@PhiNotPi *“There is an almost completely empty universe. It does not have to be completely empty, but any other mass/energy must be small enough that it has not effect on how events play out.”*

A completely empty universe is not a universe… That would be a theoretical void.

As to mass, no matter how small, there is no possible way for a universe to exist with small enough mass that it doesn’t effect how events play out. Any event that occurs in a closed system will be effected to some degree by the compounds of that system. It can’t not effect it.

@PhiNotPi *“In the universe, there is one planet and one spaceship on the planet.”*

There’s your mass… I suppose the materials used to build the spaceship were harvested from the one planet in the universe. Thus the planet has less mass than it did before the spaceship was created. The planet will also be projecting gravitational warpage upon the surrounding space/void/thingy that you propose it exists within.

@PhiNotPi *“When the spaceship is launched, it instantly accelerates to any given velocity and then stops acceleration forever.”*

Every action has an equal and opposite reaction. Therefor the acceleration propellent causes/effect upon the closed system it resides within.

@PhiNotPi *“How would one calculate the minimum possible velocity that the spaceship needs to be able into space forever, without ever coming to a halt?”*

You’d need some pretty specific data to form an equation with… mass of both planet and spaceship, sampling of average mass per cubic area of space/void/thingy, rate of entropic decay… and then determine if your space/void/thingy has an expansion rate (like our universe) or if it is in a state of contraction (if that theory is entertained), or does your universe oscillate (which requires entropic forces to be less than .001%)?

@PhiNotPi *“Here’s the catch: Since the gravity of the planet is felt everywhere in the universe, the spaceship always experiences the forever-decreasing but never zero effect of the planets gravity.”*

Decide the path… vertical, eliptical… start with accurate measurements of mass, and do the calculation

@PhiNotPi *“Does an escape velocity exist in the first place?”*

Only to the point where the gravitational pull of the planet is greater than the gravitational pull of the spacecraft. Get far enough away, and the spacecraft mass should overcome the influence of the planet mass.