Position angle of Moon's bright limb (formula)

In summary, the conversation is about finding the formula for calculating the position angle of the Moon's bright limb, which is found in "Astronomical Algorithms" by Jean Meeus. However, there is no explanation for the derivation of this formula. The formula involves trigonometric functions and uses the geocentric right ascension and declination of the Moon and Sun. One of the participants, Jeff from France, found a solution by referring to a document from the UK Hydrographic Office.
  • #1
JeffOCA
49
0
Hi everyone !

I have a question about the position angle of Moon's bright limb.
In "Astronomical Algorithms" (Jean Meeus), one can find the formula to calculate this angle (formula is tagged "46.5"), but there is no explanation about the derivation of this formula.

This is the formula "46.5" :

[tex]tan \chi = \frac{cos \delta_0.sin(\alpha_0 - \alpha)}{sin \delta_0.cos \delta - cos \delta_0.sin \delta.cos(\alpha_0 - \alpha)}[/tex]

where [tex]\alpha[/tex], [tex]\delta[/tex] are the geocentric right ascension and declination of the Moon and
[tex]\alpha_0[/tex], [tex]\delta_0[/tex] are the geocentric right ascension and declination of the Sun.

I think the derivation is maybe explained in the "Practical astronomy with your calculator" (Peter Duffett-Smith) but, unfortunately, I don't have this book at home.

Does anybody can explain the derivation of this formula 46.5 ?

Thanks (... and sorry for my approximative english)
Jeff (from France)
 
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  • #2
Of course [tex]\chi[/tex] is the so-called "position angle of the Moon's bright limb"...

Jeff from France
 
  • #3
No one ?
 
  • #4
Welcome to PF!

Hi Jeff! Welcome to PF! :wink:

Without a diagram, it's difficult to see what's what …

but the denominator is the standard spherical trig formula for cos of the side of a triangle if the other two sides are δ and 90º - δ0, and the opposite angle is α0 - α :smile:
 
  • #5


Does anyone capable of tracing a diagram of this spherical triangle in order to understqnd the relation given above ?
 

What is the position angle of the Moon's bright limb?

The position angle of the Moon's bright limb refers to the angle between a reference direction on the Moon's surface and a specific point on the Moon's bright edge. This angle is measured counterclockwise from the reference direction to the point on the bright limb.

How is the position angle of the Moon's bright limb calculated?

The position angle of the Moon's bright limb can be calculated using the formula: PA = arctan((sin(HA)/cos(δ)tan(φ)-sin(δ)cos(HA)), where PA is the position angle, HA is the hour angle, δ is the declination of the Moon, and φ is the latitude of the observer.

What does the position angle of the Moon's bright limb tell us?

The position angle of the Moon's bright limb can tell us the orientation of the Moon's bright edge relative to our reference direction. This can be useful in determining the position of features on the Moon's surface, such as craters or mountains.

Does the position angle of the Moon's bright limb change?

Yes, the position angle of the Moon's bright limb changes as the Moon orbits around the Earth. It also varies depending on the observer's location on Earth and the time of observation.

How can the position angle of the Moon's bright limb be measured?

The position angle of the Moon's bright limb can be measured using a telescope equipped with a reticle (a grid or crosshair pattern) and a clock drive. The reticle can be aligned with the reference direction, and then the clock drive can be used to track the Moon's movement and measure the position angle at a specific time.

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