GR - time dialation at center of a planet

In summary, the gravitational force at the center of a planet is zero, but the gravitational potential energy is at a peak minimum. This means that the clock rate at the center of the planet will be slower compared to the clock rate at the surface due to the difference in potential energy. The amount of gravitational "force" does not directly affect time dilation, it is the difference in potential that determines it.
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The gravitational force is zero at the center of a planet, but the GPE is at a peak minimum (most negative). What happens to the time dilation factor inside the surface of a planet of uniform density versus at the surface of that planet.?
 
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Jeff Reid said:
The gravitational force is zero at the center of a planet, but the GPE is at a peak minimum (most negative). What happens to the time dilation factor inside the surface of a planet of uniform density versus at the surface of that planet.?

Gravitational potential minimal -> clock rate minimal

Here is a visualization of the complete Schwarzschild metric (interior + exterior combined):

http://www.adamtoons.de/physics/gravitation.swf
 
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Jeff Reid said:
The gravitational force is zero at the center of a planet, but the GPE is at a peak minimum (most negative). What happens to the time dilation factor inside the surface of a planet of uniform density versus at the surface of that planet.?
A clock at the center of a planet will run slow relative to a clock at the surface (neglecting rotational effects). Time dilation isn't caused by gravitational "force", it's the result of the difference in potential. Any object in between the surface and center of a planet would "freefall" toward the center in the absence of the forces acting on it (like the material resistance of the mass of the planet).

Light traveling toward the center would blueshift, and light traveling away from the center would redshift, just like it would above the surface. That's what determines gravitational time dilation, not the amount of gravitational "force" acting on the clock.
 
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Thanks for the responses.
 

FAQ: GR - time dialation at center of a planet

What is time dilation at the center of a planet?

Time dilation at the center of a planet is a phenomenon predicted by Einstein's theory of general relativity, which states that time moves slower in areas with strong gravitational fields. This means that time will pass at a slower rate at the center of a planet compared to its surface or outer atmosphere.

How does gravity affect time at the center of a planet?

Gravity is directly related to the curvature of space-time, and it is this curvature that causes time dilation at the center of a planet. The stronger the gravitational pull, the greater the curvature, and the slower time will pass.

Can we observe time dilation at the center of a planet?

Yes, we can observe time dilation at the center of a planet through experiments and observations. For example, atomic clocks placed at different altitudes on Earth have shown that time moves slower at higher altitudes, where the gravitational pull is weaker.

Does time dilation at the center of a planet have any practical applications?

Yes, time dilation at the center of a planet has practical applications in areas such as satellite navigation and space travel. The effects of time dilation must be taken into account when calculating precise coordinates for GPS systems, and it can also affect the timing of space missions.

Is time dilation at the center of a planet the same as time dilation in space?

No, time dilation at the center of a planet is not the same as time dilation in space. In space, time dilation is caused by the speed at which an object is traveling, whereas at the center of a planet, it is caused by the strong gravitational field. However, both can result in time passing at a slower rate compared to an observer in a different reference frame.

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