You wont be able to specify the position with much precision on the edges of your star system. The limiting factor here is the fraction part of the floating point number. Your universe is about 2^58 meters across. A double has 53 bits of precision in the fractional part. This means, at the edges of the universe, you will only be able to represent the position of a ship in increments of 2^5, or about 32 meters. Floats are even worse, you can only have 24 bits of precision. This is about a precision of 2^34 meters or about 16 billion meters. Not good.
I would use 64 bit integers to store the galactic coordinates of objects in your universe. That would give you precision to about 2^-6 or about a precision of two centimeters. Of course, when rendering your scene, you wont be able to work in integers. So whenever you are rendering anything, you need to convert all of your coordinates to a local origin, then convert all active object coordinates to floats that are relative to the local origin.
EDIT: fixed computation error