Ephemeris

An ephemeris is a collection of data used to track the movement of objects in space. These tables provide the trajectory of naturally occurring bodies, such as planets and moons. They also track artificial satellites launched by humans. An ephemeris tells us the position and sometimes the velocity of these objects over specific intervals of time.

Astronomers use this information to locate celestial bodies in the sky. This data is also vital for celestial navigation and for people who practice astrology.

To describe a location in the sky, an ephemeris often uses a spherical polar coordinate system. This system relies on two main measurements called right ascension and declination. It may also include the distance from a specific starting point, known as the origin.

These tables can track many different phenomena. They can predict eclipses and the phases of the Moon. They can also show planetary stations or apparent retrograde motion, which is when a planet seems to move backward. Some tables even include the positions of minor bodies like Chiron or the inclination of Saturn's rings.

Historically, these tables were printed in books. Calculating them was one of the first uses for mechanical computers. In the 9th century, al-Khwārizmī created important tables.

During the 12th century, the Tables of Toledo became a standard in Europe. These were based on Arabic sources. Later, in the 13th century, the Alfonsine Tables were compiled in Spain. They were created to fix errors in the Tables of Toledo. The Alfonsine Tables remained the European standard for nearly 300 years.

As mathematical theories changed, so did the accuracy of the tables. In 1474, Regiomontanus published day-to-day ephemerides in Germany. Christopher Columbus used these tables in 1504 while shipwrecked in Jamaica. He used them to successfully predict a lunar eclipse for the local people. In 1551, the Prutenic Tables were published based on the theories of Copernicus. Later, Johannes Stadius published tables using the Copernican heliocentric model. While this model was elegant, it still used epicycles and had errors. For example, it could be off by ten degrees regarding the position of Mercury.

Scientific understanding improved significantly with Johannes Kepler. In 1627, he published the Rudolphine Tables. These were based on the idea of elliptical planetary motion. This was a major step forward for accuracy. In 1975, astronomer Owen Gingerich used digital computers to study these old tables. He found that the error patterns in the tables were as unique as fingerprints. These patterns showed how different scientists used different mathematical parameters.

Modern ephemerides are very different from the printed books of the past. Today, most scientific ephemerides are sophisticated software programs. After electronic computers arrived in the 1950s, scientists began using numerical integration to compute positions. This allows them to generate the position of a planet or comet at almost any time. Some systems, like the Jet Propulsion Laboratory Development Ephemeris, are highly advanced. Other systems, such as the VSOP or the Ephemeride Lunaire Parisienne, use complex mathematical expansions. These modern tools can cover positions for many centuries into the past and future.

Despite this high technology, some uncertainties remain. The movement of planets can be affected by the perturbations of asteroids. Because the masses and orbits of many asteroids are not well known, their effects are hard to predict. To stay accurate, NASA's Jet Propulsion Laboratory revises its ephemerides nearly every year. They have done this consistently since 1981. This constant updating helps ensure that spacecraft can navigate safely through the solar system.

Ephemeris data is part of the technology we use every day. For instance, GPS signals include ephemeris data to calculate where satellites are in orbit. This is essential for the accuracy of your location on Earth. Even today, printed books like the Nautical Almanac or Air Almanac are used. They serve as a reliable backup for navigation if electronic devices are unavailable. Whether through a smartphone or a printed book, the ephemeris helps us understand our place in the universe.