To rotate around a point, you just draw a circle around that...
Moon.X = Earth.X + cos(period) * distance
Moon.Y = Earth.Y + sin(period) * distance
To control the speed, just control the period yourself; basically it is angle from 0 to 360, the rendering speed depends on by how much you increment the period. So, just increment the period with time delta, don't forget to subtract 360 whenever it gets over 360. It is neater that way.
period=period+rotationspeed*timedelta
period > 360 ; period = period - 360