Education Article #6: For the Joy of Sharing

An Introduction to Nakshatras (1/3)

By Dr. Ravi Shankar Iyer
CEO of Accenture Center of Excellence at IIT Madras, Chennai, India

Foreword by Venkat
During the course of teaching astrology, exploring astronomy became my passion and I do include a section on astronomy in my classes. Some fascinating surprises I discovered (to give a few examples): Saturn is less dense than water, Jupiter’s moon formation mimics our Solar system formation, Mercury’s spin takes longer than its orbit around the Sun, and Venus with its gigantic shield volcanoes. Knowing about the various peculiarities and abnormalities in the outer space brings a lasting shift in our perspectives than just assimilating information.

The ability / inability to discover the reasons behind the nature of the celestial unknowns, brings us on the intersection of belief, science, fascination and curiosity. Dr. Shankar takes us through a well laid route to discover the lunar mansions (known as nakshatras). To prepare us, he introduces the foundational concepts and terms in astronomy. His research with references to Sanskrit words, understanding in ancient Indian texts and suitable pictures makes it a source of insightful information to absorb.


In this article (the first in a series), Dr. Shankar introduces the basic terms in astronomy in a logical sequence to help us appreciate the celestial movements, forces and positions in relation to the natural phenomena. This forms the foundation to understand nakshatras (lunar mansions) in the vocabulary which is relevant to it.

Dr. Shankar is the CEO of the Accenture Center of Excellence at IIT, Madras (in Chennai, India), where he is setting up multiple laboratories and research initiatives in Industrial IoT and robotics.

Dr. Shankar has a Bachelor’s degree from IIT Madras, and Master’s and PhD degrees, from IISc, Bangalore. He loves travelling having visited over 40 countries and lived in 7. He is an avid reader, and loves teaching.

Earlier, Dr. Shankar was the Senior Director at Conexant, heading the Embedded Wireless Networking Group in Asia. He has also had stints with Motorola and Siemens in the UK, US and Singapore. At Motorola, his team won TMC magazine’s Internet Telephony Product of the Year award for 2002. He has founded four startups – GrayCells, TeleSilikon, Bubble Motion and VoiceBell – and mentored over 30 startups, primarily in healthcare and blockchain. He has over 20 patents and more than 30 publications in prestigious technical journals.

An Introduction to Nakshatras (1/3)

What are nakshatras?
According to Wikipedia,
“Nakshatra is the term for lunar mansion in Hindu astrology and Indian Astronomy. A nakshatra is one of 27 (sometimes also 28) sectors along the ecliptic. Their names are related to a prominent star or asterisms in or near the respective sectors.”

Confused?
Well, let’s unpack this.
What is a lunar mansion? Again, this is what the Wikipedia has to say –
“… lunar house is a segment of the ecliptic through which the Moon passes in its orbit around the Earth.”

So, what is the ecliptic?
To understand this, and other terms that we would need in understanding nakshatras, we need a basic introduction to astronomy.

Astronomy – An Introduction

We all know that the Earth rotates about its axis once every 24 hours, and revolves around the Sun, once in about 365 days. We also know that the Moon revolves around the Earth once a month (about 29.5 days). These cycles influence bodily, tidal and other factors important to human beings – the duration of the year determines the arrival of the seasons and rain-bearing clouds – important in agriculture; the equinoxes determine useful hours of work (that’s why we still have daylight savings in countries like the US and UK), the rising and setting of the Moon determines tides (useful for fishermen and sailors), menstrual periods and so on.

But beside these, there are other cycles that are useful for our discussion. These have been collectively termed the Milankovtich Cycles (after Serbian scientist Milutin Milankovitch, who hypothesized that the long-term, collective effects of changes in Earth’s position relative to the Sun are a strong driver of Earth’s long-term climate). For now, we will focus on two important determinants of Milankovitch cycles. These are:

  1. The angle Earth’s axis is tilted with respect to Earth’s orbital plane, known as obliquity; and
  2. The direction Earth’s axis of rotation is pointed, known as precession.

Obliquity

The Earth’s axis of rotation is tilted as it travels around the Sun. The angle of this tilt is known as its obliquity. Obliquity is why Earth has seasons. Over the past few million years, it has varied between 22.1° and 24.5° with respect to Earth’s orbital plane around the Sun . The greater Earth’s axial tilt angle, the more extreme our seasons are, as each hemisphere receives more solar radiation during its summer, when the hemisphere is tilted toward the Sun, and less during winter, when it is tilted away. These effects aren’t uniform globally — higher latitudes receive a larger change in solar radiation than areas closer to the equator.
Earth’s axis is currently tilted by 23.4°, or about halfway between its extremes, and this angle is very slowly decreasing in a cycle that spans about 41,000 years. It was last at its maximum tilt about 10,700 years ago and will reach its minimum tilt (about 22.1°) about 9,800 years from now.

But why does the Earth tilt?

To answer this, we need a bit of scientific history. People have long wondered why Earth has a large moon unlike its immediate rocky neighbors (Mars, Venus and Mercury). The lunar rock samples retrieved by Apollo astronauts were found to be almost identical to the Earth’s crust. It was therefore surmised that they were ejected from Earth in some violent event.

Theory has it that about 4.6 billion years ago, the dust and gas orbiting around our nascent Sun (called its accretion disc/disk) gathered into larger clumps, which through gravitational attraction and collision formed larger planets. Such a process of forming planets has a bunch of stages, the last of which is called the giant impact phase. That’s when the planets are big, and there’s a lot of them, running into one another, getting moved around, and in some cases getting ejected out of the solar system.

Through computer simulations of the early solar system, scientists estimate that Earth suffered around 10 giant collisions. Each altered the tilt of the Earth by knocking it one direction or the other. In the last of these encounters (about 4.4 to 4.5 billion years ago), a rocky planet, roughly the size of Mars (it’s been given the name Theia), smashed into Earth. Theia was traveling at more than 10 kilometers per second. The kinetic energy released in this collision was huge — enough to immediately melt both the bodies, causing them to coalesce into what we now call Earth. Theia also hit the Earth at such an angle and with such force that it sent pieces of both the planets flying into space. That debris mixed and settled into orbit around Earth and eventually coalesced into the Moon.

It is estimated that the collision caused Earth’s axis to wobble by up to 80°. Earth also rotated at a much higher rate (a day was about 5 hours long). Since then, the extent of wobble (obliquity) has decreased, and the speed of rotation slowed down to their current rates, due primarily to the gravitational pull of the Sun, the Moon and the giant gas planets in our neighborhood.

One point to be kept in mind is that the Earth presents the same tilt orientation throughout its revolution around the Sun (see Figure 1). This orientation changes slowly, by 1° in about 72 years due to precession.

Why do we have eclipses?

A solar eclipse happens at new moon, when the moon passes between the sun and Earth. A lunar eclipse happens at full moon, when the Earth, sun and moon align in space, with Earth between the sun and moon. During a lunar eclipse, Earth’s shadow falls on the full moon because the Sun, earth and Moon are in a straight line. We typically have between four and seven eclipses – some partial, some total, some lunar and some solar every year. But, why aren’t there eclipses at every full and new moon?

The moon takes about a month to orbit around the Earth. If the moon orbited in the same plane as the ecliptic, we would have a minimum of two eclipses every month. There’d be an eclipse of the moon at every full moon. And, approximately two weeks later there’d be an eclipse of the sun at new moon for a total of at least 24 eclipses every year. So, why don’t we?

The reason is that the moon’s orbit around Earth is inclined to Earth’s orbit around the sun by about 5°. Twice a month the moon intersects the ecliptic at points called nodes. If the moon is going from south to north in its orbit, it’s called an ascending node. If the moon is going from north to south, it’s a descending node.

Figure 1: The tilt of the earth remains unchanged during its orbit around the sun over a year.

This leads us to the next mystery. Our moon, unlike the moons of other planets moves along the ecliptic instead of the equatorial plane. Why? Next, why is it tilted at an angle of about 5°?

Simulation studies published in 2016 in Nature attribute these to the collision with Theia. Given the nature of the formation of the Moon, it was never quite on the equatorial plane of Earth and was orbiting it at a relatively large distance on a different plane (tilted differently than both the ecliptic and the equatorial plane). The Moon is also slowly drifting away from the Earth at a rate of about 3.78 cm per year. Over time, the grip of Earth’s gravity is weakening and the effect of the Sun’s gravity increasing on the Moon, and hence its path. The Moon’s plane of orbit around the Earth is slowly converging to the ecliptic, being merely 5° off.

Precession

As Earth rotates, it also wobbles slightly upon its axis, like a slightly off-center spinning top. This wobble is due to tidal forces caused by the gravitational influences of the Sun and Moon that cause Earth to bulge at the equator, affecting its rotation. This wobble takes the form of a circular motion of the axis with each period having a duration of about 25,771.5 years (see Figure 2). This phenomenon is called axial precession (precession, in short).

Figure 2: The blue line on top shows the precession of the polar axis. It completes a circle in about 25771.5 years.

One of the effects of precession is the presence/absence of pole stars. Today, we have a northern pole star in Polaris (Dhruva Tara in Sanskrit). Polaris however became the northern pole star only around 500CE. It will continue to be the pole star till about 3000 CE. From around 1700 BCE until just after 300 CE, Kochab (Beta Ursae Minoris) and Pherkad (Gamma Ursae Minoris) were twin northern pole stars, though neither was as close to the pole as Polaris is now. Thuban was the naked-eye star closest to the north pole from 3942 BCE until 1793 BCE. Around 12,000 BCE, the bright star Vega in the constellation Lyra was the north star and will regain the pole position around 14,000 CE.

Figure 3: Time lapse photograph of the northern sky shows the circular movement of stars about the polar axis, and the pole star is located (almost) at the center of this circle.

Movements of Sun and Moon

As viewed from Earth, the ecliptic is nothing but the plane containing the (apparent) path that the Sun traces out in the sky over a year. In the rest of this article, we will talk about the movement of the Sun – this will imply the apparent movement of the Sun as seen from Earth.

In addition to the ecliptic, there’s another plane of importance – the celestial equatorial plane. Imagine a plane slicing through the Earth along the equator and extending infinitely in all directions. As discussed earlier in section “Obliquity”, the Earth is tilted at an angle of approximately 23.4°. Hence, the celestial equatorial plane is also tilted at the same angle with respect to the ecliptic. This can be better visualized with Figure 4.

This tilt also explains the movement of the Sun. In a year, the Sun appears to move from the southern hemisphere to the north (Uttarayana in Sanskrit), appears to come to a pause at the Tropic of Cancer (latitude 23.4° N — due to the tilt) on the day of the Summer solstice (Latin “Sun standing still”) and starts moving south (Dakshinayana in Sanskrit), till it appears to pause at the Tropic of Capricorn (latitude 23.4° S) on the day of the Winter solstice, before commencing its sojourn north. During this sojourn, the Sun crosses the equator twice each year. When the Sun crosses the equator, the durations of night and day are equal. Such days are called equinoxes.

Figure 4: The celestial equator, the ecliptic and the tilted polar axis

Again, when the Sun reaches the northernmost part of its sojourn in the sky, the duration of day is at its maximum in the northern hemisphere, and minimum in the southern hemisphere. Today, this happens during summer in the northern hemisphere (and winter in the southern hemisphere). This is called the summer solstice in the northern hemisphere, and winter solstice in the south. Similarly, when the Sun is at its southernmost point, the northern hemisphere experiences the shortest day (longest night), and the southern hemisphere experiences its longest day (shortest night). This day is called the winter solstice in the northern hemisphere, and summer solstice in the south. This means that the winter solstice (irrespective of the hemisphere) always has the shortest day (longest night), and summer solstice always implies the day with the longest day (shortest night).

Today, the two equinoxes fall in the months of March and September respectively, and the solstices in the months of December and June. In the Northern Hemisphere, the March equinox is called the vernal or spring equinox while the September equinox is called the autumnal or fall equinox. In the Southern Hemisphere, the reverse is true. During the year, equinoxes alternate with solstices cyclically. This is illustrated in Figure 5.

Figure 5: The solstice-equinox cycle

No matter where one is on Earth (except for the North and South Poles), one has a due east and a due west point on the horizon. These points mark the intersection of the horizon with the celestial equator. The equinox sun is always on the celestial equator. Therefore, no matter where one is on Earth, the celestial equator intersects the horizon at due east and due west. This means that the sun rises due east and sets due west, for everyone, at the equinox. This was used by the ancients to identify equinoxes (typically the spring equinox) as the beginning of the year. In the Indian Saka calendar, the new year begins on the day after the spring equinox. Ancient edifices show the importance assigned to equinoxes by designing architectural structures to frame the Sun during an equinox. Figure 6 shows the Sun aligned perfectly in the apertures of the gopuram of the Ananthapadmanabha temple in Tiruvananthapuram during the spring equinox. Similar planned structures can be seen in the main temple at Angkor Wat (Cambodia), Machu Pichu (Bolivia) and even at Stonehenge.

Figure 6: Movement of the setting Sun framed by apertures in the gopuram of the Ananthapadmanabha temple in Tiruvananthapuram on the day of the vernal equinox.

In the next part, we will discuss nakshatras, their Sanskrit and Latin names, the constellations they lie in, and how they provide a frame of reference for us to make many astronomical calculations.

  1. The plane in which the Earth orbits the Sun (the orbital plane) is called ecliptic.
  2. Viparitayana in Sanskrit, meaning “moving in the opposite direction”. Today, the summer solstice is called Karkatasankranti and the winter solstice, Makarsankranti (or Mahasankranti). The reason behind these names will be explained in a subsequent article.
  3. Equinox (singular) literally means ‘equal night (and day)’.

By Dr. Ravi Shankar Iyer
CEO of Accenture Center of Excellence at IIT Madras, Chennai, India

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