have discussed several methods for determining the age of the earth. There is another highly informative manner by which one can independently determine the age of the solar system, that is by calculating the age of the sun itself. Here is how it goes,
1) The abundance of Helium and Hydrogen at the sun's core is determined by Helioseismology (LINK). It's a technique where the Shockwaves in the sun are used to calculate composition, density etc. It is found that whole Helium is at 27% by mass in most of the sun, near the core it rises rapidly to peak at about 65% at the center.
2) The reason for this increasing Helium is nuclear fusion, the primary driver of sun's energy. This process consumes 4 hydrogen atoms to make one helium atom releasing 26.7 MeV of energy in the process per reaction.
3) The rate of radiation energy from the sun can be determined by instruments on ground or in satellites. Sun is radiating energy at 3.9*10^26 Watts.
4) Fusion reaction only occurs at the core of the Sun. Helium concentration both at the Sun's outer surface and in Jupiter provide the initial concentration of Helium in the solar nebula our of which Sun formed. The two data values match and from this we deduce that initial He concentration was 27%
5) From Helioseismology it follows then that 4.2% of Sun's mass is from Helium produced internally at the core by fusion.
6) 1 MeV = 1.6*10^(-13) joules
So rate of Helium conversion happening at the core =Energy Radiatoated by sun in a second/ Energy released per Helium nuclei formef
= 3.9*10^26/(26.72*1.6*10^-13) = 9.1*10^37 helium nuclei formed per second.
Mass of Helium nuclei is 6.64*10^-27 kg.
Mass of Sun is 1.99*10^30 kg
7)Assuming a highly simple model where the sun has produced Helium at this steady rate always and sun has not lost much mass due to radiation etc.
Age of sun = Total Mass of Helium produced by fusion over time/Mass of Helium produced per second
=(0.042*1.99*10^30 kg) /(6.64*10^-27*9.1*10^37 kg/s)
= 1.4*10^17 seconds
= 4.4 billion years.
More precise models give the date to be 4.6 billion years, so we are not too far off using such simple calculations.
Thus along with the consistent values from multiple radioactive decay based age data for Earth, moon, Mars and meteor rocks; we now have an entirely independent nuclear fusion based data for age of the Sun that also matches the age calculations.
Brilliant analysis. Kudos, man! I'm literally in awe.