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

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


$t_0$ 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


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

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  • $\begingroup$ 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
  • 1
    $\begingroup$ 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