Mathematics – Logic
Scientific paper
Dec 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006agufmsh43a1506r&link_type=abstract
American Geophysical Union, Fall Meeting 2006, abstract #SH43A-1506
Mathematics
Logic
1616 Climate Variability (1635, 3305, 3309, 4215, 4513), 1650 Solar Variability (7537), 5225 Early Environment Of Earth, 7537 Solar And Stellar Variability (1650), 7538 Solar Irradiance
Scientific paper
The "Faint Young Sun" has been a paradox of astrophysics. The standard solar model predicts that 4 billion years ago Earth was too cold to support life. Geology and the fossil record contradict this prediction. The paradox and possible solution are a fascinating combination of astrophysics, relativity and the Earth sciences. Models predict that 4 billion years ago the Sun shone with only 70 % of its present luminosity. Since power P is related to temperature T by the Stefan-Boltzmann Law P ∝ T4, Earth temperature would have been only 91 % of its present value. That temperature is approximately 283K, so temperature in the past would have been only 258K. Earth's surface would have frozen solid, making evolution of life very unlikely. Geology shows evidence of extensive sedimentation 4 billion years ago. Other geological markers corroborate the presence of liquid water on Earth during this period. Paleontology dates the earliest organisms at least 3.4 to 4 billion years old. Clearly liquid water and life both existed when the model predicts Earth was frozen solid. This conflict with observations is the Faint Young Sun paradox. Fortunately, Relativity and Space/Time can help save the standard solar model. The Sun converts its fuel to energy according to E=mc2. Unified Space/Time predicts that c is given by: GM=tc3. Where t is age of the Universe, GM combines its mass and gravitational constant. Solving, we have c(t)=(GM)^{1/3} t^{-1/3}. Billions of years ago, solar output and temperature were therefore higher than originally calculated. Earth is estimated to be 4.6 billion years and the Universe 13.7 billion years old, 1.5 times its age at the time of Earth's formation. Energy e=mc2 is adjusted by (1.5)^{2/3} = 1.31 times the initial estimate. Multiplying by that estimate of 70 %, the Sun's actual output was 0.917 of the present value. Temperature was then (0.917)^{1/4} = 98 % of today's value. If we start with an estimate of 76 %, the Sun's true output was exactly the present value. The "paradox" leads to an extraordinary confirmation of Theory. The solar constant may indeed be constant, allowing life to have evolved on Earth for billions of years. Prediction of a changing c can be more precisely corroborated using observations of Type Ia supernovae. Earth's temperature provides additional data points to supplement supernova data from a more distant past. This corroborating data distinguishes Theory from "accelerating universe" ideas. Theory also may help determine whether CO2 warmed Earth's temperature in the past. In conclusion, the "Faint Young Sun" is not a problem but a window from the Earth sciences to astrophysics and cosmology. Geology and the fossil record can help verify "fossil" values of fundamental measurements, determining whether those values are indeed constant.
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