“If a heavy object with rest mass M moves past you with a velocity comparable to the speed of light, you will be attracted gravitationally towards its path as though it had an increased mass.”
I think the opposite would be true.
the time exposure would be a very large factor in determining
the amount of force you would feel.
if something moves past you at the speed of light , you probably would never feel it or see it.
a = f/m
186 thousand miles per second and the amount of space that you
take up along with your mass , you might not even budge at all.
just think of the distance to the moon each second.
the moon is apx 180,000 miles away.
the force that you would feel would be a gradient from
0 - what ever the gravity is of the mass
then for 186,000th of a second you would feel the full force of its gravity.
then after the 186,000th of a second the gradient decreases back to 0
if you were floating in space you would begin to accelerate slightly
(that would all depend on the mass its velocity , your mass and its distance from you.)
but any resistance to movement here on earth would probably be greater that the moving mass could supply as a gravitational force to accelerate you.
note: I don't believe that a mass increases with velocity.
you can try this with two magnets.
hold 1 in each hand.
now very quickly move one of them past the other.
now try the same thing only move it much slower.
I know that the above is magnetic not gravitational just
in case someone wanted to point that out to me.
I am trying to not leave myself open to those obvious replies.
something else to ponder.
if a bullet were traveling at the speed of light
in space , I would be more willing to believe that the bullet
would be compressed into an even smaller size.
now , if I build my spaceship thinking that it will compress vs expand at c then it wont implode.
note: just for those who might comment on the fact that
there isn't much in space to cause the ship to compress
I will reply that at c there might be plenty.
even in our accelerators where we consider it a vacuum there
are plenty of particles inside , we have never made a complete vacuum.
and at c running into those particles would tend to compress a spaceship.