two asteroid mysteries

Part 1 Mystery 1

Most small asteroids have an angular momentum (at least
I am not aware of one that doesn't). The instantaneous
rotation axis goes through the center of gravity, but
moves along an irregular cone. The intersection of this
cone with the surface of the asteroid is an irregular
closed line separating an area of potential lower angular
momentum from an area of a higher angular momentum.
Because of the law of conservation of angular momentum
the instantaneous axis of rotation is constrained to
follow the boundary between these two areas. The resulting
motion is called tumbling. When there is an impact on the
asteroid, the angular momentum may change by increasing or
decreasing. As a result the two areas will change accordingly.
It may ocurr that the impacts may be of such a type that the
areas of potentially greater or smaller angular momentum
become so small as to be negligible. When that happens
(which probability in my opinion is astronomically sic.
small) the asteroid no linger tumbles, but rotates about a
constant axis. To continue to rotate, all subsequent
impacts would have to be in the 'equatorial' plane and
at right angles to the axis of rotation.
Now about the mystery. The asteroid Eros does mot tumble.
It rotates. My conclusion is that the phenomenon that
caused it to rotate is of relatively recent origin, say
a few hundred million years, and has not been impacted
since. How and why did it acquire this motion. It has
been suggested that solar radiation may over millions
of years produce such an effect. If true, then why do
the other asteroids still tumble?
A secondary question relates to this: Why did the
investigators of the Near probe of Eros decide to take
the risky maneuvre to try to land the probe at the
equatorial region? It would have been so much simpler
to land more slowly at either polar area without worrying
about the timing of the landing to avoid the probe from
being hit by the rotating body?

Zdenek Jizba:

Now about the mystery. The asteroid Eros does mot tumble.
It rotates. My conclusion is that the phenomenon that
caused it to rotate is of relatively recent origin, say
a few hundred million years

Say several thousand years at most.

, and has not been impacted
since. How and why did it acquire this motion?

Indeed. I deny all responsibility.
(I expect there are another 56, including Deimos and Phobos.)

It has
been suggested that solar radiation may over millions
of years produce such an effect.

Hahaha! Solar radiation is the cure-all. (Especially when mixed with a
large jolt of whisky.) I bet those suggesters are stand-up comedians?

If true, then why do
the other asteroids still tumble?

Indeed, why oh why? You are perceptive.

I nominate you for a Nobel prize. Seriously.

Can someone confirm that Eros is not tumbling? I have watched a
five-second movie of Eros and imagine that I see some slight tumbling.

As the period of Eros' orbit is 1.76 year and it closely approaches the
orbit of Earth, its orbit appears to resonate with that of Earth.

It seems likely that the orbits of other Earth-orbit approachers also
resonate with the orbit of Earth, like 887 Alinda, 1862 Apollo, 1936 CA
Adonis, 1580 Betulia, 1620 Geographos, 1950 LA nr.1980, 1915
Quetzalcoatl, 1864 Daedalus, 1972 RA, 1981 Midas, 1943 Anteros, 1976 UA
Hathor, 1976 WA, 1977 HA, 1978 RA Ra-Shalom.

Of the about forty Earth approachers in the table I am using Eros
appears to have the least excentric orbit and (for Amor asteroids) one
of the shorter years. The short year, the orbital resonance and the
least excentric orbit must be associated with the least excentric
rotation of Eros. In my book "Making sense of astronomy & geology" (for
a lenghty review by physicist David Salkeld see my livejournal page; I
do not always agree with him, though) I attribute the orbital and
rotational characteristics and the shape of planets to electromagnetic
effects. Per force the same principle appears to me applicable to Eros.
I note that Anteros has similar orbital characteristics as Eros. Does
Anteros also not tumble?