1. The problem statement, all variables and given/known data 2. Relevant equations From Wikipedia: E = the sidereal period of Earth (a sidereal year, not the same as a tropical year) P = the sidereal period of the other planet S = the synodic period of the other planet (as seen from Earth) 3. The attempt at a solution This problem requires me to actually "think" / make out / derive such an equation to calculate the time it takes for another opposition planetary alignment to re-occur between Earth and Mars. The problem, as shown in the diagram, gives me pure facts and I simply have no idea of how to start. For example, I do not know what are the important variables I must incorporate to compose such equation and I don't know how to mathematically relate the circular motion of Mars and Earth. I have found an article on wikipedia showing me the way to calculate this so called synodic period which I believe is what I am looking for. But, wikipedia doesn't tell me how exactly this equation is derived and I really want to learn the derivation. So anyone, please guide me.