Let me work this one out very roughly. You can refine the numbers if needed. The redshift fraction is GM/Rc
2 where G is the universal gravitational constant, M is the mass of the sun, R is the Sun's radius, and c is the speed of light. How to work that out, given that I don't remember G, M, or R and don't want to Google around?
I do remember that it takes light about 8 min to get here from the sun. So the distance D to the sun is ~8 min*c. And you can see by eye that R is about D/220.
We also have that the acceleration of the earth toward the sun is 4π
2D/year
2=GM/D
2.
So GM/Rc
2= 220*GM/Dc
2= 240*4π
2D
2/year
2c
2= 220*4π
2(8min/yr)
2. So there you have it, ~ 2*10
-6. That's around a fifth of a second per day.
Mike W.
(published on 08/01/2012)
