I am having troubles with the gravitational time dialtion equation.

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Discussion Overview

The discussion revolves around the gravitational time dilation equation and its application to the sun's gravitational effects on nearby objects. Participants explore the implications of the equation, particularly in scenarios involving distances close to the Schwarzschild radius.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant attempts to apply the gravitational time dilation equation but encounters nonreal answers when calculating time changes at a distance of 20 meters from the sun.
  • Another participant clarifies that the radius in the equation must be measured from the center of the sun, which is approximately 700,000 km, suggesting that distances less than this are not valid.
  • There is a question about whether the equation fails when applied to black holes, particularly if the sun were to become denser and its radius decreased significantly.
  • Participants discuss the limitations of the time dilation formula, noting that it is applicable only for objects outside the event horizon of a black hole.
  • One participant raises a point about the treatment of black holes, questioning whether they should be considered as points when close to the Schwarzschild radius.

Areas of Agreement / Disagreement

Participants generally agree that the radius must be greater than the Schwarzschild radius and that the time dilation formula has limitations when applied to black holes. However, there is no consensus on the implications of these limitations or the treatment of black holes in this context.

Contextual Notes

The discussion highlights the dependence on definitions of radius and the conditions under which the gravitational time dilation equation is valid. There are unresolved questions regarding the behavior of the equation near the Schwarzschild radius.

zeromodz
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Okay, I am just fooling around with the equation

Δt' = Δt * √( 1 - 2GM/RC^2)


To find out the suns gravitational effects on close ojbects
I keep getting a nonreal answer. I can derive the equation to this.

Δt' = Δt * √( 1 - (Schwarzschilds Radius)/R)


The suns Schwarzschilds radius of the sun is is 2954.14m
So if I want to see how much time will change in 30 seconds from 20 meters away I do
30*√(1-2954.14/20)

Then i get a non real answer. What am I doing wrong. Does this equation just have a limit from certain distances or does it just break the laws of physics if an objects time slows down from 20 meters away. If I am not doing anything wrong, could someone give me an equation that works for this stuff.

Thanks in advanced.
 
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Radius is calculated from the center of the sun. So you cannot have radii that are less than what the radius of the sun is, which is something like 700 000 km.
 
R is your distance from the centre of the sun
 
So does that mean this equation fails when dealing with black holes? What if the sun were to become really dense and the radius shrinks to a more plausible number like 100 meters. Would this equation still fail?
 
The radius won't drop below the Schwarzschild radius nor will another object be able to reach a distance from the Radius less than the S-radius.
 
The time dilation formula you used is for objects hovering outside the event horizon of a black hole. You cannot hover inside the event horizon of a black hole.
 
I suspect the black hole should not be treated as a point when close to the S-Radius. Is this correct?
 

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