How an ephemeris works
An ephemeris is a computed table or model of planetary positions over time. The site's tools call a library that computes positions for any instant from a numerical model.
What it is
The library uses models of the planets' orbits, fitted to observations, to give the position of each body in a chosen frame. The site asks for the geocentric position of each graha at the birth instant.
How it is worked out or read
The output is then converted from the equatorial to the ecliptic frame and from tropical to sidereal by subtracting the ayanamsa. The steps are listed on the method page.
Where it appears on this site
The method is on the method page, and the birth chart uses it for each graha.
What an ephemeris is
An ephemeris is a table or a computer model that gives the positions of the Sun, Moon and planets for any moment. Printed ephemerides, once essential for every astrologer, list positions at a fixed time each day, and the user interpolates for the exact birth time. Modern software computes positions directly for the exact moment, using mathematical models of the solar system that have been fitted to centuries of observations and decades of spacecraft data.
Where the numbers come from
The most precise ephemerides are produced by large numerical integrations of the solar system, such as the DE series from the Jet Propulsion Laboratory. These follow the gravitational pull of every major body step by step. Many astrology programs, including the widely used Swiss Ephemeris, are built on these integrations. Lighter libraries, such as the one this site uses, rely on series expansions fitted to those integrations, which are compact enough to run in a web browser and accurate to within about an arcminute for the planets over many centuries, far finer than any reading requires.
Corrections along the way
To give the position an observer actually sees, the model applies several corrections. Light-time correction accounts for the minutes or hours light takes to reach the Earth, so the planet is shown where it was when the light left it. Aberration accounts for the Earth's own motion. Nutation and precession account for the slow wobble of the Earth's axis. And the difference between Universal Time and the uniform time used in the equations, called delta T, is added for the given date. Each correction is small, but together they matter at the level of arcminutes.
From tropical to sidereal
An ephemeris gives tropical positions, measured from the moving equinox. Jyotish needs sidereal positions, so the calculator subtracts the ayanamsa for the same moment. Because the ayanamsa grows by about fifty seconds of arc a year, it too is computed for the exact date. The choice of ayanamsa, Lahiri, Raman or KP on this site, is the main reason two Jyotish programs built on the same ephemeris can still give slightly different results.
Why this matters to a reader
Knowing how an ephemeris works helps a reader judge where differences come from. When two charts disagree by a fraction of a degree, the cause is almost never the ephemeris; it is usually the birth time, the time zone, the ayanamsa or the house system. When they disagree by much more, a data-entry error is the most likely cause.