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Continuation of: What is the definition of a "pole" of a celestial body?

uhoh's answer says that distinct bodies should have a center of mass. If the body is spherical, then the COM will be near the middle of the body. By definition, the body's rotational axis should pass though COM and the extreme ends of this rotational axis should be considered "poles".

But what about bodies whose COM lies outside the body itself? For instance, crazy C-shaped objects. In this cases, the COM lies outside the body, the axis of rotation does not intersect the body's surface and so technically, there are no "poles" for such bodies. So, how should we describe the "extreme ends" of the body?

Note: There are a few bodies where there are no stable poles but they have their reasons. Saturn's moon Hyperion and the asteroid 4179 Toutatis lack a stable north pole. They rotate chaotically because of their irregular shape and gravitational influences from nearby planets and moons, and as a result the instantaneous pole wanders over their surface, and may momentarily vanish altogether.

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    $\begingroup$ I would say that in absence of an inner magnetic field or a more or less stable rotation vs a defined plane or axes then there aren't poles of sort. Instantaneous rotational poles do obviously exist. $\endgroup$
    – Alchimista
    Dec 6, 2020 at 9:31
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    $\begingroup$ Hard to prove the negative, but I don't think there are any C-shaped asteroids. Such a body would need to be rigid enough to support its mass against its own gravity (so not a rubble pile). There are some asteroids with significant concavities, but I can't find any for which the COM would be outside the body. Even if it did exist, and doesn't have a "pole"... so what... What do we need "poles" for anyway? $\endgroup$
    – James K
    Dec 6, 2020 at 15:19
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    $\begingroup$ @uhoh mentioned en.wikipedia.org/wiki/67P/Churyumov%E2%80%93Gerasimenko which to my mind is more "r" shaped than "c" shaped, but still seems to have a decent chance of the axis of rotation intersecting the object in other-than-exactly-two-evenly-spaced places. $\endgroup$
    – Jack Schmidt
    Dec 6, 2020 at 21:35
  • $\begingroup$ @JamesK poles can be helpful in describing the extreme ends of the body just like north pole and south pole; incidentally 433 eros is kind of elongated peanut or shoe shaped asteroid. $\endgroup$
    – Nilay Ghosh
    Dec 7, 2020 at 2:53

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For such a body (if it exists) the axis of rotation would not intersect with the surface of the body, so there is no "pole" on the surface.

This might cause a few issues for cartography software, but apart from that there's no particular requirement to define "extreme ends" of an asteroid. For cartography, a simple "longitude" and "Latitude" grid would not be appropriate, and some kind of custom solution.

As a further practical issue, a highly concave body, such as comet 67P, would have a high chance of having a "tumbling" motion, and so the axis of rotation would not be fixed and the "poles" of rotation would not be fixed.

For Comet 67P there is a "custom solution"

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