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Okay, I wanted to try and find a way to apply circular motion and gravitational field calculations to elliptical orbits to prove why all orbits must have opposite periapsis and aopsis and only one of each (as oppose to for example two opposite aopsis and two opposite periapsis) but I couldn't do it. Anyone with more experience give me a hand, it would be handy if the derivation tried to use relatively simple mechanics because I'm second year A level in the UK. Cheers