Stop for a moment and think why would it be impossible? Cos it wouldnt. It is quite possible to draw a circle on a plate, so why is it impossible on a plane?
Drawing a circle is the same as getting a satellite into orbit?Good thing gravity and motion keeps the circle on the plate so it doesn't fall off. Please think next time.
But is cannot be proven not to be a flat plane unless you can be at every point of it at the same time
In which case the maths would fail along with space missions which use the math.In your (flat) world lunar eclipses don't occur because that would require the earth (which is flat) to have the moon (which might be flat) to be in the earths shadow. Is the sun flat too?