How strong would need to be gravitational shield on the ship if would encountered meteorite dust in diameter 50mm² at that speed?
This . . . is going to be tough to answer. One of the issues is that it's impossible for non-massless particles to travel at the speed of light; moreover, any object going near it will have an enormous amount of kinetic energy. Add to that the fact that we can't go anywhere near that speed and you have a tough, if not impossible, question to answer.
This can only be reasonably answered by talking about shielding used in spacecraft (admittedly going way slower than the speed of light). There are a few options used on the ISS:
- The Whipple bumper: Helpful for impacts with high-velocity objects, this configuration uses a metal plate attached a short distance away from the main structure of the vehicle. The initial "bumper slows down the incoming particle enough so the "catcher" plate behind it can resist the further impact.
- The multishock (aka stuffed Whipple) bumper: This is similar to the Whipple bumper, but it inserts more layers of material in between the bumper and the catcher. Like the normal Whipple bumper, the outer bumper is often made with aluminum.
- The mesh double bumper: This uses "metallic mesh" to protect the spacecraft.