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A clock on the surface of the Earth (assuming it does not rotate) will accumulate around 0.0219 seconds less than a distant observer over a period of one year (assuming the observer is using Schwarzschild coordinates).

In comparison, a clock on the surface of the sun will accumulate around 66.4 seconds less in a year.

How is this possible and what causes this phenomenon.

Reference: Wikipedia

The formula for calculating the time dilation caused by a non-rotating mass is

$$ t_o = t_f \sqrt{1 - \frac{2GM}{c^2r}} = t_f \sqrt{1 - \frac{r_s}{r}} $$

where:

$t_0$ is the proper time between events A and B for a slow-ticking observer within the gravitational field

$t_f$ is the coordinate time between events A and B for a fast-ticking observer at an arbitrarily large distance from the massive object

$G$ is the gravitational constant

$M$ is the mass of the object creating the gravitational field

$r$ is the radial coordinate of the observer (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate),

$c$ is the speed of light

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closed as unclear what you're asking by Danu, John Rennie, ACuriousMind, Kyle Kanos, Jim Aug 20 '14 at 13:18

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ You seem to just be copying wikipedia. What are you confused about? $\endgroup$ – Danu Aug 20 '14 at 10:07
  • $\begingroup$ Are you asking how your equation is derived, or are you asking what the physicial origin of the time dilation is? $\endgroup$ – John Rennie Aug 20 '14 at 10:10
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    $\begingroup$ Your 0.0219 seconds per year is off by a good deal. It's about 0.49 seconds per year. You missed two effects that are much larger effects than the Earth's gravitation. We're orbiting the Sun at 30 km/s at about 1 AU from the Sun. The special and general relativistic effects from this orbit are responsible for the bulk of the time dilation. The Earth's gravitational field, not so much. $\endgroup$ – David Hammen Aug 20 '14 at 11:29
  • $\begingroup$ This is your second "Why?" type question in rather short order. That's not the best approach to learning physics. $\endgroup$ – David Hammen Aug 20 '14 at 11:31
  • $\begingroup$ Yes John I am mostly wondering about the physical origin of gravitational time-dilation. I have come across the reply that 'Why' is outside the domain of physics but I was wondering if there are any speculative theories or thought experiments or explanation of probable theories (not yet accepted by Science faculty). $\endgroup$ – Vanita Ashar Aug 20 '14 at 12:39