The physical length of the ruler as a fraction of the circumference of the big circle is the same as the angular length of the ruler as a fraction of 360: length _ 8 circumference 360 Since circumference = 27T X radius and the radius of the big circle is the distance to the ruler/planet: length 8 2w % distance = 360 Solving for the physical length of the ruler yields: e length = 2w x distance x 360 This general equation can be used along with the distance to your planet to work out a conversion factor that will convert your moon's orbital semi-major axis from arcseconds to AU; i.e. in the above equation, we will set length = a [AU], o=all, and calculate conversion factor [" /AU] = 33330 X W x distance. conversion factor = type your answer... "/AU. Note: in order for units to work out, we had to multiply by the number of degrees per arcsecond (") in the above formula