1554 - Johannes Stadius published Ephemerides novae et auctae, the first major ephemeris computed according to Copernicus' heliocentric model, using parameters derived from the Prutenic Tables. Although the Copernican model provided an elegant solution to the problem of computing apparent planetary positions (it avoided the need for the equant and better explained the apparent retrograde motion of planets), it still relied on the use of epicycles, leading to some inaccuracies - for example, periodic errors in the position of Mercury of up to ten degrees. One of the users of Stadius's tables is Tycho Brahe.
1679 - La Connaissance des Temps ou calendrier et éphémérides du lever & coucher du Soleil, de la Lune & des autres planètes, first published yearly by Jean Picard and still extant.
1975 - Owen Gingerich, using modern planetary theory and digital computers, calculates the actual positions of the planets in the 16th Century and graphs the errors in the planetary positions predicted by the ephemerides of Stöffler, Stadius and others. According to Gingerich, the error patterns "are as distinctive as fingerprints and reflect the characteristics of the underlying tables. That is, the error patterns for Stöffler are different from those of Stadius, but the error patterns of Stadius closely resemble those of Maestlin, Magini, Origanus, and others who followed the Copernican parameters."
For scientific uses, a modern planetary ephemeris comprises software that generates positions of planets and often of their satellites, asteroids, or comets, at virtually any time desired by the user.
After introduction of computers in the 1950's it became feasible to use numerical integration to compute ephemerides. The Jet Propulsion Laboratory Development Ephemeris is a prime example. Conventional so-called analytical ephemerides that develop series expansions for the coordinates have also been still developed, but of much increased size and accuracy as compared to the past, by making use of computers to manage the tens of thousands of terms. Ephemeride Lunaire Parisienne and VSOP are examples.
Typically, such ephemerides cover several centuries, past and future; the future ones can be covered because the field of celestial mechanics has developed several accurate theories. Nevertheless, there are secular phenomena which cannot adequately be considered by ephemerides. The greatest uncertainties in the positions of planets are caused by the perturbations of numerous asteroids, most of whose masses and orbits are poorly known, rendering their effect uncertain. Reflecting the continuing influx of new data and observations, NASA's Jet Propulsion Laboratory (JPL) has revised its published ephemerides nearly every year since 1981.
Scientific ephemerides for sky observers mostly contain the positions of celestial bodies in right ascension and declination, because these coordinates are the most frequently used on star maps and telescopes. The equinox of the coordinate system must be given. It is, in nearly all cases, either the actual equinox (the equinox valid for that moment, often referred to as "of date" or "current"), or that of one of the "standard" equinoxes, typically J2000.0, B1950.0, or J1900. Star maps almost always use one of the standard equinoxes.
Scientific ephemerides often contain further useful data about the moon, planet, asteroid, or comet beyond the pure coordinates in the sky, such as elongation to the Sun, brightness, distance, velocity, apparent diameter in the sky, phase angle, times of rise, transit, and set, etc.
Ephemerides of the planet Saturn also sometimes contain the apparent inclination of its ring.
Celestial navigation serves as a backup to the Global Positioning System. Software is widely available to assist with this form of navigation; some of this software has a self-contained ephemeris. When software is used that does not contain an ephemeris, or if no software is used, position data for celestial objects may be obtained from the modern Nautical Almanac or Air Almanac.
An ephemeris is usually only correct for a particular location on the Earth. In many cases, the differences are too small to matter. However, for nearby asteroids or the Moon, they can be quite important.