Gravitational Attraction of a Massive Particle

[GuyWQuestion]

I was wondering what equations govern calculating the gravitation attraction of a massive particle (say a proton) traveling at near light speed? Thanks!

[espen180]

What is your current level of understanding of physics and mathematics?

[GuyWQuestion]

Lets go with college level Algebra, but I've taken college level Calculus, just don't remember most of it.

[espen180]

Okay. Just to be precise, we don't know how the gravitational field looks around single particles because we don't have a working quantum theory of gravity yet. We can say quite a bit about more massive objects though.

Unfortunately, college undergraduate level algebra and calculus is insufficient in order to understand the equations of GR, the matematical framework for which is differential geometry and tensor calculus. As such, giving you the equations immediately would be meaningless. I suggest you take a look at Prof. Susskind's video lecture series on GR, which is available fo free on youtube;

Here is the link to the Special Relativity lecture series: http://www.youtube.com/watch?v=BAurgxtOdxY
General relativity lecture series: http://www.youtube.com/watch?v=hbmf0bB38h0

[pervect]

Because all objects are affected by gravity, we can't actually measure a "gravitational field" in the same sense that we can measure , say, an electric field. In some specialized circumstances we can work around this lack of a reference particle that would be "unaffected by gravity", but the case of a moving mass isn't one of those special circumstances.

What we could measure, in principle, is the tidal gravitational field of a moving particle - the accelerations induced in nearby test particles relative to each other. Unfortunately, the detailed presentation on it gets rather technical. It's known as the Aichelburg - Sexyl solution, and in general terms, it looks like a plane wave, similar to the electromagnetic case, which behaves in a similar manner.