If you have already determined GMT, then you can now begin to calculate the positions of the planets using the Ephemeris.
It is more convenient to use Ephemerides for midnight (they should indicate 00-00 or Midnight). This could be the American Ephemeris (The American Ephemeris at Midnight by Neil. F. Michelsen) or the Swiss Ephemeris (Swiss Ephemeris for 6000 years).
How to use Ephemerides? Open the Ephemeris for, say, September 1982.
IN left column from top to bottom you see the days of the month. IN top row you see icons indicating the planets: Sun, Moon at 00 o'clock, Moon at noon (Noon), Rising Lunar Node, then Mercury, Venus, Mars and all the other planets in order.
At the intersection of the date you are interested in and each column, the position of the planet at midnight GMT for that date is indicated. And the position of the Moon is also indicated at noon for convenience in calculations - since the Moon moves very quickly.
In the column for each planet, the degree is indicated first, then the Zodiac sign, then arc minutes and arc seconds (or tenths of a degree). For example:
Typically we only use degrees and arcminutes, no arcseconds.
Look at the column where the position of the Sun is indicated. You see that from September 1st to September 23rd the numbers increase. The sun moves through the sign of Virgo at a rate of approximately 1° per day. Each Zodiac sign occupies 30°. Having passed the sign of Virgo, the Sun moved into Libra - and from September 24, the countdown began from the 1st degree of Libra.
Planets move from at different speeds. The further to the right the column is located, the farther the planet is from the Sun in the sky and the lower it is angular velocity. For example, Pluto only moved 1° during the entire month.
The planet can seem to stop and go to reverse side(from the point of view of an earthly observer). In such cases, the numbers begin to decrease. For example, in September 1982, Mercury stopped at 17° 30" Libra on September 19 and went in the opposite direction ( retrograde movement denoted by the letter R).
Additional table
Now look at the additional table that is located in the Ephemeris at the bottom of the page, under the table for October.
IN left column Astro Data you can find the exact moment of rotation of the planets with Greenwich Mean Time.
Find the line: Mercury R 19 10:57. This means that Mercury went retrograde on September 19 at 10:57 GMT.
This column also indicates aspects major planets. Typically, such a table refers to two months at once, so what you see at the top of it refers to September, and what is slightly lower refers to October.
Column Planet Ingress shows the transition of planets to the sign of the Zodiac (planets and signs of the Zodiac are indicated by icons, but I will write in words).
So you see:
Venus Virgo 7 21:38 (Venus moved into Virgo on September 7 at 21-38 hours).
Mars Sagittarius 20 1:20 (Mars moved into Sagittarius on September 20 at 1-20 o'clock).
Sun Libra 23 8:46 (The Sun moved into Libra on September 23 at 8-46 am).
And just below in the same column you see data for October.
Now the column Last Aspect - Ingress. There are two such columns - on the left for September, to the right for October. Last Aspect is the last aspect (i.e. angle with another planet) of the Moon before the Moon moves into next sign Zodiac (Ingress). Let's look at the column for September (there are icons here, but I will call them words). Read the top line:
2 6:43 Pluto trine Pisces 2 16:11 (September 2 at 6-43 o'clock. The Moon makes a trine to Pluto, and on September 2 at 16-11 o'clock the Moon moves into the sign of Pisces).
The next line in the same column:
4 13:51 Neptune square Aries 5 0:24 (September 4 at 13-51 hours the Moon squares Neptune, and on September 5 at 0-24 hours the Moon enters the sign of Aries).
Column Phases & Eclipses: Moon phases and eclipses of the Sun and Moon.
Now in SpaceEngine you can observe real solar and lunar eclipses! This video shows the full solar eclipse August 21, 2017, which will be seen in the United States.
I've been working on planetary ephemeris for the past month. Ephemeris are data tables and code fragments that allow you to calculate the exact coordinates and velocities of the planets and satellites of the Solar System at any given point in time. Previously, SpaceEngine used Keplerian orbits, which are a good approximation of the motion of a planet around the Sun (or a moon around a planet) in the absence of disturbances. But the real solar system is not so simple, there are many planets and moons that pull each other with their gravity. This perturbs their orbits, making the Keplerian solution inaccurate. The moons are most susceptible to disturbances, as you can see in the video below - their orbits precess and wobble.
To predict the movements of planets and moons, astronomers use N-body simulations on supercomputers. At the beginning, tables of initial values are obtained from observations. state vectors(coordinates and velocities) of all the main bodies of the Solar system (Sun, planets, satellites, hundreds large asteroids, and is even used analytical model rings of Saturn). Then an N-body simulation is launched, similar to the one you can run in Universe Sandbox. But, unlike a game, scientific modeling is very accurate and takes into account many different subtle effects such as unevenness gravitational potential oblate planets, mascons on the Moon and relativistic effects. Simulations are carried out up to hundreds or thousands of years in both directions - into the future and into the past. Once completed, the resulting data sets are large and not very user-friendly. Therefore, astronomers derive an analytical solution that approximates the results obtained with some accuracy, or construct more compact tables of data and derive formulas for interpolating between points in these tables. Sometimes it is possible to develop a fully analytical model of the movement of an object.
There are many such solutions (“theories”) of the movement of planets and moons: VSOP87, DE405, TASS 1.7, etc., which are then used to calculate the coordinates of objects, predict eclipses, plan space flights; They are also used in various planetarium programs. In terms of application in SE, they can be divided into two categories:
On currently I have implemented the following theories in SpaceEngine:
Outside the operating time frame of orbital theory, SE uses extrapolation. The first or last available coordinates and velocity vector of the body are calculated, and a simple Keplerian orbit is constructed from them.
There are many other theories including alternative theories for the above bodies, and theories for small satellites. I'll add some of them to SE later. Note that the VSOP87 theory does not include the Moon, and the only theory of the Moon's motion implemented for SE is DExxx, so next version The SE will ship with a DE436 data file (approx. 100MB). In the future, I plan to implement the ELP2000-82 lunar theory, so VSOP87 can be made the main model (it does not have large data files, and has a much longer operating time range than DE436). There is a more modern version of it - VSOP2013, but it also requires large data files (several 300 MB each).
SE supports all JPL ephemeris (DExxx) and can be downloaded directly from the JPL FTP server. There is great solution DE431 for planets, sun and moon - it has a huge working time span of 30,000 years (from -13200 to 17191), but its data file weighs a whopping 2.6 GB. In theory, SpaceEngine should work with it, but I haven't tested it; SE may run out of memory (SE currently loads the entire file into RAM, and is limited to 4GB, like a 32-bit application). The available files on the JPL server end at DE431, but in the upper folders there are ASCII files and a utility asc2eph.f that can be used to convert them to the binary format supported by SE (you need to install a Fortran compiler to compile and run the utility). The JPL server also has data tables for hundreds of asteroids and all the simulated satellites, but their total size is several tens of gigabytes - I think this is overkill for SE.
I have also implemented analytical models axial rotation planets and moons, based on the IAU Working Group on Cartographic Coordinates and Rotational Elements (WGCCRE) document. They model the precession of the rotation axes of bodies and small periodic disturbances, but are valid only in a limited period of time, like orbital theories. Precession earth's axis it is not modeled there; it requires another analytical model. The rotation of the Moon is also modeled by the DE436 solution, so there are two alternatives.
To support analytical orbital theories, I changed the way SE renders orbital lines. Previously, each body generated its own “model” of the line; its shape and size depended on the orbital parameters. But then I realized that since all Keplerian orbits are conic sections (ellipse, parabola or hyperbola), they can be drawn with just three various models, with appropriate scaling and displacement - circle, parabola and hyperbola. It's very elegant and quick method, because now you can use instancing to display thousands of orbits at once. Memory and loading time are also saved (there is no need to create and store thousands of models). Real-time updating of changing orbits (analytical planetary orbits, as well as ship orbits) is now completely free - you just need to calculate a new scale/shift for these three models.
Before you criticize anything, figure it out first...
To do this, we need to find a post in this community called , find the 20th century there, go to the link and find the file corresponding to 1987
Scroll down the pages until you see exactly this
What is there and what does it mean?
Read the inscriptions in the upper left corner
This is the month and year for which the ephemeris is given. Month October, year 1987.
Read the inscription in the upper right corner
This means that the ephemeris is given on MIDNIGHT Greenwich Time.
It is clear that 0 hours 00 minutes on October 5 occurs on the night between October 4 and 5, and not between October 5 and 6. If they meant exactly midnight between October 5 and 6, they would write it as 24 hours 00 minutes.
Let's look at the first columns in the table
The first column indicates the day of the week and day
T 1 is Thursday, the first
F 2 - Friday, second.
The letter designations are taken from the English names of the days of the week - the first letters. This S Sunday M onday T uesday W ednesday T hursday F riday S aturday Our days of the week are deeply purple, so we won’t focus on this.
The second column is the sidereal time of birth. Let's take note of where to look for it, because we will need it later.
Let's look at the third column, where the Sun is.
There is a strange designation there:
This represents 17 degrees, 17 minutes and 10 seconds of Libra. Let's convert it to absolute value - we get 197 degrees 17 minutes.
We round up to minutes, since our time of birth is still not exact (yeah, we’ll also have midwives atomic clock Check time to the nearest second. Right now. And my mother, believe me, somehow had no time for this...)
Let's calculate the location of the Sun for the first working example. After homework 2 we should have got what we calculate for October 14 02 hours 15 minutes GMT
Let's subtract from the larger coordinate (this is 21 degrees 6 minutes - we take rounding) the smaller one (this is 20 degrees 06 minutes). we get 1 degree or 60 minutes).
60 minutes is the distance the sun traveled from midnight on October 14th to midnight on October 15th. But we are interested in where the sun was at 2 hours 15 minutes. So in an hour the sun will pass 60/12 minutes, i.e. 5 minutes. In 2 hours 15 minutes (2.25 hours) it will travel 5" times 2.25 = 11 degrees 45 minutes. Now we look at which midnight coordinate is smaller - the earlier (October 14) or the later (October 15). Less coordinate for October 14. Therefore, we add the resulting result to it, i.e. 20g06m+0g11m45s = 20g17m45s. What? Libra. Why Libra? We put our finger on the coordinates of our date and slowly move up. The first zodiac symbol we will meet is Libra, next to October 1st.
We take our leaf, put a protractor in the middle, combining 0 Aries and 0 protractor and mark `20^@18"`Libra. It will be `200^@18"` absolute value. Well, it's hard to poke by hand, poke somewhere between 20 and 21 degrees, in the middle.
Thus, we calculate and mark the Sun, Moon, Mercury, Venus, Mars, Saturn, Uranus, Neptune, Pluto, Black Moon, Proserpina (we take its coordinates from a separate table, which is in this post
This service allows you to select files accurate ephemeris knowing the date of observation. Just enter the date and click "Select".
Assignment of accurate ephemeris - more precision processing static observations. Their use in processing does not guarantee high quality, but can increase the number of fixed solutions if the work was carried out in difficult conditions(limited view in a city with dense buildings, near trees, etc.).
The data is calculated and stored publicly on the FTP servers of the International GNSS Service and the NASA Space Geodesy Data Archive.
The best final ephemeris is calculated and published with a delay of 12-18 days. In real time (or with a delay of several hours) the so-called. ultra-rapid and rapid products. Their accuracy is worse than that of the final ones, but at the same time significantly better than that of navigation ones.
The files are stored in packed form and can be unpacked by most archivers, for example 7zip
Utilities
The World Coordinate Converter
The site is based on voluntary principles, therefore, upon entering, it asks about donations in its favor. Mainly useful if you need to convert coordinates between different international systems coordinates, and some state ones (the parameters of which are open to public access, not about Ukraine), for example ETRF89, WGS84, WGS84 Web Mercator and publicly available state
Geocalculator NDIGK
The same geocalculator civil service Ukraine on issues of geodesy, cartography and cadastre.
TrimbleRTX
A service for post-processing from Trimble, the result is produced in the form of ETRS and ITRF of various implementations. Required long-term observations for acceptable accuracy. Based on observations international stations and some of their own. Free, but with registration
AusPOS
Geoscience Australia post-processing service from the Australian government, produces the result in the form of ITRF2014. Long-term follow-up is required for acceptable accuracy. Relies on observations from international stations. Free, no registration required.
GNSS Survey Planners
Tools for planning GNSS measurements for a certain period, allow you to estimate in advance the visible satellites at given angle cutoffs, their position above the horizontal. These tools will be useful when planning the optimal shooting time in places with poor sky visibility (quarries, cities) and when using single-system receivers.
What are astrological ephemeris tables? Why are they needed? In astronomy, an ephemeris is a table of the celestial locations of the Moon, Sun, planets and other space objects, calculated over equal time intervals. For example, at twelve o'clock at night every day.
Stellar ephemerides are tables that indicate the apparent positions of stars, subject to the influence of nutation, procession and aberration. Also called ephemeris is a formula that is used to calculate the moment of arrival of the instant of the next moment of minimum for darkened variable systems stars
Application
How are ephemeris tables used? They are used to determine the coordinates of the observer. This term also refers to the position data of synthetic Earth satellites used for navigation, for example, in the NAVSTAR (GPS), Galileo, and Glonass systems.
Information about the location of satellites is presented as part of special messages. Under these circumstances, we talk about ephemeris transmission.
Historical editions
It is known that in 1474 Regiomontanus published his famous ephemeris tables in Nuremberg. This work contained ephemerides for the years 1475-1506, which were calculated for each day. This book contained tables of planetary positions, conditions for conjunctions of luminaries and eclipses.
Modern editions
Today, ephemeris tables are published in the most important astrological collections: “Astronomical Yearbook” (published by the Russian Academy of Sciences since 1921), Nautical Almanac, American Ephemeris, Berliner Astronomisches, Connaissance des Temps. In addition, there are websites that can help you calculate ephemeris. They are created by both enthusiasts and professionals.
Thus, it is known that on the NASA website Fred Espeñac published data on the positions of the planets solar system, Moon and Sun for 1995-2006. And on the website of the Institute for Calculation of Ephemeris and Celestial Mechanics there is a calculator for the coordinates of space objects. In addition, there is a library with which you can make astronomical calculations on an Excel sheet using the ephemeris of Switzerland, JPL and Moschières.
Calculation
Ephemeris tables are in service with every astrologer. Today, the movement of objects around the Sun has been studied very well. Created by various astrological associations mathematical forms for calculating ephemeris, competing with each other in accuracy. These samples are described in special astronomical publications.
Old theory
The ILE version is an improvement on Brown's theory. It was first proposed by E. W. Brown in 1919 in his work Tables of the Motion of the Moon, which was improved by W. J. Eckert in 1954 in his work Improved Lunar Ephemeris. Subsequently, changes were made to the theory several more times.
This model was previously used by F. Espeignac to calculate eclipses provided by the NASA website.
New solution
Version VSOP82 describes the movement of planets around the Sun. It was proposed in 1982 by P. Bretagnon and published in the astrological almanac “Astrophysics and Astronomy” under the title “Theory of the movement of all planets - solution VSOP82”.
Another version
The ELP 2000 version describes only the ephemeris of the Moon. It was published in the astrological collection “Astrophysics and Astronomy” in 1983 by M. Chapron-Touzet and J. Chapron, as well as in the article “Ephemerides of the Moon ELP 2000”. This theory contains 7,684 periodic terms for the Moon's ecliptic latitude, 20,560 for ecliptic longitude, and 9,618 for distance. The amplitude of the minor terms corresponds to 2 cm for distances and 0.00001 arcseconds. IN simplified form the model is used by F. Espeignac to calculate eclipses published on the NASA website.
USSR Publications
What can you say about domestic astrology? Based on the DE200/LE200 version, he published ephemeris of the Moon, Sun and planets in the Astrological Yearbook of the USSR (since 1986).
JPL laboratory model
Version DE403/LE403 describes the movement of the planets around the Sun and focuses on the coordinates of the Moon. It was developed by JPL laboratory employees Standish, Williams, Newhall and Faulkner. It was published in the article “JPL DE403/LE403 Lunar and Planetary Ephemerides” (1995) in special edition the specified laboratory. Today there are new ephemeris tables developed by JPL.
Convenient tables
The positions of the planets were calculated by stargazers for many years in advance, and the results of the calculations were translated into tables. They contain data on the apparent positions of the planets, which are calculated using a computer, guided by the laws of cosmic mechanics. The positions of celestial objects in the tables are indicated with a specific step, indicating the length of time between the two related instants for which the calculation is performed. It is convenient to use the following tables in one-day increments:
- American Michelson ephemeris table for the 21st century from 2001 to 2050 and for the 20th century from 1900 to 2000.
- Rosicrucian ephemerides (1900-2000).
- Raphael tables (positions of planets for each year).
It is known that in Michelson's ephemeris the position of celestial objects is given at Greenwich midnight of each day, and the data is presented monthly. Each page contains the longitude values of the planets for two months in the form of a pair of blocks (Longitude).