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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? $\endgroup$ Commented Oct 18, 2018 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
    Commented Oct 18, 2018 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
    Commented Oct 18, 2018 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
    Commented Oct 19, 2018 at 20:16
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    $\begingroup$ I have graphs illustrating the variation in the Moon's orbital elements: astronomy.stackexchange.com/a/55112/16685 $\endgroup$
    – PM 2Ring
    Commented Feb 16 at 0:29
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NASA TLE counts period by the Ascending Node crossings, which is the Nodal Period, and as you elude to, not the same as the time between Perigee passages. The difference between the two is related to the rate of change of Argument of Perigee, which itself is linked to eccentricity and inclination, and also e.g. drag (every orbit rev has a different SMA.) There is no 'two-body' orbit in real life. So pick one that meets your needs, and make sure that you indicate which type you used.

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