Fix planetocentric rectangular coordinates

[worachate001]

Description

As mentioned in #2237 Sun & Moon are not aligned at greatest solar eclipse. I suspect that something is wrong with observer's coordinates on Earth and it's right.

There is a bug in planetocentric rectangular coordinate calculations that give wrong values of rhoCosPhiPrime and rhoSinPhiPrime. After fixing this issue, the Sun and Moon are aligned perfectly for all central solar eclipses! This should also improve the accuracy of topocentric coordinates for all objects.

Type of change

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• This change requires a documentation update

Test Configuration:

• Operating system: Ubuntu 20.04

Checklist:

• My code follows the code style of this project.
• I have performed a self-review of my own code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation (header file)
• I have updated the respective chapter in the Stellarium User Guide
• My changes generate no new warnings
• I have added tests that prove my fix is effective or that my feature works
• New and existing unit tests pass locally with my changes
• Any dependent changes have been merged and published in downstream modules

[github-actions]

Great PR! Please pay attention to the following items before merging:

Files matching src/**/*.cpp:

• Are possibly unused includes removed?

This is an automatically generated QA checklist based on modified files

[worachate001]

@gzotti Thanks.

[alex-w]

Part of code in Planes.cpp and AstroCalcDialog.cpp files are identical - why not reuse it?

[worachate001]

Part of code in Planes.cpp and AstroCalcDialog.cpp files are identical - why not reuse it?

Yes. Thinking about that, but I need a rest soon, it's almost midnight here.

[worachate001]

Update: the revision is going well until I found a new bug in AstroCalc/Eclipses. Trying to fix it before pushing this commit.
Update2: the new bug has been fixed. It seems to work well so far without any strange looking numbers.

[alex-w]

Why not use official term instead of "Sun/Moon diameter ratio"?

[worachate001]

Why not use official term instead of "Sun/Moon diameter ratio"?

This is an example of total eclipse when you're standing near the limit of umbra.

We already have 'Eclipse magnitude' below 'Eclipse obscuration' - eclipse magnitude here indicates how close you are to the northern or southern limit of umbra. It will be close to 1.0 if you are just inside the umbra.

Moon/Sun diameter ratio is different value, if we use the same term, it will be contradict to Eclipse magnitude above it. I think users may be confused of having two magnitudes at the same time.

Moon/Sun diameter ratio is central eclipse magnitude in NASA web site. If we use this value in the place below eclipse obscuration, it will cause confusion when an eclipse reaches magnitude 1.0 at 2nd contact and jump to 1.078 in this case.

[worachate001]

Example of magnitude at greatest eclipse from two sources that show different value for the same event (look at 1955 Jun 20)

Above from https://eclipse.gsfc.nasa.gov/JSEX/JSEX-AU.html
and
https://astro.ukho.gov.uk/eclipse/0311955/Bangkok_Thailand_1955Jun20.png

[gzotti]

Probably we should re-arrange the lines, though:

• Eclipse magnitude
• Eclipse obscuration
• Moon/Sun diameter ratio
• Central eclipse duration
• ...

By this, we would have the "coverage" items first, then the geographic data.

[alex-w]

Thanks for improving!

[alex-w]

@gzotti the PR is good for me, please merge it if he is good for you too