Calculating Compound Angle b/w Planet & Earth-Sun Vectors

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SUMMARY

The discussion focuses on calculating the compound angle between a planet's vector (Recl, L, B) and the Earth-Sun vector, which exists on the ecliptic. The recommended method involves converting both vectors into Cartesian coordinates, normalizing them to unit length, and then using the dot product followed by the arccosine function to find the angle. This approach is straightforward and effective, depending on the initial vector representation.

PREREQUISITES
  • Understanding of vector representation in astronomy, specifically (Recl, L, B) coordinates.
  • Knowledge of Cartesian coordinate conversion techniques.
  • Familiarity with vector normalization processes.
  • Basic understanding of trigonometric functions, particularly the arccosine function.
NEXT STEPS
  • Research how to convert spherical coordinates to Cartesian coordinates.
  • Study vector normalization techniques in mathematical contexts.
  • Learn about the dot product and its applications in vector analysis.
  • Explore the use of arccosine in calculating angles between vectors.
USEFUL FOR

Astronomers, astrophysicists, and students studying celestial mechanics who need to calculate angles between planetary vectors and solar vectors.

Philosophaie
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A certain planet has a vector (Recl, L, B). The Earth and Sun vector exists on ecliptic. I need to know how to calculate the compound angle between the planet vector and the Earth-Sun vector.
 
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Philosophaie said:
A certain planet has a vector (Recl, L, B). The Earth and Sun vector exists on ecliptic. I need to know how to calculate the compound angle between the planet vector and the Earth-Sun vector.
There are a number of different possible approaches. Which is easiest will depend on the form in which the vectors are given.

One approach is to express each of the two vectors in Cartesian coordinates, normalise them both to length 1 (ie divide each by its length), take the dot product (sum of componentwise product) , then apply the arcos function.
 
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