[Ethan Clive Osgoode]

If you're looking at an object that's exactly one light-day away, and stationary relative to the Earth, it's apparent position should be accurate

And if the object is 1/2 light day away, where would it's real position be?

[tacticalogic]

And if the object is 1/2 light day away, where would it's real position be?

Need more information. It's "real" position relative to you is going to depend on where you're standing, and what direction that 1/2 a light day is, relative to the Earth's rotation.