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How to verify a statement about the position of Moon?

I found this set of sentences in the Wikipedia article on the Celestial Sphere: The celestial sphere can thus be thought of as a kind of astronomical shorthand, and is applied very frequently by astronomers. For instance, the Astronomical Almanac for 2010 lists the apparent geocentric position of the Moon on January 1 at 00:00:00.00 Terrestrial Time, in equatorial coordinates, as right ascension 6h 57m 48.86s, declination +23° 30' 05.5". Implied in this position is that it is as projected onto the celestial sphere; any observer at any location looking in that direction would see the "geocentric Moon" in the same place against the stars. For many rough uses (e.g. calculating an approximate phase of the Moon), this position, as seen from the Earth's center, is adequate.
I am wondering how to verify this statement with Mathematica's date and time functionality. I have the following code:

AstroPosition[
 Entity["PlanetaryMoon", "Moon"], {"Equatorial", 
  "Date" -> 
   DateObject[{2010, 1, 1, 0, 0, 0.`}, "Instant", "Gregorian", 0.`, 
    "TT"]}]

I have an output that is not precise enough to compare to the right ascension of 6 hours, 57 minutes, and 48.86 seconds. I have 6 hours and 57 minutes and 48.9 seconds, which 48.86 seconds could be rounded to but I am wondering how to show more details about the data in an equatorial coordinate system.
Here are some other things I tried to see the right ascension more precisely:

This code returns cartesian coordinates with the unit of astronomical units, which is not what I

AstroPosition[
Entity["PlanetaryMoon", "Moon"], {"Equatorial", 
"Date" -> 
DateObject[{2010, 1, 1, 0, 0, 0.`}, "Instant", "Gregorian", 0.`, 
"TT"]}]["Data"]

I tried using FullForm to display the full number but it stores it as an XYZ

FullForm[
 AstroPosition[
  Entity["PlanetaryMoon", "Moon"], {"Equatorial", 
   "Date" -> 
    DateObject[{2010, 1, 1, 0, 0, 0.`}, "Instant", "Gregorian", 0.`, 
     "TT"]}]]

list not a number.

How can I see the extended precision for the right ascension?

POSTED BY: Peter Burbery
2 Replies

MixedUnit["RightAscensionHMS"] and MixedUnit["ArcDMS"] worked successfully. Here is the content.

ap = AstroPosition[
  Entity["PlanetaryMoon", "Moon"], {"Equatorial", 
   DateObject[{2010, 1, 1, 0, 0, 0.}, "Instant", "Gregorian", 0., 
    "TT"]}]
AstroPosition[{104.45357536810378`, 23.50152305129125, \
0.002402213329988384}, {"TETE", 
  "Date" -> DateObject[{2010, 1, 1, 0, 0, 3.92901711165905*^-8}, 
    "Instant", "Gregorian", 0., "TT"]}, "RADec"]
UnitConvert[Quantity[ap["RightAscension"], "AngularDegrees"], 
     MixedUnit["RightAscensionHMS"]]
Quantity[MixedMagnitude[{6, 57, 48.8580883449}], 
 MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", 
   "SecondsOfRightAscension"}]]
UnitConvert[Quantity[ap["Declination"], "AngularDegrees"], 
 MixedUnit["ArcDMS"]]
Quantity[MixedMagnitude[{23, 30, 5.4829846485}], 
 MixedUnit[{"AngularDegrees", "Arcminutes", "Arcseconds"}]]
POSTED BY: Peter Burbery

Take the astro position you computed:

ap = AstroPosition[Entity["PlanetaryMoon", "Moon"],
       {"Equatorial", DateObject[{2010, 1, 1, 0, 0, 0.}, "Instant", "Gregorian", 0., "TT"]}]

Then you can extract the coordinates you are interested in, which are given in degrees, and manually convert them into mixed units:

In[39]:= UnitConvert[Quantity[ap["RightAscension"], "AngularDegrees"],MixedUnit["RightAscensionHMS"]]
Out[39]= Quantity[MixedMagnitude[{6, 57, 48.8581}], 
   MixedUnit[{"HoursOfRightAscension", "MinutesOfRightAscension", "SecondsOfRightAscension"}]]

In[40]:= UnitConvert[Quantity[ap["Declination"], "AngularDegrees"], MixedUnit["ArcDMS"]]
Out[40]= Quantity[MixedMagnitude[{23, 30, 5.48298}], 
  MixedUnit[{"AngularDegrees", "Arcminutes", "Arcseconds"}]]

Then you can see more digits, and we can check that the results agree to the precision quoted by the Wikipedia.

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