Calculation of the position of celestial bodies and ephemeris theories
Most recently, I read about the calculation of the position of celestial bodies in the firmament and would like to contribute to this matter. In one of the comments on the aforementioned article, a 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 disturbing factors as possible. There is no analytical solution for a system of 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 relatively new methods of numerical integration (such as the Everhart method), this procedure is very costly, and if the solution is sufficiently accurate for a small Since a period of time is under the power of an average PC, then integration on global time ranges is a difficult and time-consuming task. therefore, the problem was solved as follows: to find the positions of celestial bodies by integration and to approximate these positions by some function, and to 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 these are the most popular theories of 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 missions of the AMS. Today there is a huge list of versions of this theory. The most popular of them is 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 particular era - individual factors.
The formula for these coefficients is the Chebyshev polynomial . By the way, the 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 of O. Montebrook - “Astronomy on a personal computer” ( Rutracker.org )
All this lies on the ftp site of NASA. In ASCII text format: ftp://ssd.jpl.nasa.gov/pub/eph/planets/ascii/
There is probably something worth commenting on here. Having entered , for example, this folder , we will see a file similar to the following: ascp1600.403, it is easy to understand that this is a coefficient for the era of 1600, and the theory version is DE403.
There are three columns in such files - each of them corresponds to a coordinate in space.
However, looking at the size of these files, it becomes clear that using them in your work is not convenient. Therefore, there are their binary versions: ftp://ssd.jpl.nasa.gov/pub/eph/planets/bsp/
So we got the binary we need, but the question is: what should I do with it? Fortunately, ftp has examples of implementing 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, of course, is not as popular as the previous one, however, I can recommend it for beginners. There is the main drawback of this theory - it describes the positions of only the planets and the sun. The form of the formula in this theory is a trigonometric series.
It’s as simple as simple, just go to the website http://www.neoprogrammics.com/vsop87/source_code_generator_tool/ and select the desired language, data format in the settings.
It is in the simplicity of preparation that the main advantage of this ephemeris lies.
Having ready-made code, I think many of us can already do something with it. But, if you still need a little hint on it, then 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.
Sources are on ftp IPA RAS: ftp://quasar.ipa.nw.ru/incoming/EPM/Data/ . The name of the folder corresponds to the theory version. Each theory has a binary and a text file, as implemented in DE. And here also text files weigh quite a lot, so you should use binaries
It is this theory that seems to be one of the smallest 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 most accurate. The least accurate of all the above is VSOP87. DE and EPM are fairly accurate, it is worth noting that the latter takes into account relativistic effects. However, VSOP 87 was used for almost all the applied tasks that I still solved, the fact is that although its accuracy is lame, it is not noticeable when compared with elementary observations (there may be deviations by tenths or hundredths angular second).
I will say a little in addition, regarding 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, no other explanation comes to my mind, because it is quite 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 disturbing factors as possible. There is no analytical solution for a system of 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 relatively new methods of numerical integration (such as the Everhart method), this procedure is very costly, and if the solution is sufficiently accurate for a small Since a period of time is under the power of an average PC, then integration on global time ranges is a difficult and time-consuming task. therefore, the problem was solved as follows: to find the positions of celestial bodies by integration and to approximate these positions by some function, and to 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 these are the most popular theories of 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 missions of the AMS. Today there is a huge list of versions of this theory. The most popular of them is 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 particular era - individual factors.
The formula for these coefficients is the Chebyshev polynomial . By the way, the 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 of O. Montebrook - “Astronomy on a personal computer” ( Rutracker.org )
Where to get it?
All this lies on the ftp site of NASA. In ASCII text format: ftp://ssd.jpl.nasa.gov/pub/eph/planets/ascii/
There is probably something worth commenting on here. Having entered , for example, this folder , we will see a file similar to the following: ascp1600.403, it is easy to understand that this is a coefficient for the era of 1600, and the theory version is DE403.
There are three columns in such files - each of them corresponds to a coordinate in space.
However, looking at the size of these files, it becomes clear that using them in your work is not convenient. Therefore, there are their binary versions: ftp://ssd.jpl.nasa.gov/pub/eph/planets/bsp/
How to apply?
So we got the binary we need, but the question is: what should I do with it? Fortunately, ftp has examples of implementing 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, of course, is not as popular as the previous one, however, I can recommend it for beginners. There is the main drawback of this theory - it describes the positions of only the planets and the sun. The form of the formula in this theory is a trigonometric series.
Where to get it?
It’s as simple as simple, just go to the website http://www.neoprogrammics.com/vsop87/source_code_generator_tool/ and select the desired language, data format in the settings.
It is in the simplicity of preparation that the main advantage of this ephemeris lies.
Having ready-made code, I think many of us can already do something with it. But, if you still need a little hint on it, then 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 it?
Sources are on ftp IPA RAS: ftp://quasar.ipa.nw.ru/incoming/EPM/Data/ . The name of the folder corresponds to the theory version. Each theory has a binary and a text file, as implemented in DE. And here also 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 smallest 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 .
Precision Notes
It is worth noting that not all theories are most accurate. The least accurate of all the above is VSOP87. DE and EPM are fairly accurate, it is worth noting that the latter takes into account relativistic effects. However, VSOP 87 was used for almost all the applied tasks that I still solved, the fact is that although its accuracy is lame, it is not noticeable when compared with elementary observations (there may be deviations by tenths or hundredths angular second).
Finally
I will say a little in addition, regarding 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, no other explanation comes to my mind, because it is quite competitive in relation to other theories.