Calculation and programming 1995-2005 by Jukka T. Tulkki. The methods of calculation bases on VSOP87 (Variations Séculaires des Orbites Planétaires) planetary theory published by Bretagnon – Francou. Program code of the software contains several hundred pages.

SOLAR analemma * Obliquity of the Ecliptic * motion of the Earth * Daytable: Right Ascension * Declination * Distance to the Earth * Parallax of the Moon * Topocentric Right Ascension * Topocentric declination * Azimuth of the Moon * Altitude of the Moon * Moon rise * Azimuth of rising * Moon transit * Transit altitude * Moon Set * Azimuth of setting * Solstices and equinoxes * Phases of the Moon * Grafical altude and azimuth * Perigee and apogee of the Moon * Obliquity of the Ecliptic * Monthtable: Julian day * Equation of Time * Right ascension of the Moon * Declination of the Moon * Moon rise * Azimuth of rising * Moon Transit * Transit altitude * Moon set * Azimuth of setting * Angular diameter of the Moon * Distance to the Earth * Referencevalues * ELSE: Timezones * Helpfiles * Glossary * over 1600 locations etc.

Copyright © Jukka T. Tulkki 2005-2010. All rights reserved.

GENERAL

The position for the Moon is computed using the Bretagnon and Francou "VSOP87" (Variations Séculaires des Orbites Planétaires) planetary theory. This is based on the older JPL DE200 numerical integration (which still forms the basis of the tabulated planetary positions in the "Astronomical Almanac"). Instead the complete theory LUNAR2010 uses the most important terms, allowing the calculation of the position of the Moon with an error not exceeding 1’’.

In all cases, positions are initially computed in a heliocentric reference frame, and then rigorously reduced to a geocentric frame, applying corrections for light travel time, gravitational deflection of light and annual aberration. The geocentric position is then converted to a topocentric position.

ABOUT THE BASICTABLE

Obliquity of the Ecliptic 1900 – 2100
Obliquity of the ecliptic of the angle between a body's equatorial plane and orbital plane. The effects of Precession and Nutation cause the value of these angles to change from between 21.55 and 24.18 degrees. To clear shape just click the label Clear Obliquity of Ecliptic.
The motion of obliquity of ecliptic is descend between 1900 and 2100.

Equinoxes and Solstices of the Year
In the table above are the equinoxes and solstices of the year. On the basictable are all links and commands to choice the locations and time. There is also the commands for Timezones, glossary and the helpfiles. The functions of the basictable

Solar Analemma
Analemma is a figure-of-eight shape that results if the Sun's position in the sky is recorded at the same time of day throughout the year. Because the Earth's rotation axis is not perpendicular to its orbit the position of the Sun varies. The Earth's orbit is elliptical, not circular. To clear shape just click the label Clear Analemma.

The shape is drawn as the location would be on the polar circle, where altitude of the Sun at December solstice is 0 degree. The highest position at June solstice is about 47 degrees. The motion starts below to the left and is zero first time at 15. April.

The orbital Motion of the Earth
Click the button below Compute. Now you see all heliocentric and geocentric coordinates of the Sun (and the Earth), aberration, obliquity of ecliptic, right ascension, declination, equation of time and apparent angular diameter of the Sun.

If you click the button Follow On you can see the orbital motion of the Sun (or Earth) second by second. To stop computing click button Follow Off.

OBSERVER LOCATION AND TIME

Time
This dialog specifies the date and time of observation. Note that the time is taken to be in the observer's local time zone, possibly corrected for the effect of daylight saving time, as specified in the Observation Location Dialog. The Now button sets the time and the Today button sets the date from the computer's clock. You can choice also time from the clock or date from the calendar. On the calendar you also can see the weekday of the date. To set the time to midnight, click the Midnight button. This sets the time to 24:00:00 while leaving the date unchanged. To set the time to midday, click the Midday button. This sets the time to 12:00:00. If the Daylight saving time ("summer time") button is checked, local time is considered to be one extra hour ahead of UT.

Different Times
Because of the irregularities in the Earth's rotation, the theories of motion of astronomical bodies do not use Universal Time (GMT), but a uniform timescale called Terrestrial Dynamical Time (TDT). PLANET2010 uses TDT internally for all its calculation of positions, etc, but obviously the user specifies the time for which a map is required in UTC (or rather, in local time, which is converted to UTC).

The difference between TDT and UT is called "delta T", and currently has a value of approximately 1 minute. It is currently increasing at a rate of somewhat less than 1 second per year. The problem is that the value of delta T can only be determined historically (typically by analyzing the motion of the Moon), and current and future values can only be estimated, whilst values for the distant past (before the advent of modern astronomy) are uncertain to the order of many minutes.

The "Astronomical Almanac" lists the values of delta T for every year from 1620 onwards (currently up to 1994), and provides estimates of its value for the current time. PLANET2010 has all this data stored, and interpolates or extrapolates in this table to find values of delta T for dates between 1900 and 2100.

For dates beyond the year 2000, an estimate of delta T is made using the method of L V Morrison and F R Stephenson, "Astronomical Algoritms" Jean Meeus (Willmann-Bell 1991). This dialog contains information about the observer. The information can be divided into several categories:

Position Information
The latitude and longitude of the observer, in degrees, minutes and seconds. This information can be obtained from a local map. For most purposes, a position correct to the nearest degree will be perfectly adequate; an error in location of one degree corresponds to a change of about 4 minutes in rise and set times of objects. Longitude is in degrees, + if West, - if East, latitude is in degrees, + if North, - if South and time difference from GMT in minutes. + if west of GMT, - if east of GMT

Location Databases
There are in this product two different databases. The main database consists of 600 locations all over the world and 1218 locations in Finland. The second database is for user´s own locations. It means that you can add new positions in this user´s database, not in the main database. The coordinates can be found from maps, GPS, almanacs and many tables.

In the main database click buttons A…Z and for Finnish locations button Location in Finland. Then the listbox below can be used to select a location. If a name is selected from the list, the location appears on the Observation Location and the appropriate latitude, longitude and time zone information are automatically filled in.

For your own locations click the button User Database. Only this database you can use right from all the table Ephemerides of the planets. It’s then very easy to compare different locations e.g. when the planet is rising or how long time the planet is above the horizon.

You can add your own entries to the location list by clicking the button New. Fill all information of location and click Enter. The new location is now the last one, but when you open this dialog next time, it is in the right alphabetic place. Deleting the location is as simple. Select the location and just click the button Delete.

Yearly Altitude of the Sun
Here you can see the highest and lowest altitude of the Sun of the location you have choice. The highest altitude on the northern hemisphere is at June solstice 20..21.6. and the lowest altitude at December solstice 20…22.12.

ABOUT THE DAYTABLE

The Ephemerides of the Observation Time

The values of right ascension, declination, parallax, topocentric right ascension, topocentric declination, azimuth, altitude and topocentric angular diameter are in degrees, minutes and seconds and also as decimalnumbers. The mean error in the computed positions of the Moon is under 1.0 second of arc. The Earth-Moon distance is in kilometers.

The Ephemerides of the Day
The values of Moon rise, azimuth of rise, time of transit, altitude of transit, Moon set and azimuth of set are in degrees, minutes and seconds and also as decimalnumbers.

Equinoxes and Solstices of the Year
In the table above are the equinoxes and solstices of the year.

Phases of the Moon
The first table above right includes the phases of the Moon; full Moon, first quarter, new Moon and last quarter.

Perigee and Apogee of the Moon
The second table below right includes perigee and apogee of the moon of the revolution.

Obliquity of Ecliptic
The angle between a body's equatorial plane and orbital plane. The effects of Precession and Nutation cause the value of these angles to change from between 21.55 and 24.18 degrees.

This dialog specifies the time (local date and time of observation, GMT, Julian day and time), the location, the coordinates of the locations, the user date and time, the ephemerides of the observation time and date. There is also graphical altitude and azimuth and some other informations.

Computing the positions
Click the button Compute. You can compute with your own date and time by clicking the button Compute User Date. You can use also the Follow method frequency being 1 second up to 30 seconds. Printing is possible in black and white and also in colour. The backstyle of the dialog is black and white or colour.

Location
The location with latitude, longitude and time zone information is the same you have chosen in the Location Dialog, but with spinbutton you can quickly change the location to another if it is in the user database.

Date and time
The date and time are the values you can also choice. The Julian day is a continuous count of days thereof from the beginning of the year –4712. The Julian time is a fraction of a day.

User Date and Time
There are scrollbars to choice user´s own date and time. Choice the date and time and click button Compute User Date to computing comparisons between different dates.

ABOUT THE MONTHTABLE

This dialog specifies the date, Julian day, equation of time, right ascension, declination, rise of the Moon, azimuth of rising, time of transit, altitude of transit, set of the Moon, azimuth of setting, topocentric diameter of the Moon and Earth-Moon distance.

Computing the positions
Computing the position click the button Compute. The location with latitude, longitude and time zone information is the same you have chosen in the Location Dialog, but with spinbutton you can quickly change the location to another if it is in the user database. When you click the compute button again it computes values of the new location.

The possible difference of the values between the day and the month tables causes of the computing time. In the table of the month computing time is always 12 at noon local time.

Location
The location with latitude, longitude and time zone information is the same you have choice in the Location Dialog., but with spinbutton you can quickly change the location to another if it is in the user database.

Julian Day
The Julian day is a continuous count of days thereof from the beginning of the year –4712. The Julian time is a fraction of a day.

Equinoxes and Solstices of the Year
In the table above are the equinoxes and solstices of the year.

Reference Values
The table above right includes the highest altitude on June solstice and the lowest altitude on December solstice

All the Tables are Printable in black and white and also in colour.