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Something is wrong with altitude returned by MoonPosition

Posted 8 years ago

For two observers at antipodal locations, the function MoonPosition returns contradictory altitude values.

The altitude of a celestial object as seen by an observer at North pole is the negation of the altitude as seen by an observer at South pole. Since both observers share the same horizon circle. Altitude 10° when seen from North pole is -10° when seen from South pole.

Moreover, since the shared horizon coincides with the equator, the declination of the object is the same as the altitude seen from North.

But altitude values returned by MoonPosition are different (altitude/declination is the last element):

northPole = GeoPosition@{90, 0};
southPole = GeoPosition@{-90, 0};
timeOfObservation =DateObject[{2016, 02, 28, 18, 0, 0}, TimeZone -> 0];

MoonPosition[northPole, timeOfObservation]
{23.93 \[Degree], -13.10 \[Degree]}  

MoonPosition[southPole, timeOfObservation]
{156.07 \[Degree], 11.34 \[Degree]}

MoonPosition[northPole, timeOfObservation,  CelestialSystem -> "Equatorial"]
{14.909 (()^(h)), -12.224 \[Degree]}

However, the function SunPosition is OK in this respect:

SunPosition[northPole, timeOfObservation]
{266.43 \[Degree], -7.98 \[Degree]}

SunPosition[southPole, timeOfObservation]
{273.57 \[Degree], 7.98 \[Degree]}

SunPosition[northPole, timeOfObservation, CelestialSystem -> "Equatorial"]
{22.743 (()^(h)), -7.976 \[Degree]}
POSTED BY: Hans Milton
5 Replies
Posted 8 years ago

Yes, you are right, of course. Its the parallax. The figures works out. Taking values for earth polar radius and mean distance to the moon from W|A I get 11.31° for the altitude as seen from South pole. When declination is -12.224°.

I wrote my post when investigating how to find the lat/long coordinates of the Moon's substellar point. Using horizontal coordinates as seen from the poles. But the substellar point doesn't involve the earth radius. While the altitude does. And that makes a difference for objects that are "near". Not seeing this was my mistake.

POSTED BY: Hans Milton

The Ancients calculated the distance of the Moon from the Earth using precisely that angular discrepancy you noticed. The lines joining North and South poles with the moon are not parallel. They meet at an angle, which is almost two degrees, as Jeff showed.

POSTED BY: Gianluca Gorni

Essentially, your premise is true for an object at infinity. The Sun is far enough away that this approximation nearly fits, but the Moon is close enough that there is a measureable parallax effect. Using simple trigonometry using the polar diameter of the Earth as one arm of a triangle and the distance to the moon as the other arm of the triangle, we get the following approximation of what you are seeing (just an approximation):

In[8]:= ArcTan[
  2 GeodesyData["ITRF00", "SemiminorAxis"]/
    PlanetaryMoonData["Moon", "DistanceFromEarth"]]/Degree

Out[8]= 1.83271

So, almost 2 degrees difference. Which is approximately what your computation is showing.

POSTED BY: Jeffrey Bryant

I suppose the difference is the angular amplitude of the Earth diameter as seen from the moon. It is of that order of magnitude. The sun is so much farther away that the angular amplitude is negligible.

POSTED BY: Gianluca Gorni
Posted 8 years ago

Gianluca,

Thanks for your response. But could you please elaborate a bit?

Hans

POSTED BY: Hans Milton
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