The gravity forces on Earth and Sun is different and in Interstellar, they said something like high gravity slows time. So if we say Sun is N billion years old, that must be earth time but on Sun's own clock, it may be much less.
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1$\begingroup$ It Is less, but not much less. $\endgroup$– Leos OndraDec 21, 2022 at 7:05
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$\begingroup$ @LeosOndra About 2 microseconds per second slower, so not that much. $\endgroup$– David HammenDec 21, 2022 at 23:54
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$\begingroup$ Possibly of interest would be the timescales used to account for the relativistic effects of Earth's movement around the Sun, and the gravity of the Solar System. Barycentrict Dynamic Time, and Barycentric Coordinate Time. $\endgroup$– Greg MillerDec 24, 2022 at 15:22
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1 Answer
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Escape velocity from the surface of the Sun is 617.6 km/sec, or about 0.00206 times the speed of light. Denoting this ratio (escape velocity / speed of light) as $\beta$, time dilation at the surface of the Sun is $1-\sqrt{1-\beta^2}$. Thus time dilation at the surface of the Sun makes a clock at the surface of the Sun tick slower than a clock far from the Sun by about a minute (67 seconds) per year, or by about 10000 years during the 4.6 billion years over the Sun has existed. Note that that 10000 years is less than the uncertainty in the Sun's age.
answered Dec 21, 2022 at 7:24
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2$\begingroup$ +1 for a nice clean and informative answer! For those who'd like to read further about what happens to things orbiting close to the Sun: Parker Solar Probe passing extremely close to the Sun; what relativistic effects will it experience and how large will they be? $\endgroup$– uhohDec 21, 2022 at 21:46