Time and the Sky

Before we can talk about tithi or nakshatra or any of the five limbs, we have to talk about something simpler — something so simple we normally do not think about it. What is a day?

You probably want to answer “24 hours.” That is true, and it is also incomplete. There are at least three different things in the sky that we use to measure a “day,” and they do not agree with each other exactly. There are also two different things called a “year” in Indian astronomy, and they too do not agree exactly. The Indian calendar uses several of these definitions at different points, which is one of the reasons it can feel complicated. Untangling them is the entire purpose of this chapter, and once they are untangled, everything afterwards becomes much easier.

The three motions you need to remember

Stand outside on a clear day. Three things are happening that are relevant to us, even though you cannot feel any of them.

1. Earth is spinning on its own axis. One full spin takes about 24 hours. This is what makes the Sun appear to rise and set, and it is the basis of the civil day.
2. Earth is orbiting the Sun. One full orbit takes about 365.25 days. This is what gives us a year, and what makes the Sun appear to move slowly through different background stars over the course of the year. This apparent annual path of the Sun is called the ecliptic (क्रान्तिवृत्त).
3. The Moon is orbiting the Earth. One full orbit relative to the stars takes about 27.32 days (the sidereal month). But because the Earth is also moving around the Sun during that time, the cycle of Moon phases — new moon to new moon — takes a bit longer, about 29.53 days (the synodic month). Hold on to this distinction; it shows up again immediately.

Almost everything in the panchang comes out of those three motions and how they line up with each other on a given day. Tithi is about the Moon’s position relative to the Sun. Nakshatra is about the Moon’s position against the background stars. Vara — the weekday — is about Earth’s spin. Yoga and karana are arithmetic combinations of the same two angles. So really, the panchang is a careful, repeatable answer to the question where is everything in the sky right now, and what does that combination mean?

Why a “day” has more than one definition

Here is something most people never notice. There are two different ways to measure how long it takes Earth to spin once on its axis, and they give two different answers.

The solar day सावन / सौर दिन

A solar day is from one solar noon to the next solar noon — that is, the time between the Sun being directly overhead (or, more precisely, on the local meridian) and the Sun being on the meridian again. Averaged over a year, it is exactly 24 hours. This is called the mean solar day (सावन दिन). It is what our wristwatches measure.

The sidereal day नक्षत्र दिन

A sidereal day is from a particular distant star being on the meridian to the same star being on the meridian again. This is approximately 23 hours, 56 minutes, and 4 seconds — about four minutes shorter than a solar day.

Why are they different?

Because Earth does two things at once. While it is spinning on its axis, it is also moving along its orbit around the Sun. After one full spin (which takes a sidereal day), the Earth has moved a little bit along its orbit — about 1° (since 360° in a year ÷ 365 days). The distant star is back overhead, but the Sun is not quite overhead yet, because we have changed position relative to it. Earth has to spin for about four more minutes to bring the Sun back overhead. That extra rotation is the difference between a sidereal day and a solar day.

The equation of time

We just said the average solar day is 24 hours. The word averageis doing some work there. In any given week the Sun does not actually return to the meridian at exactly 24-hour intervals. Sometimes it is a few minutes early, sometimes a few minutes late. The cumulative discrepancy between “real Sun time” and “clock time” is called the equation of time (काल-समीकरण), and over the course of the year it ranges roughly from −14 minutes to +16 minutes. There are two reasons:

1. Earth’s orbit is an ellipse, not a circle. By Kepler’s second law, Earth moves a bit faster when it is closer to the Sun (early January) and a bit slower when it is farther (early July). This makes the apparent solar day slightly longer or shorter than 24 hours.
2. Earth’s axis is tilted.The Sun’s motion along the ecliptic does not project onto the celestial equator at a uniform rate. Even if Earth’s orbit were a perfect circle, this alone would create a smaller wobble in the equation of time.

The classical Indian astronomers were aware of these effects. Aryabhata in 499 CE computes corrections of exactly the same kind, called manda (मन्द) and shighra (शीघ्र)corrections, in order to get from a body’s mean position to its true position. We mention this because the panchang you are reading uses these same corrections — under modern names — to compute accurate sunrise, sunset, and tithi end-times for your location.

Sunrise as the anchor

Here is the part that surprises most people. In the Western calendar, a day begins at midnight — an arbitrary moment when nothing visible is happening. In the Indian tradition, a day begins at sunrise (सूर्योदय). This single choice changes a lot of how the panchang works.

Why sunrise? Because sunrise is something you can actually see. Before clocks, before time zones, before atomic time — sunrise is the one moment everyone in a region can agree on without instruments. Anchoring the day to sunrise meant the calendar was always verifiable.

It also has a practical consequence: the panchang for any given location depends on where that location is, because sunrise happens at different clock times in different places. The panchang for Ujjain at 6:32 AM is not the panchang for Mumbai at 6:32 AM, even on the same date. We will come back to this when we talk about choghadiya and muhurta, which slice the time between sunrise and sunset into pieces.

There is a small subtlety even in “sunrise.” The traditional astronomical definition is the moment when the centre of the Sun’s disc crosses the local horizon, refraction accounted for. Some traditions instead use the moment when the upper limb (top edge) of the Sun first becomes visible. The two differ by about a minute or two depending on latitude. This panchang uses the standard centre-of-disc definition.

The day, the month, the year

With those three motions in hand, we can sketch the calendar.

• The day is one rotation of the Earth — measured from sunrise to next sunrise.
• The month in the Indian calendar is one cycle of the Moon — typically from one new moon to the next new moon (this is the amanta (अमान्त) system used in most of South India and the Jain tradition), or in some regions from one full moon to the next full moon (the purnimanta (पूर्णिमान्त) system used in much of North India). About 29.53 days. Both systems agree on which days are which tithi; they only disagree on which tithi marks the boundary of the month.
• The year is one orbit of the Earth around the Sun. About 365.25 days.

And immediately you see the problem. 12 lunar months × 29.53 days = 354.36 days, which is about 11 days short of a solar year. So if we only counted lunar months, our seasons would drift. After three years we would be a full month off. After thirty-three years we would be a full year off.

The Indian calendar solves this by occasionally inserting an extra month — called adhik maas (अधिक मास) — roughly every 32–33 months, to keep lunar months and solar years in sync. The rule is precise: an adhik maas occurs when a lunar month begins and ends without the Sun crossing into a new sign of the zodiac during it. The opposite case — a lunar month during which the Sun crosses two zodiac signs — is called kshaya maas (क्षय मास) and is removed from the count. Kshaya maas is rare; adhik maas is the common case. We will not need this detail until much later, but it is good to know it is there.

Two different “years” — sidereal and tropical

Just as there are two definitions of a day, there are two definitions of a year, and they differ by an amount that is small but cumulative. This is a topic that confuses even experienced readers, and the difference is one of the central debates in modern Indian calendar reform. We will be brief here and revisit it whenever it matters.

Sidereal year नाक्षत्र वर्ष

The sidereal year is the time it takes Earth to return to the same position relative to the fixed background stars. It is approximately 365.2564 days. This is the year as the ancient observers measured it: by watching when a particular star (say, Spica or Aldebaran) returns to the same position at sunset.

Tropical year सायन वर्ष

The tropical year is the time it takes Earth to return to the same position relative to the seasons — for example, from one spring equinox to the next. It is approximately 365.2422 days. This is the year that the Western Gregorian calendar tracks, because keeping seasons aligned with calendar dates is what civic life cares about.

Why they differ — precession of the equinoxes

The sidereal year is about 20 minutes longerthan the tropical year. Why? Because Earth’s rotational axis is not perfectly fixed in space. It wobbles, very slowly, in a circle — like a spinning top whose axis traces a cone over time. One full wobble takes about 25,800 years. This wobble is called the precession of the equinoxes (अयन-चलन), and it means the position where the Sun crosses the equator each spring drifts slowly backwards through the zodiac at about 50.3 arcseconds per year — roughly 1° every 72 years.

The classical Indian astronomers knew about precession. Bhaskara II discusses it. Some siddhantas use it; some do not. The practical consequence today is that the Indian zodiac and the Western zodiac, which once started at the same point, have drifted apart by about 24°. We are about 1700 years past the moment they coincided.

Sayana and Nirayana zodiacs

This drift produces the most consequential split in modern Indian astrology and astronomy. The nirayana (निरयण) system fixes the zodiac to the stars — so that the Aries-Taurus boundary, for example, is always in the same place against the background of distant suns. The sayana (सायन)system fixes the zodiac to the seasons — so that the Aries-Taurus boundary moves slowly with precession, but the spring equinox is always at 0° Aries. The Western tropical astrology tradition uses sayana. Classical Indian astronomy uses nirayana. This is why a person born “under the sign of Capricorn” in a Western horoscope might be told they are actually a Sagittarius in an Indian horoscope — both calculations are correct; they are using different zodiac conventions. The difference between them is the precession amount, called ayanamsha (अयनांश), currently about 24° and growing about a degree every 72 years.

This panchang uses the nirayana sidereal zodiac with the standard Lahiri ayanamsha, which is the most widely used modern convention in Indian astronomy. We will mention nirayana again when we get to nakshatras and rashis.

Putting it together — what does a single date describe?

Suppose you ask, “What was happening in the sky at sunrise on 15 August 2026 in Mumbai?” Here is what the panchang has to compute.

1. The exact local sunrise time, accounting for Mumbai’s latitude/longitude and the equation of time.
2. The Sun’s longitude on the ecliptic at that moment, in the nirayana zodiac.
3. The Moon’s longitude on the ecliptic at that moment, in the same zodiac.
4. From those two longitudes, several derived quantities:
   • The angular separation Moon − Sun, modulo 360, divided by 12° → tells us the tithi.
   • The Moon’s longitude divided by 13°20’ → tells us the nakshatra.
   • (Moon longitude + Sun longitude) divided by 13°20’ → tells us the yoga.
   • Half the tithi → tells us the karana.
5. The day of the week (vara) is just counted from a reference epoch.

That is the entire panchang in one sentence: it is the result of computing two angles (Sun’s longitude and Moon’s longitude) at the moment of local sunrise, and then dividing those angles by the appropriate sub-divisions. Every other column you will see in the daily panchang is either one of these primary values or a derived schedule of time-windows based on them. We will spend the next several chapters making each step concrete.

What we have so far

At the end of this chapter, you should be comfortable with a few ideas:

• The panchang is reading the sky. Three motions matter: Earth spinning, Earth orbiting Sun, Moon orbiting Earth.
• A “day” can mean a solar day (24h average) or a sidereal day (23h 56m 4s), and the difference is real and matters.
• The Indian day starts at sunrise, not midnight — and this is why panchang is location-dependent.
• The equation of time (a non-trivial daily wobble) and precession of the equinoxes (a 25,800-year wobble) are real astronomical effects already accounted for in classical Indian astronomy.
• There are two zodiacs. Sayana follows the seasons, nirayana follows the fixed stars. Indian astronomy uses nirayana.
• Lunar months and solar years do not divide evenly, so the calendar uses an extra month occasionally to stay in step.

That is the foundation. In the next chapter we tackle the first of the five limbs — tithi, the lunar day. This is also where we meet the Jain six-ghati rule that defines the tradition this panchang follows.