Let's imagine a asteroid that travels with 0.99999999999999999c.

(I know it's impossible).

Anyway... Relativistic mass of such object would be almost equal to earth's stationary mass.

Now let's imagine that such object passes closely to me (assuming I'm immortal etc.). According to $F_g=GMm/r^2$ (Where M is relativistic mass of this asteroid and m is my mass) such an object would attract me.

So would I gravitate after it? Would I gain it's speed constantly falling on it? Or maybe it would just pulled me for a moment, but then I would return to my ol' good non-relativistic speed in "everyday reference system"?

Or maybe something else would happen? What happens with gravity of relativistic, NON ACCELERATINNG objects? (Let's assume that there's something that makes this asteroid speed constant).

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    $\begingroup$ "(I know it's impossible)". Why? Motion is relative. In the reference frame of a proton with a speed of $0.999... c$, relative to the asteroid (not impossible) it is the asteroid that has this speed. $\endgroup$ Jul 18, 2014 at 23:49
  • $\begingroup$ This is related to the question of whether or not an object can "move so fast" that it becomes a black hole. So I'm voting to close as a duplicate of physics.stackexchange.com/q/3436/9887 $\endgroup$ Jul 18, 2014 at 23:55
  • $\begingroup$ @AlfredCentauri Do I understand it properly that there wouldn't occur incerase in gravitational force. Not a single newton? I don't care about black holes. It's a shame, but I don't know much about general relativity. $\endgroup$
    – user46147
    Jul 20, 2014 at 8:01
  • $\begingroup$ In relativity, gravity is not a force. The fact is simply this: the Newtonian gravitational force formula is fine in the low-speed, low mass-energy limit of general relativity. However, you're stipulating that the system is ultra-relativistic while, at the same time, using the Newtonian concept of gravitational force and the special relativistic (outdated) concept of relativistic mass. But that's simply not a valid way to think about this problem. $\endgroup$ Jul 20, 2014 at 12:34
  • $\begingroup$ @AlfredCentauri So I wouldn't feel even a tiny attraction? $\endgroup$
    – user46147
    Jul 20, 2014 at 21:35