Why the Moon's speed varies
The Moon's speed varies from about 11 to about 15 degrees a day, because its orbit is elliptical and it is pulled by the Sun.
What it is
The main variations come from the eccentricity of the Moon's orbit, which changes its distance from Earth, and from the Sun's gravitational effect, which speeds and slows the Moon in a cycle of about a month.
How it is worked out or read
This is why a tithi can last from about 19 to 26 hours, and a nakshatra's length varies. A fixed-speed model would give wrong end times, so the site uses the full lunar model.
Where it appears on this site
See how the Moon's position is calculated and tithi end times.
How much the Moon's speed changes
The Moon's average motion is about 13 degrees 10 minutes a day, but its actual daily motion ranges from roughly 11 degrees 45 minutes to about 15 degrees 15 minutes. The reason is that its orbit around the Earth is an ellipse. Near perigee, its closest point, the Moon moves fastest; near apogee, its farthest point, it moves slowest. The cycle from one perigee to the next, the anomalistic month, takes about 27.55 days, slightly longer than the sidereal month.
Effect on nakshatras and tithis
Because the Moon covers a nakshatra of 13 degrees 20 minutes, a fast Moon passes through a nakshatra in about 21 hours, and a slow Moon takes about 27 hours. So the time the Moon spends in a nakshatra varies by six hours or more. Tithis vary even more, from about 19 to about 26 hours, because they depend on the Moon's speed relative to the Sun, and the Sun's speed also varies a little. This is why a panchang lists end times for each element: no fixed table could predict them.
It is also why a tithi can be skipped, when one begins after sunrise and ends before the next, or repeated, when one spans two sunrises.
Effect on the dasha balance
The Vimshottari dasha balance at birth is set by how far the Moon has travelled through its nakshatra. The Moon's speed matters here through the birth time: a fast Moon moves through the nakshatra more quickly, so an error of a few minutes in birth time shifts the Moon by more arc, and so shifts the dasha balance more. As a rough guide, the Moon moves about half a minute of arc per minute of time. In a Venus nakshatra, where the full twenty years correspond to 800 minutes of arc, each minute of arc is about nine days, so a one-minute error in birth time shifts the dasha dates by about four to five days.
Why mean motion is not enough
Older almanacs sometimes used the mean motion of the Moon with a few corrections, which could place nakshatra and tithi changes many minutes or even hours from their true times. Modern ephemerides, including the one used on this site, compute the Moon's true position with many terms of correction, accurate to a small fraction of a minute of arc. For a reader comparing an old almanac with a modern one, the Moon's speed variation is often the source of the difference.
Seeing it for yourself
Open the panchang page for two weeks running and note the nakshatra end times each day. The intervals between successive end times will lengthen and shorten through the month as the Moon moves from perigee to apogee and back. It is a simple way to see an ellipse in an almanac.