Ephemeris in the context of Celestial navigation

Celestial cartography, uranography,astrography or star cartography is the aspect of astronomy and branch of cartography concerned with mapping stars, galaxies, and other astronomical objects on the celestial sphere. Measuring the position and light of charted objects requires a variety of instruments and techniques. These techniques have developed from angle measurements with quadrants and the unaided eye, through sextants combined with lenses for light magnification, up to current methods which include computer-automated space telescopes. Uranographers have historically produced planetary position tables, star tables, and star maps for use by both amateur and professional astronomers. More recently, computerized star maps have been compiled, and automated positioning of telescopes uses databases of stars and of other astronomical objects.

Celestial mechanics is the branch of astronomy that deals with the motions and gravitational interactions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to produce ephemeris data. The computation of the motion of the bodies through orbital mechanics can be simplified by using an appropriate inertial frame of reference. This leads to the use of various different coordinate systems, such as the Heliocentric (Sun-centered) coordinate system.

In a binary system of objects interacting through gravity, Newtonian mechanics can used to produce a set of orbital elements that will predict with reasonable accuracy the future position of the two bodies. This method demonstrates the correctness of Kepler's laws of planetary motion. Where one of the bodies is sufficiently massive, general relativity must be included to predict apsidal precession. The problem becomes more complicated when another body is added, creating a three-body problem that can not be solved exactly. Perturbation theory is used to find an approximate solution to this problem.

In astronomy, an epoch or reference epoch is a moment in time used as a reference point for some time-varying astronomical quantity. It is useful for the celestial coordinates or orbital elements of a celestial body, as they are subject to perturbations and vary with time. These time-varying astronomical quantities might include, for example, the mean longitude or mean anomaly of a body, the node of its orbit relative to a reference plane, the direction of the apogee or aphelion of its orbit, or the size of the major axis of its orbit.

The main use of astronomical quantities specified in this way is to calculate other relevant parameters of motion, in order to predict future positions and velocities. The applied tools of the disciplines of celestial mechanics or its subfield orbital mechanics (for predicting orbital paths and positions for bodies in motion under the gravitational effects of other bodies) can be used to generate an ephemeris, a table of values giving the positions and velocities of astronomical objects in the sky at a given time or times.

A total solar eclipse occurred on 3 May 1715. It was known as Halley's Eclipse, after Edmond Halley (1656–1742) who predicted this eclipse to within 4 minutes accuracy. Halley observed the eclipse from London where the city of London enjoyed 3 minutes 33 seconds of totality. He also drew a predictive map showing the path of totality across the Kingdom of Great Britain. The original map was about 20 miles off the observed eclipse path, mainly due to his use of inaccurate lunar ephemeris. After the eclipse, he corrected the eclipse path, and added the path and description of the 1724 total solar eclipse.

Drawing upon lunar tables made by the first Astronomer Royal John Flamsteed, William Whiston produced a more technical predictive eclipse map around the same time as Halley. Both Halley's and Whiston's maps were published by John Senex in March 1715.

The Old Farmer's Almanac is an almanac containing weather forecasts, planting charts, astronomical data, recipes, and articles. Topics include gardening, sports, astronomy, folklore, and predictions on trends in fashion, food, home, technology, and living for the coming year. Published every September, The Old Farmer's Almanac has been published continuously since 1792, making it the oldest continuously published periodical in North America. This little book is considered “a gardener’s bible”, including gardening articles and the best days for planting crops. It is published by Yankee Publishing Inc. which also publishes a Canadian edition to cover all of North America. The publication follows in the heritage of American almanacs such as Benjamin Franklin’s Poor Richard's Almanack.

In astronomy, planetary mass is a measure of the mass of a planet-like astronomical object. Within the Solar System, planets are usually measured in the astronomical system of units, where the unit of mass is the solar mass (M_☉), the mass of the Sun. In the study of extrasolar planets, the unit of measure is typically the mass of Jupiter (M_J) for large gas giant planets, and the mass of Earth (M_🜨) for smaller rocky terrestrial planets.

The mass of a planet within the Solar System is an adjusted parameter in the preparation of ephemerides. There are three variations of how planetary mass can be calculated:

The JPL Small-Body Database (SBDB) is an astronomy database about small Solar System bodies. It is maintained by Jet Propulsion Laboratory (JPL) and NASA and provides data for all known asteroids and several comets, including orbital parameters and diagrams, physical diagrams, close approach details, radar astrometry, discovery circumstances, alternate designations and lists of publications related to the small body. The database is updated daily when new observations are available. In April 2021 the JPL Small-Body Database started using planetary ephemeris (DE441) and small-body perturber SB441-N16. Most objects such as asteroids get a two-body solution (Sun+object) recomputed twice a year. Comets generally have their two-body orbits computed at a time near the perihelion passage (closest approach to the Sun) as to have the two-body orbit more reasonably accurate for both before and after perihelion. For most asteroids, the epoch used to define an orbit is updated twice a year. Orbital uncertainties in the JPL Small-Body Database are listed at the 1-sigma level.

On 27 September 2021 the JPL Solar System Dynamics website underwent a significant upgrade.

Augmentation of a global navigation satellite system (GNSS) is a method of improving the navigation system's attributes, such as precision, reliability, and availability, through the integration of external information into the calculation process. There are many such systems in place, and they are generally named or described based on how the GNSS sensor receives the external information. Some systems transmit additional information about sources of error (such as clock drift, ephemeris, or ionospheric delay), others provide direct measurements of how much the signal was off in the past, while a third group provides additional vehicle information to be integrated in the calculation process.

Nevil Maskelyne FRS FRSE (/ˈmæskəlɪn/; 6 October 1732 – 9 February 1811) was the fifth British Astronomer Royal. He held the office from 1765 to 1811. He was the first person to scientifically measure the mass of the planet Earth. He created The Nautical Almanac, in full the British Nautical Almanac and Astronomical Ephemeris for the Meridian of the Royal Observatory at Greenwich, using Tobias Mayer's corrections for Leonhard Euler's Lunar Theory tables.

The equation of time describes the discrepancy between two kinds of solar time. The two times that differ are the apparent solar time, which directly tracks the diurnal motion of the Sun, and mean solar time, which tracks a theoretical mean Sun with uniform motion along the celestial equator. Apparent solar time can be obtained by measurement of the current position (hour angle) of the Sun, as indicated (with limited accuracy) by a sundial. Mean solar time, for the same place, would be the time indicated by a steady clock set so that over the year its differences from apparent solar time would have a mean of zero.

The equation of time is the east or west component of the analemma, a curve representing the angular offset of the Sun from its mean position on the celestial sphere as viewed from Earth. The equation of time values for each day of the year, compiled by astronomical observatories, were widely listed in almanacs and ephemerides.

GPS signals are broadcast by Global Positioning System satellites to enable satellite navigation. Using these signals, receivers on or near the Earth's surface can determine their Position, Velocity and Time (PVT). The GPS satellite constellation is operated by the 2nd Space Operations Squadron (2SOPS) of Space Delta 8, United States Space Force.

GPS signals include ranging signals, which are used to measure the distance to the satellite, and navigation messages. The navigation messages include ephemeris data which are used both in trilateration to calculate the position of each satellite in orbit and also to provide information about the time and status of the entire satellite constellation, called the almanac.

Terrestrial Time (TT) is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of Earth.For example, the Astronomical Almanac uses TT for its tables of positions (ephemerides) of the Sun, Moon and planets as seen from Earth. In this role, TT continues Terrestrial Dynamical Time (TDT or TD), which succeeded ephemeris time (ET). TT shares the original purpose for which ET was designed, to be free of the irregularities in the rotation of Earth.

The unit of TT is the SI second, the definition of which is based currently on the caesium atomic clock, but TT is not itself defined by atomic clocks. It is a theoretical ideal, and real clocks can only approximate it.

In metrology, ephemeris time (ET) is time in association with any ephemeris (itinerary of the trajectory of an astronomical object). In practice it has been used more specifically to refer to:

1. a former standard astronomical time scale adopted in 1952 by the IAU, and superseded during the 1970s. This time scale was proposed in 1948, to overcome the disadvantages of irregularly fluctuating mean solar time. The intent was to define a uniform time (as far as was then feasible) based on Newtonian theory (see below: Definition of ephemeris time (1952)). Ephemeris time was a first application of the concept of a dynamical time scale, in which the time and time scale are defined implicitly, inferred from the observed position of an astronomical object via the dynamical theory of its motion.
2. a modern relativistic coordinate time scale, implemented by the JPL ephemeris time argument T_eph, in a series of numerically integrated Development Ephemerides. Among them is the DE405 ephemeris in widespread current use. The time scale represented by T_eph is closely related to, but distinct (by an offset and constant rate) from, the TCB time scale currently adopted as a standard by the IAU (see below: JPL ephemeris time argument Teph).

Most of the following sections relate to the ephemeris time of the 1952 standard.