NavList:

   

Reply

I compared my Lunar software to the Occult program to test the effect of
the lunar limb profile. Occult takes that into account. Lunar does not.
I used occultations by the Moon in the near future:

http://www.lunar-occultations.com/iota/iotandx.htm

Gam Vir (Porrima), sig Sco (al Niyat), and del Sco (Dschubba) were
excluded because they are double. (A close double is OK.) The choice of
observer sites was random. Sometimes a site was selected because it was
near the top of the list (Abu Dhabi) or because it was interesting
(Easter Island). If I were doing this again, I would pick sites to get
an approximately uniform occultation distribution on the Moon limb.

The test method was to compute immersion and emersion times with Occult.
For those times I calculated lunar distances with Lunar 4.4. In most
cases the star was below the magnitude 3.0 cutoff in the Lunar catalog,
so I got its data from the SIMBAD site.

I assumed any failure to get zero lunar distance was entirely due to my
software. The standard error (root of the mean squared error) was 1.07″
for the 10 events (5 occultations, immersion and emersion for each).

The Moon position from Lunar is the position of its center of gravity.
However, that point is a little different from the mean limb center of
figure. In the Astronomical Almanac eclipse predictions, corrections in
ecliptic latitude and longitude are applied to adjust for the
difference. See page A79:

https://archive.org/details/binder1_202003/page/n93/mode/2up?view=theater

The main window of Lunar has a "solar eclipse corrections" check box to
apply the corrections. In theory they should also improve occultation
computations. In my test the standard error decreased a little, from
1.07″ to 0.87″.

However, a lunar distance observation with a sextant is much different
from an occultation. The observer oscillates the body and makes its
motion tangent to the limb. A low power telescope in the hand cannot
resolve limb irregularities that are obvious in an occultation.

In lunar distance calculations I believe a typical limb error from my
Lunar program is about 0.5″. That's a mix of calculation, observation of
the limb profile display in Occult, and guess. First, how large is the
arc that affects the perception of the limb in a sextant observation? I
guessed 8°, that is, 4° either side of the true tangent point. Such an
arc is 2.2′ in great circle measure and departs 2.3″ from a straight line.

I analyzed the limb display in Occult for each of the 10 occultations in
my test. At each occultation, I obtained the height of the visible limb
with respect to the mean (circular) limb at five points: at the contact
point, and 2 and 4 degrees (position angle) either side of contact. I
computed the sample standard deviation of the five values. That gave a
value for limb irregularity in the vicinity of each immersion or
emersion. The 10 values were averaged (root mean square). Result was
0.50″ for the typical semidiameter variation in an 8° arc of the limb.

It soon became obvious there was a great deal of luck in what limb
details were sampled. Often I measured a limb height close beside a
narrow peak or valley which would have made a large difference. But such
small details would not be visible in a sextant.

I have in mind a second test with more occultations and a more uniform
distribution on the limb.

--
Paul Hirose
sofajpl.com

   

Reply