What astrological tables Efemerides? What are they necessary for? In an astronomy, Efemerid is called the table of the celestial location of the moon, the sun, planets and other space objects calculated through the same periods of time. For example, for twelve hours of the night every day.

Star ephemeris are called tables in which the visible position of the stars is indicated, the influence of the nation, procession and aberration. Also, ephemeride is called the formula, with which the moment of arrival of the next moment of the minimum for darkened variables of stars is calculated.

Application

How are ephemeride tables used? With the help of them, the coordinates of the observer are determined. This term also refers to the position of the positions of the synthetic satellites of the Earth used to navigate, for example, in the NAVSTAR system (GPS), Galileo, GLONASS.

The location information of satellites is presented as part of special messages. Under these circumstances, they are talking about the transfer of ephemeride.

Historical publications

It is known that in 1474, Regiomontan published his famous ephemerid tables in Nuremberg. In this work there were ephemerides on 1475-1506, which were designed for every day. This book contained tables of planets, connectivity conditions shining and eclipses.

Modern editions

Today, ephemerid tables are published in the most important astrological compilations: "Astronomical Yearbook" (published wounds since 1921), Nautical Almanac, American Ephemeris, Berliner Astronomisches, Connaissance Des Tempps. In addition, there are sites with which you can calculate ephemerides. They are created both enthusiasts and professionals.

So, it is known that the Supinyak Fred published these positions of the planets solar system, Moon and Sun for 1995-2006. And on the website "Institute of Calculation of Ephemerid and Heavenly Mechanics" there is a coordinate calculator of space objects. In addition, there is a library with which you can carry out astronomical calculations on the Excel sheet using Switzerland ephemerides, JPL and Moshier.

Payment

Efemeride tables are in service with each astrologer. Today, the movement of objects around the Sun has been studied very well. Mathematical forms for calculating ephemeride, competing with accuracy, are created by different astrological associations. These samples are described in special astronomical publications.

Old theory.

ILE version is an improved Brown's theory. She was first offered by E. W. Brown in 1919 in his work "The Moon Travel Tables", which was improved by W. J. Ekert in 1954 in the work "Improved Moon Efemerid". In the future, changes were made several times a few times.

This model was previously used by F. Espenyak to calculate the eclipses provided by the NASA site.

New solution

Version VSOP82 describes the movement of the planets around the sun. It was proposed in 1982 by P. Brethanon and printed in astrological almanacia "Astrophysics and Astronomy" called "the theory of movement of all planets - the solution of VSOP82".

Another version

ELP 2000 version describes only the efemerides of the moon. She was published in the astronomological collection "Astrophysics and Astronomy" in 1983 M. Shapron-Tuza and J. Shapron, as well as in the EFEMERIDE EFEMERID ELP 2000. This theory contains 7,684 periodic member for the ecliptic latitude of the moon, 20 560 - for ecliptic longitude and 9,618 - for distance. The amplitude of younger members corresponds to 2 cm for distances and 0.00001 seconds of the arc. In a simplified form, the model is applied by F. Espenyak to calculate eclipses promulgated on the NASA website.

Publications of the USSR

And what can be said about domestic astrology? Based on the version of DE200 / LE200, the Efemerides of the Moon, the Sun and the Planets "Astrological Yearbook of the USSR" (starting since 1986).

JPL Laboratory Model

The DE403 / LE403 version describes the movement of the planets around the Sun and focuses on the coordinates of the moon. She was developed by the employees of the laboratory JPL Standish, Williams, Newholle and Falkner. It is published in the article "Lunar and Planetary Ephemerides JPL DE403 / LE403" (1995) in a special edition of the specified laboratory. Today there are new ephemeris tables developed by JPL.

Comfortable tables

The position of the planets is as learned by asterlets for many years, and the results of calculations are translated into the tables. These are the data of the visible positions of the planets, which are calculated using a computer, guided by the laws of space mechanics. The positions of the celestial objects in the tables are specified with a specific step that denotes the length of the time between the two connected moments to which the calculation is performed. It is convenient to apply the following tables in a step in one day:

  • The American Table of Michelson Eumeride for the XXI century from 2001 to 2050 and for the twentieth century from 1900 to 2000.
  • Rosencraisor ephemerides (1900-2000).
  • tables of Raphael (positions of the planets for each year).

It is known that in the ephemerides of Michelson, the position of heavenly objects is given to Greenwich midnight every day, and the data are presented in the monthly. On each page, the values \u200b\u200bof the longitude of the planets are placed in two months in the form of a pair of blocks (LONGITUDE).

Before hazing anything, you first disperse ...

To do this, we need to find a post in this community, called there to find the XX century, go to the link and find the file, corresponding to 1987

Scroll down the pages until you see it

What is there and what does it mean?

Read the inscriptions in the upper left corner

This month and year, to which ephemerides are given. Month October, year 1987.

We read the inscription in the upper right corner

This denotes that ephemerides are shown on Midnight of Greenwich Time.

It is clear that 0 hours 00 minutes October 5, it happens on the night between October 4 and 5, and not between October 5 and 6. If you had a midnight between October 5 and 6, then they would write as 24 hours 00 minutes.

Consider the first columns in the table

The first column indicates the day of the week and the number

T 1 is Thursday, the first
F 2 - Friday, second.

Letter notation taken from the English names of the days of the week - the first letters. it S.unday. M.onday. T.uesday. W.ednesday T.hursday F.riday. S.aturday for us the days of the week deeply purple, so we will not sharpen on it.

The second column is the star time. Take a note, where to look for it, because it will be needed in the future.

Let's look at the third column where the sun.

There are a strange designation:

Indicates it is 17 degrees, 17 minutes and 10 seconds of the scales. We translate into absolute value - we get 197 degrees of 17 minutes.

Round up to minutes, because we still do not exactly (yeah, we will have an atomic clock with an atomic hour with an up to a second time. Right now. And mom, believe me, it was somehow not up to that ...)

Let's calculate the location of the Sun for the first working example. After homework 2 We had to get that we believe for October 14, 02 hours 15 minutes GMT

Letting out of the greater coordinates (this is 21 degrees of 6 minutes - we take rounding) less (this is 20 degrees 06 minutes). We get 1 degree or 60 minutes).

60 minutes is the distance that the sun passed from midnight October 14 until midnight October 15. But we are interested, where the sun was 2 hours 15 minutes. So, the sun will take 60/12 minutes, i.e. 5 minutes. 2 hours 15 minutes (2.25 hours) It will pass 5 "multiply by 2.25 \u003d 11 degrees 45 minutes. Now we look - what a midnight coordinate is less - earlier (October 14) or later (October 15). Less Coordinate on October 14th. Therefore, we will add the result to it. Those. 20G06m + 0G11M45C \u003d 20G17M45C. Crowing, we get `20 ^ @ 18" `. What? Scales. Why scales? We put your finger on the coordinates of our date and slowly go up. The first symbol of the zodiac, which we will meet - there will be scales, near October 1.

We take our leaf, we apply a transportation in the middle, combining 0 Aries and 0 of the transportation and mark `20 ^ @ 18" `Weighs. It will` 200 ^ @ 18 "` absolute value. Well, manually it is difficult to poke, poke somewhere between 20 and 21 degrees, in the middle.

Thus, we calculate and celebrate the sun, the moon, Mercury, Venus, Mars, Saturn, Uranus, Neptune, Pluto, Black Moon, Proserpin (its coordinates take from a separate table, which in this post

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If you have already identified GMT, now you can proceed to calculate the position of the planets on ephemeris.

It is more convenient to use ephemeris at midnight (there must be 00-00 or Midnight in them). This can be American Ephemerides (The American Ephemeris at Midnight by Neil. F. Michelsen) or Swiss Ephemeris (Swiss Ephemeris for 6000 years).

How to use ephemeris? Open ephemerides, suppose for September 1982.

IN left column From top to bottom you see the days of the month. IN top row You see the icons denoting planets: the sun, the moon at 00 an hour, the moon at noon (noon), the upstream moon node, then Mercury, Venus, Mars and all other planets in order.

At the intersection of the date of interest to you and each column, the location of the planet on Midnight of Greenwich for this date is indicated. And the position of the moon is also indicated at noon for convenience in the calculations - since the moon moves very quickly.

In the column for each planet, the degree is first indicated, then the zodiac sign, then angular minutes and angular seconds (or the tenths of degrees). For example:

Usually we use only degrees and angular minutes, without angular seconds.

Look at that column where the position of the Sun is indicated. You see that from September 1 to September 23, the numbers are increasing. The sun comes on the sign of the virgin at a speed of about 1 ° per day. Each zodiac sign takes 30 °. Having passed the sign of the Virgin, the sun passed into the scales - and from September 24 the countdown began from the 1st degree of scales.

Planets are moving at different speeds. The relevant the column is located, the farther from the sun is the planet in the sky and the lower its angular speed. For example, Pluto passed over the entire month only 1 °.

The planet may seem to stop and go to reverse side (from the point of view of the earth observer). In such cases, the numbers begin to decrease. For example, in September 1982, Mercury on September 19 stopped at point 17 ° 30 "Weighs and went in the opposite direction ( retrograd movedenoted by the letter R).

Additional Table

Now look at the additional table, which is located in ephemeris at the bottom of the page, under the table for October.

IN left column Astro Data You can find an accurate moment of turning planets indicating Greenwich's time.

Find a line: Mercury R 19 10:57. This means that Mercury became retrograde on September 19 at 10:57 hours in Greenwich.

As well as in this column indicated aspects large planets. Typically, such a table refers to two months at once, so what you see in the upper part of it relates to September, and the fact that a little lower - by October.

Column Planet Ingress. Shows the transition of the planets as a sign of the zodiac (the planets and signs of the zodiac are indicated by icons, but I will write words).

So, you see:

Venus Venus 7 21: 38 (Venus switched to the male on September 7 in 21-38 hours.).
Mars Sagittarius 20 1:20 (Mars switched to Sir September 20 at 1-20 hours).
Sun scales 23 8:46 (the sun passed into scales on September 23 at 8-46 hours.).

And just below in the same post you see the data for October.

Now Column Last Aspect - Ingress. Two such columns - to the left for September, to the right to October. Last Aspect is the last aspect (i.e. angle with another planet) of the moon before moving the moon in next sign Zodiac (ingress). Let's see the column for September (here icons, but I will call them words). We read the upper line:

2 6:43 Pluto Trigon Fish 2 16:11 (September 2 at 6-43 hours. The moon makes trigon to Pluto, and on September 2 at 16-11 hours. The moon goes into fish sign).

Next line in the same column:
4 13:51 Neptune Quadrature Aries 5 0:24 (September 4, at 13-51 hours. The moon makes the square to Neptune, and on September 5 at 0-24 hours. The moon goes into the sign of Aries).

Column Phases & Eclipses.: Phases of the moon and the eclipse of the sun and the moon.

And I would like to contribute to this thing. In one of the comments to the aforementioned article, the conversation about ephemeride theories, such as DE and others, are minimized. However, there are many such theories and we will analyze some of the most significant in my opinion.

What it is?
In order to accurately count positions heavenly Tel, you need to take into account as many disturbing factors as possible. An analytical solution for a system of more than two no (exception - private solutions of Lagrange), therefore the equations of motion of the bodies are solved numerically, but even taking into account the new methods of numerical integration (such as the Everhart method), this procedure is very expensive, and if a fairly accurate solution for a small The time interval under the average PC, the integration on global time ranges is a complex and time-consuming task. Therefore, the problem was decided as follows: to find the positions of heavenly bodies using integration and approximate these positions by some function, and at the output to get coefficients for this function. It is a set of these coefficients and is called, as a rule, an ephemeride theory.

DE.

Probably this is the most popular theory of the movement of the celestial bodies. The appearance of this theory is associated with the development space Technology And the need for accurate calculation of the position of the planets for AMC missions. For today, there is a huge list of versions of this theory. The most popular of them is DE405. This theory can be read here: http://ssd.jpl.nasa.gov/?Planet_EPH_EXPORT
The coefficients are divided into temporary blocks, i.e. For a separate era - separate coefficients.
Formula for these coefficients - Chebyshev polynomial. By the way, it was Polyenna Chebyshev one of the most suitable for creating an ephemeride theory. The principle of working with such polynomials is described in the book of O. Montebruck - "Astronomy on personal Computer"(Rutracker.org)
Where to get?
All this lies on the FTP site NASA. In ASCII text format: ftp: //ssd.jpl.nasa.gov/pub/eph/planets/ascii/
Here, probably, it is worth commenting. Going, for example, in this folder, we will see the file of about the following type: ASCP1600.403, it is easy to understand that this is a coefficient on the era of 1600, and the DE403 theory version.
In such files there are three columns - each of them meets the coordinate in space.
However, looking at the size of these files, it will become clear that it is not convenient to use them. Therefore, there are their binary versions: ftp://ssd.jpl.nasa.gov/pub/eph/planets/bsp/
How to apply?
So we got the binary you need, but the question is: what to do it? Fortunately, on FTP there are examples of implementing programs on different languages: ftp://ssd.jpl.nasa.gov/pub/eph/planets/

VSOP 87.

This theory is certainly not so popular as the previous one, however, it is I can recommend it for beginners. There is a major drawback of this theory - it describes only the planets and the sun. The formula type in this theory is a trigonometric series.
Where to get?
It is simpler simple, just go to the site and choose the desired language, data format in the individual.
It is in the simplicity of obtaining and is the main advantage of this ephemerida.
Having ready-made code, I think many of us can do something with it. But, if you still need a slight tip on it, you can contact here

EPM.

About this ephemeride theory is very few mention. It was created at the Institute of Applied Astronomy of the Russian Academy of Sciences. There are 3 versions of this theory, appropriate EPM 2004, EPM 2008, EPM 2011.
Where to get?
The source code is on FTP IPA RAS: FTP://quasar.IPA.nw.ru/incoming/epm/data/. The name of the folder meets the values \u200b\u200bof the theory. In each theory there is a corresponding binary and text file, as implemented in DE. And here also text files weigh quite a lot, so it is necessary to use the binaries
How to apply?
It is this theory that seems to be one of the smash complex in the implementation. Nevertheless, her developers took care of us and led several examples in different languages: ftp://quasar.ipa.nw.ru/incoming/epm/.
The theory itself is built on the polynomials of Chebyshev, they are also quite well described.

Notes on accuracy

It is worth noting that not all theories are most accurate. The least accurate of all, above listed - VSOP87. DE and EPM are quite accurate, it is worth noting that the latter takes into account the relative effects. However, almost all applied tasks that I still have decided to have been used by VSOP 87, the fact is that at least its accuracy is lame, but nevertheless, it is not noticeable when comparing with elementary observations (there may be deviations for tenths, hundredths Angular second).

Finally

I will say a little in addition, about the EPM theory. I learned about this theory from a personal conversation, she is known in rather narrow circles, and it enjoys some users, apparently it is somehow connected with the disinterest of the institute in the spread of this theory in wide ranges, another explanation does not occur to me, for it is quite Competitively capable of relation to other theories.