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Mikael17
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- TL;DR Summary
- time dilatation inside the sun
How can time dilation, lets say 500000 km inside the sun be calculated ?
Gravitational Time Dilation Inside the Sun
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In summary, "Gravitational Time Dilation Inside the Sun" explores how the intense gravitational field of the Sun affects the passage of time. According to general relativity, time runs slower in stronger gravitational fields, meaning that time experienced near the Sun is dilated compared to that on Earth. The paper discusses the implications of this phenomenon for understanding solar processes, such as nuclear fusion, and its significance in the context of astrophysics and cosmology. It emphasizes the relationship between gravity, time, and the fundamental nature of the universe.
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Using the appropriate spacetime metric, which i must admit I don't know. Try searching the Internet for it.
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Dale
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This would be the interior Schwarzschild metric:
https://en.m.wikipedia.org/wiki/Interior_Schwarzschild_metric
One of the assumptions is constant density, so that probably isn’t the best assumption, but it should be a reasonable approximation given the resulting simplification
https://en.m.wikipedia.org/wiki/Interior_Schwarzschild_metric
One of the assumptions is constant density, so that probably isn’t the best assumption, but it should be a reasonable approximation given the resulting simplification
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Ibix
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To do much better you'd need a density and pressure profile, and I would suspect you'd have to do it numerically. Especially if you stopped pretending it was a non-rotating sphere.Dale said:
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Dale
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Yes. I agree that anything more exact than this would probably have to be numerical.Ibix said:
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Hill
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Here is a "recipe" from MTW's Gravitation:
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Ibix
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Is ##n## (23.28c and d) defined somewhere? Number density of particles?
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Hill
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Here:Ibix said:
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Ibix said:
Dale said:
The weak field approximation is going to be way more accurate than the interior Schwarzschild metric in this case. Input a solar model for the density and voila.Dale said:
(I actually did this computation not too long ago for a cosmology course I took for undisclosed reasons. The teacher was somehow surprised when I used the standard solar model for the density profile
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Dale
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I have to admit that it didn’t even occur to me!Orodruin said:
FAQ: Gravitational Time Dilation Inside the Sun
What is gravitational time dilation?
Gravitational time dilation is a phenomenon predicted by Einstein's theory of General Relativity, where time passes more slowly in stronger gravitational fields. This means that closer to a massive object, such as the Sun, time would pass more slowly compared to a region with weaker gravitational fields.
How significant is gravitational time dilation inside the Sun?
Gravitational time dilation inside the Sun is relatively small but measurable. Due to the Sun's mass, the time dilation effect at its core is more pronounced than at its surface. However, the difference is not extremely large because the Sun's gravitational field, while strong, is not as intense as that of more massive objects like black holes.
How is gravitational time dilation calculated inside the Sun?
Gravitational time dilation can be calculated using the formula derived from General Relativity: \( t_0 = t_f \sqrt{1 - \frac{2GM}{rc^2}} \), where \( t_0 \) is the time experienced at a distance \( r \) from the center of the Sun, \( t_f \) is the time experienced far away from the Sun, \( G \) is the gravitational constant, \( M \) is the mass of the Sun, and \( c \) is the speed of light. The closer you are to the Sun's core, the more pronounced the effect.
Does gravitational time dilation affect nuclear reactions in the Sun's core?
Gravitational time dilation does affect the rate at which time passes for nuclear reactions in the Sun's core, but the effect is extremely small. The nuclear reactions proceed at nearly the same rate as they would if there were no time dilation, because the difference in time passage is minimal compared to the overall timescale of these reactions.
Can we observe the effects of gravitational time dilation from Earth?
The effects of gravitational time dilation inside the Sun are too small to be directly observed from Earth with current technology. However, time dilation effects can be observed in other astrophysical contexts, such as near black holes or neutron stars, where the gravitational fields are much stronger and the effects are more pronounced.