What is the connection between time dilation and gravity?

[the_truth]

I asked a question concerning this subject once but the discussion dissolved into petty quibbling and I saw no links or evidence to back up or help me understand any of the statements made.

What is the relationship between time dilation and the effect of gravity?


This was my original post.

Time dilation relationship between gravity and velocity.
Spaceships A and B synchronise their atomic clocks and then perform an activity

:Spaceship A accelerates to 0.9999 times the speed of light in relation to spaceship B. Time in spaceship A will be observed by spaceship B to be running slower by the factor

(Va^2/C^2)^-0.5=Tb/Ta

Where Tb/Ta is the ratio of Tb compared to Ta and Va is the velocity at which spaceship A has accelerated from B. In this case

Tb/Ta = 1.00010001, so time at spaceship B is going 1.00010001 times faster than time in spaceship A.

;Spaceship A flies to a black hole and is affected by an acceleration of 100000ms^-2 due to the force of gravity and spaceship B remains in negligible gravity.

Has anyone found out what Tb/Ta is in relation to gravity and can a simple simultaneous equation find out a relationship between Gravity and Velocity?

 

[Phobos]

Originally posted by the_truth
I asked a question concerning this subject once but the discussion dissolved into petty quibbling and I saw no links or evidence to back up or help me understand any of the statements made.

Yeah, sorry about that. I've just locked that topic. I'll delete any nonsense that arises in this one. (notice: fair warning)

 

[Sariaht]

Yes, it can. gt = v. though what you want to do is intergrate the acceleration.
F(g) = u. I presume your circleing around the black hole...

So t_a/(1-((v_a + u)/c)²)^½ = t_b.

I didn't understand your syntax, that's all. Maybe i should practice a bit.

 

[Sariaht]

Originally posted by the_truth
(1 - (v_a/c)²)^-1/2=t_b/t_a

It's very true

The entire post was quoted and the above text was added within the body of the quote. For clarity, I just pulled out the repeated stuff. - Phobos

 

[GRQC]

Originally posted by the_truth
I asked a question concerning this subject once but the discussion dissolved into petty quibbling and I saw no links or evidence to back up or help me understand any of the statements made.
...
Has anyone found out what Tb/Ta is in relation to gravity and can a simple simultaneous equation find out a relationship between Gravity and Velocity?

I responded to your post in the other section. Gravitation time dilation is well-understood, so that would be the relationship between Ta and Tb you're after. An object in orbit around a large mass will experience both gravitational and Lorentzian (local special relativitsic) time dilation. However, there is no deeper connection between the two.