The point "5" is the Sun. It's all set - you don't have to touch it. The point "E" is the Earth. It needs its parametric equations lled in (its x8 and ye). It should have a period of 1, and the circle it travels in should have a radius of 1. It should travel counter clockwise, and start at the "3 o'clock" position. Find it's Xe and ye, and plug them in. The point "V" is Venus. It needs its parametric equations lled in (its xv and M. It should have a period of (224.7! 365.24), and the circle it travels in should have a radius of 0.723. It should travel counter clockwise, and start at the "3 o'clock" position. Find it's xv and yv, and plug them in. (I'm trying to make the numbers pretty accurate.) The "d" lines are the distances between any two objects ("es" means Earth to Sun, etc..) . Create equations for each. (And - in all honesty - do us both a favor and use xe, ye, etc.. so that we can all read the equations. just like I did up above.) Now comes the tricky part. Recall the Law of Cosines r: . Yourjob is to create an equation - using the Law of Cosines - for the angle VE-S. That's the angle measuring how far apart the Sun and Venus appear in the sky from Earth. Once you've got that, nd what the maximum value for that angle is and at what T it occurs (you may want to convert it to degrees so you have a bit more intuition about how big an angle that is). Part 2: Why does this mean you'll never see Venus at Midnight