Calculation of the position of celestial bodies and ephemeris theories
I recently read about Calculation of the position of celestial bodies in the sky and would like to contribute to this matter. In one of the comments on the aforementioned article, the conversation about ephemeris theories, such as DE and others, is briefly touched. However, there are many such theories and we will analyze some of the most significant in my opinion.
In order to accurately calculate the position of celestial bodies, it is necessary to take into account as many perturbing factors as possible. There are no more analytical solutions for the system more than two (the exception is the particular Lagrange solutions), therefore the equations of motion of bodies are solved numerically, but even taking into account the relatively new numerical integration methods (such as the Everhart method), this procedure is very costly, and if the while the average PC can do it, the integration on global time bands is a difficult and time consuming task. therefore, the problem was solved as follows: to find the positions of celestial bodies using integration and approximate these positions by some function, and obtain the coefficients for this function at the output. It is the set of these coefficients that is called, as a rule, the ephemeris theory.
Perhaps this is the most popular theory of the motion of celestial bodies. The emergence of this theory is associated with the development of space technology and the need for accurate calculation of the position of the planets for AMC missions. Today there is a huge list of versions of this theory. The most popular of them is the DE405. You can read about this theory here: http://ssd.jpl.nasa.gov/?planet_eph_export
The coefficients are divided into time blocks, i.e. for a single epoch - separate coefficients
The formula for these coefficients is the Chebyshev polynomial . By the way, Chebyshev polynomial is one of the most suitable for creating an ephemeris theory. The principle of working with such polynomials is described in the book by O. Montebrook - “Astronomy on a Personal Computer” ( Rutracker.org )
All this lies on the NASA ftp site. In ASCII text format: ftp://ssd.jpl.nasa.gov/pub/eph/planets/ascii/
Here, perhaps, is something to comment on. Going to this folder , for example, we will see a file of the following form: ascp1600.403, it’s easy to understand that this is the coefficient for the 1600 epoch, and the version of the DE403 theory.
In such files there are three columns - each of them corresponds to a coordinate in space.
However, looking at the size of these files, it becomes clear that it is not convenient to use them in work. Therefore, there are binary versions: ftp://ssd.jpl.nasa.gov/pub/eph/planets/bsp/
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So we got the binary we needed, but the question is: what to do with it? Fortunately, on ftp there are examples of the implementation of programs in different languages: ftp://ssd.jpl.nasa.gov/pub/eph/planets/
All references are given for planets, but in theory there are coefficients for small bodies of the solar system. All this is similarly located here: ftp://ssd.jpl.nasa.gov/pub/eph/
This theory is certainly not as popular as the previous one, however, I can recommend it for beginners. There is a main disadvantage of this theory - the positions of only the planets and the Sun are described in it. The kind of formula in this theory is a trigonometric series.
It’s as simple as that, just go to http://www.neoprogrammics.com/vsop87/source_code_generator_tool/ and select the desired language and data format in the settings.
It is in the simplicity of receiving that the main advantage of this ephemeris lies.
Having ready code, I think many of us can already do something with it. But, if you still need a little hint on it, you can contact here.
There are very few references to this ephemeris theory. It was created at the Institute of Applied Astronomy of the Russian Academy of Sciences. There are 3 versions of this theory, respectively EPM 2004, EPM 2008, EPM 2011.
Source codes are at the IPA RAS ftp: ftp://quasar.ipa.nw.ru/incoming/EPM/Data/ . The folder name corresponds to the theory version. In each theory there is a corresponding binary and text file, as it is implemented in DE. Here, too, text files weigh quite a lot, so you should use binaries.
It is this theory that seems to be one of the most difficult to implement. Nevertheless, its developers took care of us and gave several examples in different languages: ftp://quasar.ipa.nw.ru/incoming/EPM/ .
The theory itself is built on Chebyshev polynomials, they are also quite well described here .
It is worth noting that not all theories are the most accurate. The least accurate of all those listed above is VSOP87. DE and EPM are fairly accurate, it is worth noting that the latter takes into account relativistic effects. However, for almost all applied problems that I have solved so far, VSOP 87 was used, the fact is that although its accuracy is lame, nevertheless, this is not noticeable when compared with elementary observations (there may be deviations by tenths, hundredths angular seconds).
I will say a little in addition, about the theory of EPM. I learned about this theory from a personal conversation, it is known in rather narrow circles, and few users use it, apparently this is somehow connected with the institute’s disinterest in spreading this theory in wide circles, it doesn’t come to my mind competitive in relation to other theories.
What it is?
In order to accurately calculate the position of celestial bodies, it is necessary to take into account as many perturbing factors as possible. There are no more analytical solutions for the system more than two (the exception is the particular Lagrange solutions), therefore the equations of motion of bodies are solved numerically, but even taking into account the relatively new numerical integration methods (such as the Everhart method), this procedure is very costly, and if the while the average PC can do it, the integration on global time bands is a difficult and time consuming task. therefore, the problem was solved as follows: to find the positions of celestial bodies using integration and approximate these positions by some function, and obtain the coefficients for this function at the output. It is the set of these coefficients that is called, as a rule, the ephemeris theory.
DE
Perhaps this is the most popular theory of the motion of celestial bodies. The emergence of this theory is associated with the development of space technology and the need for accurate calculation of the position of the planets for AMC missions. Today there is a huge list of versions of this theory. The most popular of them is the DE405. You can read about this theory here: http://ssd.jpl.nasa.gov/?planet_eph_export
The coefficients are divided into time blocks, i.e. for a single epoch - separate coefficients
The formula for these coefficients is the Chebyshev polynomial . By the way, Chebyshev polynomial is one of the most suitable for creating an ephemeris theory. The principle of working with such polynomials is described in the book by O. Montebrook - “Astronomy on a Personal Computer” ( Rutracker.org )
Where to get?
All this lies on the NASA ftp site. In ASCII text format: ftp://ssd.jpl.nasa.gov/pub/eph/planets/ascii/
Here, perhaps, is something to comment on. Going to this folder , for example, we will see a file of the following form: ascp1600.403, it’s easy to understand that this is the coefficient for the 1600 epoch, and the version of the DE403 theory.
In such files there are three columns - each of them corresponds to a coordinate in space.
However, looking at the size of these files, it becomes clear that it is not convenient to use them in work. Therefore, there are binary versions: ftp://ssd.jpl.nasa.gov/pub/eph/planets/bsp/
')
How to apply?
So we got the binary we needed, but the question is: what to do with it? Fortunately, on ftp there are examples of the implementation of programs in different languages: ftp://ssd.jpl.nasa.gov/pub/eph/planets/
Small note
All references are given for planets, but in theory there are coefficients for small bodies of the solar system. All this is similarly located here: ftp://ssd.jpl.nasa.gov/pub/eph/
VSOP 87
This theory is certainly not as popular as the previous one, however, I can recommend it for beginners. There is a main disadvantage of this theory - the positions of only the planets and the Sun are described in it. The kind of formula in this theory is a trigonometric series.
Where to get?
It’s as simple as that, just go to http://www.neoprogrammics.com/vsop87/source_code_generator_tool/ and select the desired language and data format in the settings.
It is in the simplicity of receiving that the main advantage of this ephemeris lies.
Having ready code, I think many of us can already do something with it. But, if you still need a little hint on it, you can contact here.
EPM
There are very few references to this ephemeris theory. It was created at the Institute of Applied Astronomy of the Russian Academy of Sciences. There are 3 versions of this theory, respectively EPM 2004, EPM 2008, EPM 2011.
Where to get?
Source codes are at the IPA RAS ftp: ftp://quasar.ipa.nw.ru/incoming/EPM/Data/ . The folder name corresponds to the theory version. In each theory there is a corresponding binary and text file, as it is implemented in DE. Here, too, text files weigh quite a lot, so you should use binaries.
How to apply?
It is this theory that seems to be one of the most difficult to implement. Nevertheless, its developers took care of us and gave several examples in different languages: ftp://quasar.ipa.nw.ru/incoming/EPM/ .
The theory itself is built on Chebyshev polynomials, they are also quite well described here .
Accuracy Notes
It is worth noting that not all theories are the most accurate. The least accurate of all those listed above is VSOP87. DE and EPM are fairly accurate, it is worth noting that the latter takes into account relativistic effects. However, for almost all applied problems that I have solved so far, VSOP 87 was used, the fact is that although its accuracy is lame, nevertheless, this is not noticeable when compared with elementary observations (there may be deviations by tenths, hundredths angular seconds).
Finally
I will say a little in addition, about the theory of EPM. I learned about this theory from a personal conversation, it is known in rather narrow circles, and few users use it, apparently this is somehow connected with the institute’s disinterest in spreading this theory in wide circles, it doesn’t come to my mind competitive in relation to other theories.
Source: https://habr.com/ru/post/204986/
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