From the Flat Earth Wiki:

Gravity

Gravity is a fundamental force in Round Earth Theory and is the theoretical attraction between physical objects with mass, the force being proportional to their given mass. Many Flat Earth models omit Gravity entirely.

You can see how that would simplify things in one way, but it does surely make it more complicated in others.  Particularly when read together with

Stars

The sun, moon, and stars are all rotating around a central point over the North Pole. The underlying cause for this rotation is a vast cornucopia of stellar systems orbiting around its center of attraction - an imaginary point of shared attraction. This is an extrapolated and more complex binary star movement. Think of a binary (two) star system which moves around an invisible common barycenter. Now add a third body which shares that common center of attraction. Now a fourth. When we add enough bodies the system looks like a swirling multiple system.
...
Each star in a cluster is attracted to one another through gravitational vectors.....

And then there's

Antimoon

The Antimoon is a moon of nearly identical size to the normal moon. It is theorized that the Antimoon passes between the Earth and the Moon to account for the waxing and waning effects of the moon. The Antimoon is very dark and undetectable by any means except when it passes in front of the moon.
 
At which point, I have to say, I'm getting a suspicion that this fellow is having a lend of me....