Infinite world / night and day

Firstly, Infinite world.
Have the actual arianne world a sphere. Simple.
Seconldly, Night and day.
Without the sphere world, this wouldn't be very
useful. Have it so the day and night goes around the
world, like in real life. So on one side of the world
it is day, and on the other side it is night. And day
slowly rotates round the world, a complete day (from
midnight to midnight) could be about 3 to 4 hours in
real time, or something.