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To calculate the period of an orbit with strong perihelion precession we could just pick an arbitrary point in the sky, and time how long it takes for it to pass it again. But wouldn't we get different values for some orbits depending on whether that specific orbit reached the distance of the semi-major axis?

For example, let's say planet Vulcan's perihelion precesses by 10 degrees per orbit. If we started the measurement of its period 1 degree after it had reached perihelion, and waited for it to return a full 360 degrees, then it would have completed a full orbit without ever reaching the distance of a full semi-major axis. We would get different values if we had waited e.g. 5 or 10 degrees.

Is it a case of a sample orbit always being "close enough" for an approximation, or is there an exact technical definition?

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    $\begingroup$ How are you defining the period of an object with strong perihelion precession? $\endgroup$ – probably_someone Oct 18 '18 at 16:21
  • $\begingroup$ That's my question! I'm trying to figure out how it is defined, and whether it technically varies per orbit. $\endgroup$ – Paul Oct 18 '18 at 16:42
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Sure we can. In that case we would have the sidereal period different from the interval between perihelia. Compare to Earth's orbit, where the sidereal year is different from the tropical year due to axis precession.

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  • $\begingroup$ But wouldn't some sidereal periods be longer than others, depending on whether they reached a full semi-major axis or not? $\endgroup$ – Paul Oct 18 '18 at 16:41
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    $\begingroup$ @Paul Yes, we see this with the Moon's orbit. You might enjoy this article which suggests using the effect as an educational tool. $\endgroup$ – rob Oct 19 '18 at 20:16

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