Large eyes to look the heavens

Large Eyes to look the heavens

Debi Prasad Choudhary

Los Angeles, 02/05/2014

God gifted divine vision to his friend and disciple in a battlefield to enable him see his “cosmic self”. While listening to this episode in the story of Mahabharat from my granny, I wished such a vision to see the cosmos. Twenty years later, the sight of Saturn, Jupiter and Orion Nebula through a moderate telescope, reminded me of the feelings of God’s friend if he had really seen these objects all at once!! Telescopes are large eyes to look at the tiny light glows in the sky situated far away.

Human eye is a sophisticate camera with a complex lens of about 8 mm size. In broad daylight, we use only a small part about 2mm of this this lens through which light enters to make an image inside the eye. As we enter a low light area the iris fully opens up for the light to enter through entire 8 mm lens. Usually it takes some time for this to happen, so we cannot clearly see in the first few moments of entering the dark from bright illuminated area. The 8 mm lens collect enough light to see the stars of about 6th magnitude and can distinguish two stars separate by about 1 arc minute. The range of color that our eye can see is limited to the colors of rainbow.

Light is electromagnetic wave because the electric field and the magnetic field vibrate in planes perpendicular to the direction of its propagation. The distance between the maximum vibrations in same direction is called wavelength. The two extreme color of rainbow are violet and red have wavelengths 400 nanometer and 700 nanometer respectively.  The electromagnetic waves of long wavelength are of lower energy compared to shorter wavelength. There are electromagnetic waves beyond this visible range. The electromagnetic waves of wavelength lower then 400 nanometer are x-ray waves that are used in dentist office, UV waves that cause skin problem if sunscreen is not used while lying in beach. The waves with larger than 700 nanometer wavelength are Infrared that we use for pain reliever, radio and microwave that are used for communication via TV, radio stations and mobile phone technology. All these electromagnetic waves are exactly same as the light we see with our necked eye, but have different wavelength. The stars and galaxies in the sky produce light in a wide range from very short to very long wavelengths.

Light propagates in the form of waves that prevent the formation of sharp shadow of knife-edges. Infect, if you closely look at the shadow of a sharp object like a knife-edge, you will find dark and bright bands that are produced due to diffraction. The same effect limits us distinguishing two pennies kept side by side beyond about 225 ft. In order to distinguish them, we need to increase the size of our eye (make it bigger than about 8 mm), which is not possible. The other alternate is to use a telescope that has a bigger lens.

The wave nature of light has another consequence. As the light wave front from a distant star passes through the earth’s atmosphere, different parts move at different speed through packets of air with different density. By the time it reaches our eye the light wave is distorted from its original shape before entering the earth. Since the air pockets with different density move, we see the stars twinkle. The planets do not twinkle because they are situated relatively nearer and send many light waves slightly separated in space. These days, we can repair the distortion using modern image stabilizer technology somewhat similar to the one available in many cameras (adaptive optics) and prevent the star from twinkling.

Astronomers build telescopes and detectors to look at them in all wavelengths in minute detail. About 400 years ago, Galileo used the telescope to discover dark spots on the sun and moons of Jupiter that made great impact in modern science. While working as a professor in Padua University in Italy, he used to buy lenses in neighboring town Venice and select the best ones after examining them by looking at the stars. The stars would look like a point of bright light if the lens were perfect. But, since the images in blue, yellow and red color are made at different distances from the lens, they might still look blurred.

The bigger lenses are used to make telescopes to see faint stars by collecting more light. Large lenses are supported only at the periphery, so they become bent due to their own weight making it impossible to make them larger than about one meter size. This difficulty can be overcome by using reflecting mirrors of spherical shape, since they can be supported from the back. Mirror based telescopes produce images of color at same distance from the reflecting surface. But, the light reflected from the outer part of large spherical mirrors are focused at different distance that also results in blurred images. So, large reflecting telescopes are made with mirrors that are not spherical but parabolic.

The thickness of the mirrors should be about 1/6 of the diameter in order to prevent flexure leading to the distorting the parabola shape. This requirement creates problem in making mirrors for the large telescopes of sizes greater than 3 to 4 meter as they become too heavy. Making segmented mirrors and using an active support overcomes this problem. The segmented mirrors use smaller parts of a parabolic mirror held by active supports that maintain the parabolic shape. The active supports continuously tilt to adjust the orientation of mirrors to keep them in a parabolic form. The surface of the mirrors or the lens that produce the images of astronomical objects must be smooth relative to the wavelength of the light.

Since the earth rotates around north-south axis, special mounts are built to align them along local latitude and track the stars by moving at a rate of 360 degree in 24 hours. There are other sophisticate mounts and tracking systems for large telescopes. Building the enclosure or telescope dome and the location of the observatory is also an important part of these astronomical facilities. The observatories are built at high altitudes – on the top of mountains, that are dark and have clear sky for most of the year. For installing very large telescopes, like the 30-meter telescope being made by Caltech and University of California, extensive site survey is undertaken. Additional complexity arises for telescopes built for observing the sun because it heats the surroundings. The solar observatories are built surrounded by large body of water or in very high altitudes where the atmosphere is stable in presence of the sun.

A large part of light in ultraviolet, X-ray, gamma ray and Infrared is blocked by the atmosphere and do not reach the earth. Satellite based space born telescopes are built to observe the stars and galaxies in these wavelengths. These great instruments include Hubble Space Telescope, Chandra X-ray telescope and Spritzer telescope for IR light. 

The light in radio wavelength similar to FM radio or TV communication is long so the telescope surface need not be very smooth. At the same time large mirrors are needed for achieving the images of higher resolution. Many separate telescopes are used to collect light and combined to get an image from an effectively large telescope. These are called interferometers, a technique that is also used for optical wavelengths.

Like, we get lots of information about an object from the amount of light it emits and its color, telescopes serve the same purpose for astronomical sources. The information about the nature of the object is embedded in the amount of light it emits or reflects, the color or wavelength of light and amount of light wave in different orientation, which is also known as the state of polarization. Instruments are used at the focal plane of the telescopes to examine these properties of light from the astronomical sources.

Modern big eyes enable us to see the objects very faint in the sky and learn about them in all colors that are visible to our eye and beyond. Often these faint objects are situated far away, such that light from them takes many many years to reach us. This means we are able to see a star that may not be there at this time, but what it was when the light left from it. Today, we have built such large telescopes that we can see the objects that were born just after the creation of the universe. Some times, I think the fantastic imaginations of the ancient stories are taking real shape.

Beginning to understand the heavens

Beginning to understand the heavens

Debi Prasad Choudhary

Los Angeles, 02/05/2014

The rhythmic march of the sun, moon, planets and star patterns on the sky and occasional fireball shower and the appearance of sword shaped comets of different color made ancient wise man accept their influence on major earth events especially the fate of kings and emperors. When I was in 2^nd or 3^rd grade, I remember curiously listening to my father chatting with his friends about the death of an honest prime minister of India in 1966. Many were saying they know some thing like this was going to happen as the bright comet Ikeys-Seki appeared a year earlier in 1965. Now, I understand their anxiety. They were growing up in a country that got freedom from British about a decade and half ago, already fought two wars and already lost two big leaders that included Mahtma Gandhi, during which there was both a comet and an eclipse!! They knew that King Edward VII of England died in 1910, when Halley’s comet appeared in the sky. They were quoting Homer, “Like the red stars, that from his flaming Hair, shakes down diseases, pestilence and war.” I wondered, why no such thing happened for the death of our villagers that I witnessed all the time!! Well in the word of Shakespeare, “When the beggars die, there are no comets seen; the heavens themselves blaze forth the death of princes”. But, our villagers were no beggars, or princes either. Later, when my PhD supervisor suggested me to work on Comet Halley, I joked if we will survive through and he laughed and still healthy after 15 years of retirement.  

Ancient rulers built gigantic monuments such as Stonehenge, Newgrance, and Fajada Butte that served as a tool to keep track of the movement of heavenly bodies. Many years ago, I visited such a monument, a sun temple Konark, situated 90 miles from my town. The three doors of this huge temple were precisely aligned to allow entering of the sunlight into the temple throughout the year and illuminate the spokes of the wheels like a sundial. This demonstrates the precision of the observations of the north-south movement of the sun.

Such careful observations of the motion of heavenly bodies produced two important results that may be considered as the base of modern astronomy. One: The no shadow day at different locations of the earth used by Greek scholar Eratosthenes (200BC) to determine the earth’s radius. Two: Apart from the sun and moon, five bright objects (planets) in the sky did not follow the pattern of stars.  The planets shift position progressively eastward in the sky with respect to the background stars, which would sometimes slowdown, stop and reverse direction making westward swing. The westward swing is known as retrograde motion. For different planets the amount of eastward and westward shift are different. The first attempt to visualize the celestial sphere, in which all objects including earth, planets, stars, sun and moon are arranged, was made by Claudius Ptolemaeus (Ptolemy 140 AD), all heavenly bodies move around the earth. If we consider circular path of these objects around the earth, it is not possible to explain the retrograde motion and predict the position of a planet with respect to the background stars for a particular day of the year. So, Ptolemy proposed that the planets move on small circles (called epicycles) the center of which slide on larger circles that surround the earth (deferent). In spite of the complexity of mathematical calculations, this idea prevailed for more than 1000 years until Copernicus (1473 AD) proposed that the planets, including the earth move around the sun, NOT around the earth. This heliocentric universe could explain the retrograde motion of the planets easily without invoking complex geometry of circles moving on circles, but could not predict the location of planets correctly enough.

Major breakthrough happened when Tycho Brahe (1546) gathered accurate positional information of planets in the sky for several years using a sophisticate instrument that was periodically calibrated. Tycho was a wealthy nobleman who could maintain such an instrument and perform these measurements. He had a silver nose after losing on a sword duet with his cousin to settle an argument over the legitimacy of a mathematical formula! He hired Kepler to work on the data, but never shared until his death due to bladder failure after refusing to leave a banquet to relieve him (to go to restroom!). Founded on theological believe, Kepler (1571) looked for the cosmic harmony designed by God’s geometrical plan in the Tycho Brahe’s data leading to three laws of planetary motion. First law states: the planets move around the sun in an elliptical orbit, NOT circular. Ellipse is a flattened circle that has two focal points one of which is occupied by the sun. Unlike a circle, which has only one radius, an ellipsis has two axes major and minor. The second law states: while going around the sun the planets swipe equal area of ellipse in equal time. This means during same period of time the planet must move more distance when situated near the sun compared to the furthest location. The third law states: the square of the period during which planets go around the sun is equal to the cube of half major axis. Since these laws were empirically determined, they were only good for the planets moving around the sun. In 1621, Kepler applied his law to the moons of Jupiter and found that period square was not exactly equal to one unlike for the planets.

Around the same time, Galileo (1564) made a number of discoveries that had profound effect on the progress of our understanding of heavens. Using the telescope, he showed that objects move around planets like Jupiter similar to the planets moving around the sun. He dropped two balls of different mass from the tower of Pisa in Italy and found that both arrived on the ground simultaneously.  While falling, the distance increased as the square of time. If in the first minute the ball covered 2 meter, in the second minute it would cover 8 meter. Because, when a body falls freely without any air resistance, the speed changes by about 10 meter per second per second as if something is pulling from below.

This pulling force is the gravitational force, discovered by Sir Isaac Newton (1642), who said two bodies with mass m1 and m2 separated by a distance r would attract each other by a force that would increase as their mass and decrease rapidly as they are separated. Mathematically: the gravitational force F= G (m1 x m2)/r². G is called gravitational constant, which is same no matter what material we are considering or where we are testing this law. This was a profound discovery. The consequence of this law is that if we consider the sun and the earth, both attract each other with a force that depend on their mass and separating distance. Actually, because of this mutual force they circle a common center located nearer to the heavier mass. So careful observation shows that the earth and other planets do not circle the sun but around a point located near it’s surface. This is the same force that cause ocean tides.  Using mathematics he showed that such paths would be elliptical. In fact, Kepler’s laws are consequence of this force. It was so obvious to Newton that when Edmond Halley visited with the observations of the positions of a comet, immidiately he told the path around the sun must be an ellipse and it would come near the sun after every 76 years. Halley was so impressed with this work that he sold some of his property to publish all these findings in the famous book “Philosophiæ Naturalis Principia Mathematica “. This book also deals three other famous laws of motion. The first law says, if some thing is not moving or moving with constant speed it will maintain such situation until forced to change. The effect of this is experienced everyday in the form of a jerk due to sudden break or pushing the accelerator of the car. The second law states that when we apply force a heavier body is pushed with less speed compared to a lighter body. More the force, speeder the body moves. The third law states for every force we apply on a body, it exerts back equal and opposite force. Many modern technologies starting from designing a car to launch of rockets depend on these laws. But the most important achievement is that Newton’s discoveries demonstrated the universality of physical processes – the same laws of nature govern the motion of objects on earth and in havens.

Almost 300 years later, Albert Einstein (1879) said that the space, time and mass are related. When you place a mass on a flat space the geometry around it changes such that it is no longer flat. But the effects are really very small so you never notice such changes around you while walking. But, if you replace yourself with a huge object like the sun, you will notice the changed geometry of the space. This was confirmed by two important observations in early 20^th century. One of them was total solar eclipse photograph that showed some stars located behind the sun due to the light travelling from them on a path that was curved near the sun.  The other observation was the pattern of motion of mercury, which is very near the sun. Mercury becomes closer to the sun sooner than expected from the Kepler’s laws as it moves in a distorted space caused by the mass of the sun. Today, there are many more examples of this effect observed with space telescope and other advanced instruments.

Over these years, the fear of the heavens for me is replaced by curiosity and wonderment, as I am equipped with the tools of science. The sky still amazes but throwing challenges for understanding. Our civilization is in a unique position that is equipped with a plethora of scientific theories and technological innovations to enjoy the creation. We must invent different stories to entertain our next generation that cannot base on fearing the heavenly bodies.

When the Sun disappear from the sky

When the Sun disappear from the sky

Debi Prasad Choudhary

Los Angeles, 2/4/2014

It is frightening to see the sun suddenly disappear in broad daylight!! No wonder, in all parts of the world there are stories of the sun or the moon getting eaten away by animals, devils or evil souls to cause these events.  Native American folklore describe the event as the sun or the moon caught by one of the wolves witnessed by the Vikings, who saw two wolves chasing them. In some parts of the world, like Vietnam, people thought frog or toad eating them, which for me is incomprehensible, considering the sun so powerful. The Chinese folklore holds a dragon eating the sun, so they beat drum to scare the sun-eater. Again, if some thing can eat the sun, I would hardly believe it can be scared by drum noise!! According to the Cherokee Legend, the sun started profusely weeping as a rattlesnake in a complicated event involving her brother moon and humans bit her daughter. This unhappy event represents eclipse, although I would have thought moon to be the sister, being pleasant!! 

These events are seriously taken by ancient Egyptians, Greeks and Indians. Egyptians thought the sun as god, bringing light to our world in day and taking it to the world of dead in the night. At times an evil serpent god tries to stop him, causing eclipse. Greeks worshiped the sun - God Helios and observed carefully. The eclipse was some thing a bad omen. We find in Greek writing: "Nothing there is beyond hope, nothing that can be sworn impossible, nothing wonderful, since Zeus, father of the Olympians, made night from mid-day, hiding the light of the shining Sun, and sore fear came upon men. - Archilochus". Greeks also discovered that the pattern of eclipses repeat after 18 years 11 and 1/3 days called Saros Cycle.

Now, I am proud of the stories from my Granny, considering the people’s imagination of small creatures eating the sun. She said, in the beginning of the creation the ocean was churned, out of which a pot of nectar emerged. The nectar had power of making one immortal, so they were distributed only to Gods. Two demons, Rahu and Ketu, took the form of Gods and tried to steel the nectar. The Sun and the Moon recognized them and reported to the supreme God, who beheaded Rahu and Ketu before they swallowed the nectar. So, their head without the body became immortal!!! Since then, they chase the sun and the moon and occasionally eat them. But, since they do not have a stomach, the sun and the moon come out soon. However, this being an evil, inauspicious event, we used to take bath after every eclipse and go to a temple to pray and give gift to priests and learned man to do penance. As a child, I always thought, it is not my fault, I did not do any thing wrong, some body else ate the moon - why should I do the penance?

Until recently, my parents never saw an eclipse. They were in a closed-door house during a solar or lunar eclipse. I witnessed the grand fantastic view of total eclipse in 1995, while conducting an experiment to study the dust ring around the sun. In 2009, I took my parents to show another total solar eclipse. Since it happened to be in the bank of a sacred river, my father among many family members came to see the eclipse. While my father was reading Holy Scriptures, my son made sure that he does not miss those two minutes of grand view. My mother enjoyed the event the most, although she insisted to perform the post eclipse rituals, which we obelized.

This was possible because today we know clearly why the eclipses happen. As the earth goes around the sun and the moon around the earth, they cast shadow, being opaque, nonluminous objects. The solar eclipse happens, when the moon shadow falls on the earth, while lunar eclipse is resulted as the moon enters the earth’s shadow. Eclipses are called total when the earth or the moon enters the regions of complete shadow. You will notice red colored moon during a total lunar eclipse, because of the illumination of moon’s surface by the scattered sunlight from earth’s atmosphere – similar to the color of evening sky. Since earth casts a larger shadow, the lunar eclipses are more frequent and long duration compared to solar eclipses that rarely happen only for few minutes (longest being about six minutes) and never cover the entire earth.

The earth goes around the sun and the moon goes around the earth in elliptical path. Unlike the circular path, where all points on the circle are at equal distance from the center, in an elliptical path there is a point nearest to the center and a point farthest from the center that result changing distance of the moon and the sun from earth at different times - when they appear bigger or smaller. The moon goes around the earth and spins around its own axis. The spinning period and the period for going around the earth are almost same. As a result, we see only one side of the moon all the time. Depending on the orientation of the sun, which illuminates moon and earth, we see parts of the moon progressively from full moon to new moon. During the full moon the illuminated side is towards us as the earth is situated between the sun and the moon. In new moon, the moon is situated between the sun and earth, so the illuminated side is away from us. Between these two extreme situations, we see waning and waxing crescents and gibbous.  Such locations of the moon also cause tidal effects producing periodic high tides at a particular location.

The sun-earth-moon geometry is the reason we see the solar eclipses on new moon days and lunar eclipse on full moon days. So, why does it not happen every month? Because, the plane in which the moon and earth are located is tilted by about 4 degrees to the plane in which the sun and earth are located (called ecliptic plane). So, most of the time, the shadows are missed by each other. With precise orbital calculations, we can now predict when such rare situations would occur. 

Also, it is a great coincidence that the angular size of the sun and the moon are same, about half degree, which makes the solar eclipse possible. The size of the sun and the moon are 1,391,000 km and 3475 km. Their distances from earth are 149, 600, 000 km and 384, 400 km respectively.  So, they produce same angle on earth. In the sky, the sizes or distances are measured in angular scale. A circle has 360 degrees. One easy way of roughly estimating the size in the sky is to stretch your arm and keep the thump in front of your eye so that it blocks the view behind. The amount of area it blocks is about one degree. You can block two suns or moons by placing the thump in front of your eye by stretching the arm.

Because the angular size of the sun and the moon are exactly same, half a degree, the moon covers the disk of the sun. Disk of the sun means, the projection of spherical sun on the sky that looks as a disk, from which, on a normal day we receive all the sunlight, also called the photosphere. During the total solar eclipse, this part of the sun is covered, so we can see its less dense atmosphere that is mostly dominated with hydrogen and helium gas with traces of other elements at different stages of heat. The hydrogen gives a red look and Helium a yellow look. Unlike the photosphere, which is mostly white, the atmosphere looks colored, so known as Chromosphere. In fact, in 1868, during a solar eclipse in India, a French astronomer Pierre Janssen discovered Helium on the sun. At that time people thought this element exists only on the sun, so named as Helium after the Greek God Helios.  Later in 1895 helium was discovered on the earth. There are many other important scientific discoveries during the experiments conducted in the solar eclipses.

As the total solar eclipse happens, progressively the moon will cover the sun. The shadows will start becoming long and really frightening. In the end, just before the totality, a small bright glow will appear, that is known as Diamond Ring. Diamond ring appears due to the leaking of the sunlight through the uneven edge of the moon. When the sun is fully covered, the chromosphere will be seen nearer to the solar disk, surrounded by an extended corona, which is mostly white light – the sunlight scattered towards us by the surrounding electrons.  The chromosphere would some times consist of structured objects called prominences, which are magnetic field structures filled with mostly hydrogen gas. The Corona would be circular when the sun is active, and elongated if it is not active.

If the moon were located at a greater distance, we would have missed its shadow or it would never have entered earth’s shadow. So, no eclipse, no folklores and no scare. But, who knows what else would have happened. Studies show that, the current configuration of earth-moon system keeps the tilt of the earth’s axis stable, which result in periodic seasons. If that were not sot so, there would be unpredictable hot and cold situation hindering the progress of modern society. Anyway, that is another story.

Note: A total solar eclipse will be observed over North America (starting in Oregon and ending in South Carolina) on August 21, 2017. It is a once in a lifetime event, so get ready to witness.

Get more information on this event from the following websites:

http://eclipse.gsfc.nasa.gov/SEgoogle/SEgoogle2001/SE2017Aug21Tgoogle.html

http://www.eclipse2017.org

Majestic march in the sky and seasons on earth

[These blogs are created for my online astronomy class in California State University Northridge. Since they may interest wider audience, I publish them on Blogger. All comments are welcome.]

Majestic march in the sky and seasons on earth

Debi Prasad Choudhary

Los Angeles, 02/01/2014

Hot in summer, cold in winter and rain - at times furious. If that were random, I would have believed the stories from my granny and from all other civilizations. Associated with the change in season, which are periodic, there are many other clearly observable features. The summer days are long in northern continents, the shadows are shorter, and the sun rises towards north of the east direction. The pattern of stars in the summer night sky is different compared to the cold winter days, when the sun rises towards south and stay in the sky for less times producing longer shadows. Still, I thought in childhood that the Gods that govern the summer (Sun God) or God of rain or cold come to see the supreme God near our small town so we get the seasons. Some times, if they get angry, we get sever weather. So, better worship them to keep them in good humor.

Every day, we notice the majestic march of the sun in the sky that rise in the east and set in the west. Moon and few other bright objects move in the same band of the sky, as if following the sun. These bright objects look like stars but do not twinkle like them. Every month they appear in a different part of the sky progressively towards the west. Some of them suddenly make u-turn as if going backwards. From ancient time they were recognized as planets, very conspicuous objects.

Most other stars rise in the east and set in the west. Some of them rise but do not set. And, even some of them never rise or set, they are there in the sky in the evening and only change position in the night circling a bright star in the northern sky, which do not noticeably change the position ever. This star made such an impact of the civilizations that Shakespeare wrote dialogue for Caesar as:

Caesar:
"I am constant as the northern star,
Of whose true-fix'd and resting quality
There is no fellow in the firmament."

Julius Caesar (III, i, 60 – 62)

In my childhood, I learned about this star “constant star”, which was a great child devotee of one of the Gods in spite of the fact that his father worshiped another God. Consequently, his father tortured him with several cruel techniques. In the end, his father was killed by the powerful God and honored him with the constant star.

Now of course, we know that this northern star does change it position, which can be measured with telescopes. The stars that do not rise or set are called circumpolar stars as they circle around this North Star or pole star. If you take a long exposure photograph of the sky, you will get the star trails that are either circles or part of circle around the North Star. In the southern hemisphere, the different sets of stars circle in the sky, but unlike in north there is no such constant star. You can observe these phenomena from Australia, Brazil or Argentina. You can imagine a sphere around the earth called celestial sphere on which the objects of the sky move. The extended circle aligned with the equator on the celestial sphere is known as celestial equator. The earth’s longitude and latitude are projected onto this sphere to uniquely define the position of stars on the sky. The coordinates of the objects in the sky are called right ascension and declination.

Rising and setting of sun and stars happen, not because they actually circle around the earth, but the earth spins (rotation) around its axis, which is aligned along the North Star, also called pole star. If you observe carefully, you will notice that the rise time of the stars are delayed by 4 minutes every day because of the earth circles (revolution) around the sun. The axis of the earth was not always aligned along the North Star.  As the earth’ s north-south axis processes with a period of 26,000 years other bright stars in the north get aligned that affects the climate on earth on similar time scale.

This circle is inclined to the plane in which the earth circles the sun, called ecliptic plane. The planets that seem to follow the path of the sun also circle the sun on this ecliptic plane. In other words, if you imagine a plane in which the earth and sun are situated, the north-south axis around which it rotates, is inclined by 23.5 degrees. This has profound affect on the earth. This is the reason for the seasons on earth. Because of this tilting, sun is seen to be rising in different directions in summer and in winter.

In fact, the sun is slightly away from the earth in summer compared to the winter because the orbit of earth is an ellipse. So, it is not the sun-earth distance that cause the summer and winter but the tilt of its north-south axis with respect to the ecliptic plane. You may be surprised to know that this fact is unknown to almost 65% of educated people!!

So, let us explain everything we observe in summer and winter with the model in which the earth rotates around the sun with its tilted north-south axis. Due to the 23.5-degree tilt the sun appears overhead once at latitudes 23.5 north and south and twice in latitude within this range. When this happens, there are no shadow in the noon, some people observe no-shadow day. Beyond these latitudes, for example in Seattle or Chicago, this situation will never occur.  When northern hemisphere is tilted away from the sun, the bundle of rays from the sun is spread over a larger area so heat the landmass less. You can imagine a situation, when the light bean from a flashlight is incident in a plane that is inclined to the beam. In such situation, the light get spread over a larger area. As the inclination decreases, the area over which the light spread decreases resulting increased heating. This produces summer situation. The inclined beam of light from the sun also explains the larger shadows in winter.

By carefully observing the motion of the sun and stars in the sky, we could figure out the cause for seasons. That is a big achievement. Now, I do not invoke Gods for governing these phenomena on earth. May be they have bigger job to do!!