Latitude librations of grazes of the same star
All northern-limit, or all southern-limit, grazes of the same star have
nearly the same latitude libration. This is due to the fact that the star is
at a fixed ecliptic latitude (distance in degrees north or south of the
ecliptic)
and the fact that the Moon's axis of rotation points nearly to the pole of the
ecliptic. The librations are the lunar longitude and latitude of the sub-Earth
point, so the latitude libration is almost the negative of the ecliptic
latitude of
the Moon's center. So the latitude libration for southern limit grazes of a
star is very close to the negative of the ecliptic latitude of the star +0.25
deg. (the approximate angular radius of the Moon), while the latitude libration
for northern limit grazes of the star is near the negative of its ecliptic
latitude
-0.25 deg. There are variations of about 0.04 deg. due to the changing distance
to the Moon, and to the fact that the Moon's motion (especially as seen by an
observer on the rotating Earth's surface) is not parallel to the ecliptic, but
usually makes a small angle to it.
-David Dunham
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