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What is the relationship between Periapsis and Apoapsis longitude ? Are they 180° apart ? (ie) Periapsis + 180° = Apoapsis ?

Related question: if apoapsis is not known, what orbital elements are required to compute it ?

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The periapsis and apoapsis are 180° apart. According to Kepler's first law, an orbit is an ellipse with the central body at one focus. The periapsis (P), central body (F), and apoapsis (A) all lie on the major axis of that ellipse.

Elliptical orbit

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In a Keplerian orbit, yes, the apoastron and the periastron (I’ll stick to these words despite the controversy; see "Periapsis" or "Periastron"?) are 180° apart.

However, in the real world, Keplerian orbits don’t exist, and all orbits “precess” somewhat due to the gravitational influence of external bodies. This means that in practice, the apoastron and the periastron are not 180° apart.

The difference is due to apsidal precession, which has (at least) four components: General Relativity, quadrupole, tides, and perturbations. For example, for Mercury, the apsidal precession due to General Relativity is (the “famous”) 43″ per century, that due to gravitational perturbations from the other planets is 532″ per century, and that due to the Sun’s quadrupole is a mere 0.025″ per century.

This doesn’t amount to much in the case of Solar System bodies (always less than Mercury’s apsidal precession), but it can reach 19.9° per year for WASP-12b. However, this planet has a revolution period of barely more than a day, so again, the difference is not much between apoastron and periastron…

…but it’s still technically not zero!

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