Let's say I have a Dyson sphere roughly the same size of the earth with a very small "star" in the center. Continents, oceans, and people inside the sphere experience a reverse gravity in the opposite direction as the the star.
The star's output power(heat and light) is directly proportional to the equation
1 + sin(t*2pi/d)/2 + sin(t*2pi/y)/2 where
t is time in seconds,
d is the length of a day, and
y is the length of a year in seconds.
Given all of this, how would I make it so that the inside of the sphere experiences similar temperature distribution as the real Earth? Such that, reverse-Florida is hot, and Antarctica is cool.