The obliquity of the ecliptic
The obliquity of the ecliptic is the tilt of Earth's axis relative to the plane of its orbit, about 23.4 degrees. It changes slowly over time.
What it is
The site uses the mean obliquity from Meeus, a polynomial in the Julian centuries from J2000. The value decreases by about half an arcsecond a year, which matters little over the period a chart covers.
How it is worked out or read
The obliquity is used in converting the equatorial coordinates of the grahas to the ecliptic, and in the Lagna formula. A small error in obliquity changes the result only slightly.
Where it appears on this site
The method is on the method page, and the Lagna and planetary positions depend on it.
The tilt itself
The obliquity of the ecliptic is the angle between the plane of the Earth's orbit, the ecliptic, and the plane of the Earth's equator. Its present value is about 23.44 degrees. It is the reason the Sun moves north and south through the year, giving the seasons and the changing length of day. At the solstices the Sun reaches its greatest distance from the celestial equator, a declination of about 23.44 degrees north or south.
The angle is not fixed. Over a cycle of about 41,000 years it varies between roughly 22.1 and 24.5 degrees, and at present it is slowly decreasing, by about 47 seconds of arc per century.
Why calculation needs it
Planetary positions in Jyotish are given as longitudes along the ecliptic, but the rotation of the Earth happens around the equator. To find which degree of the ecliptic is rising at a given place and time, the calculator must convert between the two systems, and the obliquity is the angle that links them. The same conversion is needed to find a planet's declination, which decides whether it is north or south of the equator, and to compute sunrise and sunset, which depend on the Sun's declination.
The classical siddhantas used a value of 24 degrees, close to the true value in their era and slightly larger than today's.
Unequal rising times of the signs
One consequence of the obliquity is that the twelve signs take different amounts of time to rise. At the latitudes of most of India, signs near Mesha and Meena rise quickly, in well under two hours, while signs near Kanya and Tula rise more slowly, taking well over two hours. Indian astronomy tabulated these rising times, called rashimana or lagnamana, for each latitude. This is why the Lagna does not change at a steady rate of one sign every two hours, and why two people born an hour apart may share a Lagna in one season and not in another.
Latitude makes it stronger
The difference between short and long signs grows with latitude. Near the equator, all signs take close to two hours. Far to the north, the short signs can rise in less than an hour and the long ones take several hours, and at very high latitudes some signs barely rise at all in the usual sense. Charts for births far from the tropics need care for this reason.
On this site
The astronomical library used by this site computes the obliquity for the exact date, including its slow change and the small nutation term, before converting positions. A reader does not need to supply it; but knowing that it is there explains why the Lagna moves unevenly through the day.