A Time Dilation in Gravitational Fields: Are Equivalent Formulas?

[Emmacastellano80]

TL;DR Summary

I was trying to understand the topic of time dilation in a gravitational field, and I found these two formulas:
http://it.tinypic.com/r/1124ha0/9

http://it.tinypic.com/r/1z22l53/9

G = constant grav.
m = mass of the planet or star under consideration
g = 9.81m / s ^ 2
H = height at which the second clock is located with respect to the first which is on the ground.

My question is :
are these two formulas equivalent?

I was trying to understand the topic of time dilation in a gravitational field, and I found these two formulas:


G = constant grav.
m = mass of the planet or star under consideration
g = 9.81m / s ^ 2
H = height at which the second clock is located with respect to the first which is on the ground.

My question is :
are these two formulas equivalent?

 

[Ibix]

No. They apply in completely different circumstances. One gives the symmetric time dilation effect between observers in relative motion in flat spacetime, the other the asymmetric time dilation between hovering observers in curved spacetime.

Edit: to save people clicking on the image with annoying ads, the two equations are the Lorentz gamma factor, $1/\sqrt{1-v^2/c^2}$, and the gravitational time dilation factor between an observer at rest at infinity and another hovering at $r$ in Schwarzschild spacetime, $1/\sqrt{1-2GM/c^2r}$.

 

[Ibix]

Oh, and the third formula is the time dilation effect in a uniformly accelerated rocket. So it's possible I'm misinterpreting which two formulae are being talked about.

Which two formulae are you asking about? It would be easier if you used LaTeX to type out the maths. There are instructions in a link just below the reply box.