Calculating Time Deviation Inside the Sun

[Bjarne]

How much slower is time ticking inside the Sun, compared to the surface, and how can it be calculated?

 

[HallsofIvy]

How far inside the sun? The rate at which time moves depends upon the gravitational force at the point and that varies from the value at the surface to 0 at the center.

 

[George Jones]

Use the Sun instead of the Earth in

https://www.physicsforums.com/showthread.php?p=1543402#post1543402.

 

[Bjarne]

The math shown at the link below is above my head, but i guess the time diviation inside the Sun must be about 300000 times larger inside as inside the Earth (the mass difference between the sun and the Earth) ?
https://www.physicsforums.com/showthread.php?p=1543402#post1543402

 

[JesseM]

The math shown at the link below is above my head, but i guess the time diviation inside the Sun must be about 300000 times larger inside as inside the Earth (the mass difference between the sun and the Earth) ?
https://www.physicsforums.com/showthread.php?p=1543402#post1543402

No, time dilation isn't proportional to mass difference in that way. Just use the following equation from George Jones' link, giving the ratio of a clock at the center to a clock at the surface:

$$\frac{d\tau_{centre}}{d\tau_{surf}}=\left( \frac{d\tau_{centre}}{dt}\right) \left( \frac{d\tau_{surface}}{dt}\right)^{-1} =\frac{\frac{3}{2}\sqrt{1-\frac{2GM}{c^{2}R}}-\frac{1}{2}}{\sqrt{1-\frac{2GM}{c^{2}R}-v^{2}}}$$

With G=the gravitational constant (6.67428 *10^-11 m^3 kg^-1 s^-2), M=mass of the Sun (2 * 10^30 kg), R=radius of the sun (6.955 * 10^8 m), c=speed of light (299792458 m s^-1), and v set to zero (assuming someone at rest on the surface). There's an online calculator http://www.math.sc.edu/cgi-bin/sumcgi/calculator.pl if you need it.