The Earth Analemma and Orthonormal Coordinate Systems

In summary: An analemma enthusiastIn summary, the conversation discussed the use of orthonormal coordinate systems in deriving the Earth-Sun analemma. The speaker expressed confusion about equation (11) and asked for assistance in understanding it. The respondent explained the concept of orthonormal coordinates and how they relate to the Earth-Sun analemma, and recommended further research on the topic.
  • #1
Reuel
3
0
Hi.

I have been researching the Earth-Sun analemma and I found this document about deriving the Earth-Sun analemma via orthonormal coordinate systems.

Unfortunately I do not know very much about orthonormal coordinate systems and while I understand the first bit about elliptical angles, I get a little confused throughout the rest of the document. It really starts to lose me around equation (11). Where does that come from? What is the logic behind it?

I have already looked at the website http://www.analemma.com/Pages/Requirements/RequirementsPage.html and understood it but this other document on orthonormal systems looks to be a lot more accurate and sophisticated and less estimated.

If anyone would be willing to help me understand this paper (more or less starting with the introduction of orthonormal coordinates) I would greatly appreciate it.
 
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  • #2




Thank you for your interest in the Earth-Sun analemma and for bringing up the topic of orthonormal coordinate systems. These systems are commonly used in mathematical and scientific fields to describe and analyze the relationships between different variables or objects.

In the context of the Earth-Sun analemma, orthonormal coordinate systems are used to map the position of the Sun in the sky relative to the Earth's location. This allows us to better understand the shape and pattern of the analemma, as well as its variations throughout the year.

To understand equation (11) and the logic behind it, it is helpful to have a basic understanding of orthonormal coordinate systems. These systems use a set of mutually perpendicular axes to define a specific point or location in space. In the case of the Earth-Sun analemma, the axes would represent the Earth's orbit around the Sun and the tilt of the Earth's axis.

Equation (11) represents the transformation from spherical coordinates (latitude and longitude) to orthonormal coordinates, which are necessary for accurately determining the position of the Sun in the sky. This transformation involves using trigonometric functions to convert the spherical coordinates into the corresponding orthonormal coordinates.

I recommend reviewing the introduction to orthonormal coordinates in the paper you mentioned, as well as seeking additional resources to further your understanding of this topic. It is important to have a solid understanding of this concept in order to fully comprehend the Earth-Sun analemma and its derivation.

I hope this helps clarify some of your confusion. If you have any further questions, please do not hesitate to ask. Best of luck with your research on the Earth-Sun analemma.


 

1. What is the Earth Analemma and how is it formed?

The Earth Analemma is a figure-8 shaped curve that represents the apparent position of the Sun in the sky at the same time each day over the course of a year. It is caused by the Earth's elliptical orbit around the Sun and its axial tilt.

2. How is the Earth Analemma used in astronomy?

The Earth Analemma is used to determine the declination and right ascension of the Sun at any given time. This information is important for understanding the Earth's position in space and for celestial navigation.

3. What is an orthonormal coordinate system?

An orthonormal coordinate system is a mathematical tool used to describe the position of an object in three-dimensional space. It consists of three mutually perpendicular axes (x, y, and z) and is used to determine the location and orientation of an object.

4. How is an orthonormal coordinate system used in geodesy?

In geodesy, an orthonormal coordinate system is used to define the shape and orientation of the Earth's surface. It is used to determine the coordinates of points on the Earth's surface and to create maps and charts.

5. What are the advantages of using an orthonormal coordinate system over other coordinate systems?

An orthonormal coordinate system is advantageous because it is based on a fixed reference frame and can accurately describe the location and orientation of an object in three-dimensional space. It also allows for easy conversion between different coordinate systems, making it a useful tool in many fields of science and engineering.

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