Gravitational acceleration VS the speed of light

[Accuser]

Three preconceptions for our thought experiment:

1. Gravity's effects propagate at a rate faster than the speed of light. This is demonstrated by the fact that the Earth is not thrown out into space due to the constantly shifting position of the Sun and an 8.3 min delay of "gravity waves" pulling us toward the Sun's previous position.

2. Gravity increases proportionately to an object's mass.

3. There is no functional limit to the distance over which gravity may have an effect (the effect decreasing by the square of the distance, of course).

Imagine a Universe with physical laws identical to our own. Imagine it with no matter, anti-matter, energy, etc (excepting what I'll colloquially call "quantum turbulence"). Now imagine 2 very massive bodies which are stationary and extremely far from each other.

With only 2 bodies in this Universe, each would eventually experience the other's gravitational effects and begin to accelerate toward the other body. Assume the distance between them is sufficient that there is enough time in their transit to accelerate to near light speed. Relativity states that no body can achieve the speed of light due to the increase of mass and the slowing of local time with increased speed. However, wouldn't increased gravity exactly compensate for the increased mass of acceleration? Is there a reason that these two bodies would not achieve at least gravitational speed, given their initial position was far enough apart?

My apologies if this has been answered before, but I can't seem to find it elsewhere. Also, if you can provide an answer, I would deeply appreciate the use of layman's vocabulary ^_^

 

[George Jones]

I have removed the the URL, which violates Physics Forums rules, to which everyone agrees when they register.

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Three preconceptions for our thought experiment:

1. Gravity's effects propagate at a rate faster than the speed of light. This is demonstrated by the fact that the Earth is not thrown out into space due to the constantly shifting position of the Sun and an 8.3 min delay of "gravity waves" pulling us toward the Sun's previous position.

The effects of gravity do not propagate faster than the speed of light. See

https://www.physicsforums.com/showthread.php?p=2818297#post2818297.

 

[Accuser]

My apologies on the worthless link then. It wasn't "obviously 'crank' or 'crackpot' as I read it, but I'll chalk that up to a lack of thorough understanding of the topic.

But to get on to the question, what is it that would limit the speed of the objects?

EDIT:
To be more precise, why would they not reach the same speed as the effect of gravity?

 

[Ich]

To be more precise, why would they not reach the same speed as the effect of gravity?

They would. That speed is the speed of light.

 

[Accuser]

They would. That speed is the speed of light.

Fair enough, thanks for the fast and informative responses!