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Calculate the time it takes for the reoccurence of opposition between Earth and Mars

  1. Feb 1, 2009 #1
    1. The problem statement, all variables and given/known data
    [​IMG]

    2. Relevant equations
    From Wikipedia:
    [​IMG]
    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.
     
  2. jcsd
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