# Sun's Gravitational Redshift

*Most recent answer: 08/01/2012*

Q:

time moves slower on the sun because of its massive gravity but by how much. if i spent a day stood on the sun how much more time would have past on the earth

- andrew (age 40)

lincoln england

- andrew (age 40)

lincoln england

A:

Let me work this one out very roughly. You can refine the numbers if needed. The redshift fraction is GM/Rc

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

So GM/Rc

Mike W.

^{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

^{2}D/year^{2}=GM/D^{2}.So GM/Rc

^{2}= 220*GM/Dc^{2}= 240*4π^{2}D^{2}/year^{2}c^{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)*