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I am a newbie but as far as I understand that there are two sources of time dialations, one due to relativistic speeds and the other is due to gravitational field. If I look at these equations they do look pretty similar and if you solve it for v then you get the escape velocity, which seems not random.

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So, you need to match the exact time dilation of earth’s gravitional pull to escape from it.

So, my question is this the cause of escape velocity or something magically occur?

Qmechanic
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eonurk
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1 Answers1

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Light that is sent up redshifts.

redshift factor = energy factor (because E=hf)

redshift factor = time dilation factor (obviously)

Solving the above system of equations we get:

time dilation factor = energy factor

In the above time dilation meant gravitational time dilation.

Now let us show that: kinetic time dilation factor = energy factor

$E=\gamma mc^2$

$ t=\gamma t'$

Yes, the factor is $\gamma$

So now we understand that:

kinetic time dilation factor = ratio of energies

and

gravitational time dilation factor = ratio of energies

Oh yes, escape velocity is ratio of energies too:

kinetic energy / mass

stuffu
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