Is there Relative Mass?

Is there relative mass?

If two objects are moving parallel near the speed of light their masses are both greatly increased.

At rest & at the same distance of separation the gravitational force/metric is a given value g.

At near luminal speeds with greater masses the gravitational force/metric between them must be greater than g.

Does inertia cause any net effect of gravity to be identical to their response/behavior at rest?
I suppose since the time speed of both objects is already slowed the mass/time-speed differential for them is identical to their resting mass/time-speed differential between them?
Things such as time dilation and Lorentz contraction are only observed when there is relative motion between observer and the other object. When two things are running parallel near the speed of light they both appear massive and foreshortened to us back here on Earth, but to each of them the other guy looks perfectly normal.
We can accelerate charge particles to 1/2 c fairly easily. I seriously doubt we will ever accelerate a craft or a cannon ball to 1/2 c.

Charge can be accelerated to high speed because of the velocity of the field. That means the change in field can be quick and push harder. A fast increasing force.

Neutral objects have to be accelerated with g for continuous acceleration. We can't turn g up, like we can a field. We have to work with the g we got or find. And the change of it is slow. A set acceleration. And it takes time because of this. How fast do you think Sol can pull it? And then let it go. We can't accelerate straight into it.

It's the speed of the CHANGE in force that controls acceleration. So far c speed is the fastest propelling velocity we how could we go faster?

A new star trek plot. Scotty builds a sail that can catch expanding space and now intergalactic travel is available. And there isn't anywhere man can't go. We learned to tack that space-time expansion. We can go back to any time we see. Even forward a little to see what it all looks like now. Present view.

We would have to find something much faster than light for to go anywhere.