The Periodic Table as a mirror

Hi everyone! You might be wondering why I thought of writing about the periodic table. Well, the answer is “just for fun!”

History of the Periodic Table

The first human classification of elements was done by Antonie Lavoisier back in the 18th century. In his classification, he included certain elements like Oxygen, various compounds and even certain types of energy as light! At that time elements were not defined as the fundamental ‘substances’ of matter. People who lived back then considered elements as the most fundamental things which made up the world. They didn’t know about the difference between compounds and elements and nor did they know that light was an energy.

Lavoisier’s Classification

Time passed and different people came up with different classifications, but none of them could classify all elements according to a proper pattern and that is when the British Chemist John Newlands came into play. In about 1865 he published a research paper, describing his “Law of Octaves”, which said that when the elements are arranged in the ascending order of their atomic weights, after every 7 elements, the physical and chemical properties of every element are repeated periodically. The scientists didn’t want to believe that Chemistry was related to Music. So they rejected it.

You’ll be amazed if I say that the first ‘periodic table’ is a result of Mendeleev’s attempt to make a good text book for his students. Yes. Dmitri Mendeleev wanted a better text book for his university students, but since he could not find any, he started writing one by himself. In it, he started classifying the elements which were discovered by then in the order of their atomic masses. Following in John Newland’s foot steps, in his classification, he followed the law that “characteristics of elements is a periodic function of the ascending order of the atomic masses of the elements”.

When he was arranging the elements, he saw that some elements had to switch their places in order to keep the periodicity of the characteristics. When they were switched, the atomic masses were not in ascending order. Anyway, he arranged the elements so that their characteristics occur periodically, and gave each element an index number. He also predicted the characteristics of some elements that were yet to be discovered and kept empty spaces for them in his periodic table. When time passed, those elements were discovered, had the same characteristics Mendeleev predicted and perfectly fitted in the places which were kept by Mendeleev in his periodic table.

Mendeleev’s periodic table

Later it was discovered that the index numbers given by Mendeleev to the elements represented the number of protons and the number of electrons of an atom of that specific element which made that index number the true identity of an element. We call it the true identity of an element, because when we know the number of electrons, we can identify the electron configuration which is responsible for most of the physical and chemical properties of elements. Today that ‘index number’ is called as the ‘Atomic Number’ of the element.

The reason for some elements to switch places in Mendeleev’s periodic table was that some elements had different isotopes found in the environment. When calculating average atomic mass for an element it gets a higher or lower value than what it should get according to the trend. At that time, they had no idea about sub atomic particles. All they knew was the atom as a whole.

When talking about the history of our modern periodic table, Julius Lothar Meyer is another important scientist. He created a periodic table which was a creation of his own work, similar to the periodic table of Dimitri Mendeleev. Mendeleev’s table was based on qualitative properties, while Lothar Meyer’s table was based on quantitative properties. Lothar Meyer didn’t predict the characteristics of the elements which were yet to be found, but he created his table before Mendeleev. But the thing is that, he published it after Mendeleev. Mendeleev’s periodic table was published in 1869 while Meyer’s table was published in 1870.

Lothar Meyer’s periodic table

Order of the elements in the Periodic Table

It is not that ancient periodic table we are using today. The modern periodic table which has about 118 elements is a collective creation of many many scientists, so we cannot give the credit to one specific person. In this table also, the elements are arranged in the order of their atomic numbers. The elements are arranged in the ascending order of their number of protons which is the same as the number of electrons.

The elements are arranged according to the Aufbau principle, which states the order of the building up of electrons one by one in particular sub energy levels.

Rows of the Periodic Table

Rows of the periodic table are known as “periods”, because each row is a specific ‘period’ of characteristics. As a year of four seasons Spring, Summer, Autumn and Winter repeat after another year, when one period of the periodic table is over, another period with similar characteristics to the previous one begins.

Each period is given a positive integral value as 1, 2, 3,…etc. That integral value corresponds to the number of main energy levels an atom of an element has, but it is not the the number of energy levels which are ‘completed’ with electrons. There can be electrons in higher energy levels while the lower ones are incomplete, but the lower ones cannot be empty. Therefore the integral value of the highest energy level of an atom corresponds to the number of energy levels that atom posses. Therefore, the integral value of the period in which the element is, also represents the highest main energy level of it.

So, by looking at the period of an element, we can say how many main energy levels it has and that helps us to identify some features of that elements which are based on the number of energy levels it has.

Columns of the Periodic Table

Columns of the periodic table are known as “groups”, because since characteristics of elements occur periodically, all the elements in each group have similar characteristics. There are 18 groups in the periodic table numbered from 1 to 18 according to the ascending order of atomic numbers.

Each group is numbered in such a way that all elements in a group have the same number of valence electrons. But the group number is not always equal to the number of valance electrons of the elements in that group. The number of valence electrons is equal to the group number in periodic tables where f-block and d-block are not considered. But that relationship drops in the long form of the periodic table. That does not mean that we cannot identify the number of valence electrons of an element by looking at its place in the periodic table. There is a pattern.

Number of valance electrons of the elements in the d-block vary between 2 and 1. From group 13 to 18 the number of valence electrons is the group number – 10. For an element in the group 15, the number of valence electrons is 5. So, if we know the group number of an element we can identify its chemical properties, because most of the chemical properties are based on the reactivity of the element and the reactivity of an element is based on its number of valence electrons.

  • Group 1 – Alkali Metals
  • Group 2- Alkaline Earth Metals
  • Group 16- Chalcogens
  • Group 17- Halogens
  • Group 18- Noble Gases and etc.

Blocks of the Periodic Table

There are 4 types of sub- energy levels an atom can have. They are known as s, p, d and f. Energys < Energyp < Energyd < Energyf. s- sub energy level can posses a maximum of 2 electrons. p-sub energy level can posses a maximum of 6 electrons. d-sub energy level can posses a maximum of 10 electrons and f-sub energy level can posses a maximum of 14 electrons.

The elements in which the s-sub shell is being filled are together known as the s-block. The elements in which the p-sub shell is being filled are together known as the p- block. The elements in which the d-subshell is being filled are together known as the d-block and the elements in which the f-sub shell is being filled are together known as the f-block.

Number of groups in a Block

There are 2 groups in the s-block, 6 in the p-block, 10 in the d-block and 14 in the f-block. Why is that? If you observe closely, you will see that those numbers are somewhat similar to the maximum numbers of electrons sub shells can posses.

Since it needs 2 electrons for the s-block to be completed, there are 2 consecutive groups in that block. It is the same for all the blocks. For an example, 6 electrons of the p block is filled one by one along the 6 groups of that block across the particular period.

IMPORTANT NOTE: Maximum of only one subshell of a particular type can be there in a main energy level of an atom. For an example there cannot be 2 p-subshells in the 2nd energy level. And also, all the types of subshells cannot be seen in one energy level all the time. [1st energy level has only one subshell which is s. 2nd Energy level has only 2 subshells which are s and p, and so on. If you want to learn more about this, do a google search about ‘Quantum Numbers’]

Number of elements in a row of the Periodic Table

Before going into this sub topic, I have to tell you about the total number of electrons in a main energy level. It is always equal to 2n2 , where ‘n’ is the integral value of the energy level. We can see that the total number of electrons in energy levels are 2, 8, 18, 32,.. Now let’s go into our topic.

If we look at the periodic table, we see that the number of elements in periods are also 2,8,18 and 32! So, the question is, “Is there are relationship between the total number of electrons and the number of elements in a period?” the short answer is, “NO AND YES”.

Actually this happens because of the blocks that can be seen in a period. There is a period with only a row of the s-block and that period has 2 elements, because an s-subshell can have a maximum of 2 electrons. When there are both s and p, there are 8 elements, 2 for s and 6 for p and so on.

The total numbers of electrons in main energy levels has those numbers, due to the subshells they have. If there is only s, the number is 2. If there are s and p, the number is 8 and so on.

Those two are not connected, because a period does not represent a main energy level. The periodic table is arranged according to the Aufbau principle (the order of building up of electrons). For an example, the 4th period has the subshells 4s, 3d and 4p.

The numbers are equal due to a similar fact and that is subshells. But the reasons for them to be equal are not conceptually connected.

We can identify many trends across periods and down groups of a periodic table and there are many more advantages of the periodic table. See how all those things are connected to each other. Isn’t that amazing? Hope this helped. Thanks for reading!

What is happening to Sri Lanka?

It’s been a long time since I posted my last article. Of course I had enough time to write articles on Science and stuff, but I couldn’t make my mind, because of all these things happened and happening in Sri Lanka one after another which made me very frustrated. How can I talk about Science when I see that it has no more use for my country or world?

If we talk globally, we can see that no proper action has been taken by even the richest countries in the world to reduce emissions, although they have the ability to do it. When children school-striked and protested against the political leaders who did not take any action against climate change, what people said was, “They should go to school and learn more to become climate scientists instead of striking”. The young climate activist, Greta Thunberg’s logic is the best for this. We don’t have to learn Science and become a climate scientist to talk about this. Scientists have already identified the solutions for this problem. So the world already knows what we should do and what has to be done. What we should do is to take action immediately before it is too late. If we do not take action to save our own lives, although the proper instructions are given by Science, what is the point of learning Science?

Anyway, today I’m going to be talking about the current situation of the small island, Sri Lanka. ‘The Pearl of the Indian Ocean’ is facing a total tragedy almost in all aspects: economically, socially and environmentally.

1. Deforestation

Sri Lanka is relatively a very poor country in the world. So, it is impractical for us to stop carbon emissions completely in Sri Lanka, while rich countries like US and China work for the growth of the production process day by day. But that does not mean that we do not have a responsibility to protect our Earth for our existence.

The whole world cannot be controlled by one person or one party. That is why it is divided into countries as how a country is divided into large to small divisions like states, districts, cities and etc.. Since small and poor countries like Sri Lanka has no power to tell other countries to reduce emission, what they have to do is, protect the nature without increasing the rates of emission and keeping the nature as it had been.

As everyone knows, what truly happens here in Sri Lanka is the total opposite. Political leaders of our government sell lands of forest reserves including ‘Sinharaja’ and ‘Rambakan oya’ to different private companies and individuals for their political benefits and let them cut all the precious trees to build hotels and stuff. They block streams of water and make ponds. ‘Sinharaja forest reserve’ is a World Heritage Site. When I was little, I was taught that ‘Sinharaja’ was a rain forest which was never affected by humans. I was taught that there were no man made things in it. I was taught that it was even restricted to pluck a leaf of a plant in it. I was amazed. I thought to myself I should probably visit it. After about 3 years I visited it with the friends and teachers of the Environmental Club of our school. But what I saw at first was some backhoe holders removing blocks of soil. When I was walking inside the forest, I saw many tire tracks. I was very disappointed and worried. At present, the forest is being destructed day by day. Most of us got to know about this after what Bhagya told. I wish if I am strong and brave as she is.

It is not only forests that are being destroyed. The natural sponges; wet lands, which absorb all the excess water, are being destroyed to make constructions. We already experience the results of these activities as floods and land slides.

Those ‘leaders’ say that they do it for the development of the country. They say that they do it for the betterment of people. How can we say that it is for the betterment of people, when it dries off all the natural water springs from which people get drinking water? How can we call it a development when it kills thousands of animal species which destructs the earth’s equilibrium?

2. Elephant-human conflict

Politicians make villages by cutting down parts of forests where elephants usually live. They locate people in those villages by giving them new houses to get their votes for the elections. Our thankful Sri Lankans who never miss their duties, vote for those politicians with no second thought. Of course that is not their fault. Those innocent people have nothing to do with it. It is all because of those narrow minded selfish politicians that these innocent people suffer now. Elephants who used to live in that place come there most of the time, because it is their home. When they go there, they destruct the farms, cultivations, properties and lives of people and that is the nature of animals. They have no fault either. People and children who live their suffer a lot, because they do not have any choice apart from living there keeping all these problems to themselves.

Now they have taken actions. There are protesting against the government asking for a solution to their problem. These protests are spread in most of the parts in the country by now, but still, no solution is given.

3. Sugar scam

There are questions every where. By observing the sugar scam done by the leaders of the government of Sri Lanka, we can see how corrupted and selfish they are. They steal money from innocent Sri Lankan people for their own benefit. They use Sri Lanka for their benefit and yet people don’t understand. They do not let people know. They have the ability to handle media and lie to the people.

4. Value of a Sri Lankan rupee has decreased vastly and Prices of grocery items have increased immensely

One US dollar is nearly 200 Sri Lankan Rupees now. Arrival of an inflation of prices of grocery items can be seen. People do not have the ability to buy food and satisfy their basic human needs, because they cannot afford to. How can those heroes still fool people by saying that they are developing the country?

5. Leaders do not let people know who is truly responsible for the Easter Sunday attack

When talking about the Easter Sunday Attack, we can see that still there is no one found responsible for it. They say that they won the civil war, but we see that they are not able to find out who was behind the attack. Or do they try not to reveal it on purpose? And why is that? It’s been 2 years! Why don’t they reveal?

6. Human rights violation

When we look at the social background of Sri Lanka, there was this human rights violation. After a long time of disapproval they finally agreed for the burial of dead bodies of Covid-19 patients. If UN did not take action for this, they would have still not agreed to it.

7. Racism

8. Frauds

9. Politicians using media to make people see what ‘they’ want them to see

10. Question behind the political and environmental aspect of Sri Lanka’s sea

What were the real reasons for those whales and sharks to strand to our beaches and what are THEY trying to hide about our sea?

11. Selling parts of the country to China, India, etc.

They take debts more than needed from other countries and companies so that they can have commissions from that money. When they cannot pay them back, what they do is promise those countries to give a part of our countries. Western terminal that is to be handed over to India is an example.

This is a crisis. I wish If I could be like Greta Thunberg; school-striking in front of the Parliament for our future. Unfortunately, I don’t have that strength or confidence. I just wanted to let you foreign and local readers know about this. Thanks for reading!

Geminids Meteor Shower

Today I decided to tell you about the meteor shower, ‘Geminids’ which had its peak on 13-14 December. Most of you are aware of this meteor shower and I know that you have observed it too. This is one of the most popular and attractive meteor showers where about 120 meteors fall per hour.

In this year, 2020, it coincided with a new moon which made it clear to be observed. Since there was no moonlight to lighten our night sky, all we needed was to find a place with less light pollution.

What is a meteor shower?

You might have heard of comets. Comets are huge snow balls which orbit around the sun and most of them come from the Oort cloud and the Kuiper Belt and they have highly elongated orbits like parabolas, hyperbolas and sometimes ellipses. They are leftovers from the formation of our solar system and located far away from the inner solar system.

When they come close to the sun, the ice around them heats up, and forms a huge head of dust and gases around the nucleus, which is known as the coma of the comet. The dust and gases form a tail which stretches away from the sun for millions of miles. When a comet orbits, it leaves dust particles in its orbit and if the orbit of the earth crosses it, when the Earth passes the intersection, those dust particles burns in the Earth’s atmosphere and fall as a meteor shower.

What causes Geminids?

Although comets cause the majority of meteor showers , there are meteor showers which are caused by asteroids and Geminids is one of them.

The asteroid, 3200 Phaethon is the reason for Geminids. Some scientists’ idea is that this asteroid can be an ‘extinct’ comet. But some say that when it comes near the Sun, due to the heat, it cracks and leaves particles in its orbit and when Earth crosses its orbit, those particles burn in the atmosphere of the Earth.

What causes the attractive colours of the meteors of Geminids?

Geminids is known as one of the brightest and most attractive meteor showers, due to the multi-colour of it. You know that different elements give different colours when burnt in the air. So as that, the particles which contain different elements which were in the asteroid give attractive colours when they are burnt in the atmosphere.

In which part of the sky can we observe it?

Every meteor shower is named in the name of the constellation in which its radiant is located. In a meteor shower, the meteors are observed to be appeared from a single point in the sky and that point is the radiant of the corresponding meteor shower. The radiant of Geminids is located near the star Castor- the second brightest star of the constellation Gemini. To observe the trail of the meteor clearly, you should look 30 to 6o degrees away from the radiant.

I hope you enjoyed this article. Thank you for reading!


World’s best stargazing spots

Have you ever felt that overwhelming feeling when you look at a sky full of stars? Well, I have. It is a feeling I cannot describe. It is mysterious. It is some kind of a mixture of happiness and excitement. A sight of a dark sky filled with sparkling little stars is able to bring tears to one’s eyes. Anyway, what I’m going to tell you today is about 10 such beautiful and peaceful places which you may want to visit within your life time.

  1. The Sahara

Sahara, bordered by the Atlantic Ocean in the west, Atlas Mountains and Mediterranean sea in the north, Red sea in the east and Sahel in the south is the largest desert on Earth. It is located in Africa and it’s area is about 8 600 000 square kilometers. Its dry climate and distance from civilizations makes it an extraordinary place for star gazers around the world.

2. Namibian desert

Namibia is a country located in Africa and also known as South West Africa. According to those who have seen the sky at the Namibian desert, those who haven’t seen the southern sky under the perfect atmospheric conditions would take their breath away there. Namibian desert is very popular for sky guest farms (Astro Farms). An Astro Farm is a place equipped with an observatory where you can stay for days and observe the sky. Babak Tafreshi, director of The World at Night (TWAN), an international organization that curates and exhibits astro-photographs says, “The landscape is ideal for stargazing. Looking around you can see a 360-degree panorama of the horizon.”

3. The Empty Quarter, Arabian Peninsula

“The Empty Quarter in the south-eastern part of the Arabian Peninsula is one of the largest continuous deserts in the world, covering an area of about 250,000 sq miles (650,000 sq km). As its name suggest, the desert is almost empty of people.” says BBC Earth.

4. Atacama Desert, Chile

“Pristine night skies hang above most areas of the Atacama Desert”, says Tafreshi in BBC Earth. He further says, “Atacama beats many other dark sky places by being high and dry and clear for so many nights per year. Walking on the desert between the scattered rocks and boulders on the pale red dust feels like being on Mars but under the Earth sky.”

5. La Palma, Canary Islands

“The volcanic island of La Palma Island, part of Spain’s Canary Islands archipelago is a popular destination with astrotourists for its astonishingly clear skies. In 2002 the entire island was named a UNESCO (United Nations Educational, Scientific and Cultural Organization) Biosphere Reserve.” [1]

6. Himalayas

“The ‘crystal clear skies of high hiking treks and Himalayan villages’ are among the world’s best” says Tafreshi. Himalayas mountain range is the world’s highest mountain range and has 9 out of 10 of the world’s highest mountains including mount Everest. Himalaya is averagely 8,848 m high. Due to its height from the sea level, from there, one can see a larger portion of the sky (can see the sky below the horizon of the sea level) at a time, than someone at the sea level. And also due the less population, the light pollution is very low.

7. Volcanoes of Hawaii

“Hawaii’s high volcanoes are home to several well-known observatories. The volcanoes Mauna Kea and Mauna Loa, both more than 4,000m above sea level, are among the island’s volcanoes most famous for their views of starry skies.” says BBC Earth.

8. Western Australia

“Photographs of the west of Australia’s Outback taken by satellite reveal just how dark the region is” , says Tafreshi. He further says, “The many National Parks in the area are favourite places for stargazing” “The southern hemisphere sky is even more eye-catching than the northern view due to the Milky Way bright central area rising overhead”

With very little light pollution, there are plenty of places in WA for stargazing. Here are some.

Lake Ballard, Menzies

Dales Gorge Campground, Karijini National Park

Lucky Bay, Esperance

Roebuck Bay, Broome

Wooleen Station, Murchison

Wave Rock, Hyden

Sal Salis, Ningaloo Reef

Dryandra Woodland, near Narrogin

 Lake Ninan, Wongan Hills

Coorow Golf Club, Coorow

9.The Alps

“The last remaining natural night sky in Western Europe is in the Alps,” says Tafreshi. “One of my favourites has been Tyrol region in Austria [where it’s] easy to see the pristine night sky.”

With a latitude of 46.8876° N, The Alps has a remarkable Northern sky. The “increase in summer time sports such as mountain biking, golf, parapenting, or whitewater kayaking is now fueling the growth of the alps as a year round tourist destination. The Alps have always been popular as a mountaineering and hiking destination, but clearly this is nowhere near as lucrative for the locals as the tourist invasion during the winter season is.” [2].

10. Wyoming, US

“There are many wonderfully dark places here in the American West, which is where I’m originally from,” says Dr John Barentine, program manager at the IDA .

“Many of these sites are parks and similarly protected areas such as nature preserves. National parks in the US and elsewhere are often fantastic places to experience authentically dark night skies, since they tend to be relatively far from cities and relatively undeveloped in terms of installations of artificial lighting.”

All these 10 places are recommended by BBC Earth to observe clear starry skies. Oh I dream of visiting these places. Will visit Western Australia for sure. Hope you enjoyed this article. Thank you for reading!











Why can’t we be?

Why can't we be?

A beam of morning sunlight
fell on my book
and made me look
at the silvery dust particles
sparkling in the air.

Peaceful they
blew themselves
in the direction of the wind,
danced random ballet,
passed the beam of light
swam away from my sight
like birds
that come to Earth
and fly away
without any spite
into the skies far above.

We are not like them
Why can't we be? 

Dulshi Ranaweera


The Sky

The Sky

A man said,
“Oh! It’s raining. What a muddy day.
Today’s gonna be a very bad day.”
Then the sky said,
“Don’t you like it?
Then let it be a sunny day
with a lot of sunlight.
So you can sun bathe
throughout the day!”
and made the day sunny.
The man said,
“Oh! It’s sunny. What a sweaty day.
Today’s gonna be a very bad day.”
The sky changed the day: rainy, sunny,
snowy, misty,
but still she could not
satisfy the man.
At the end of the day,
The man said,
“I hate you, sky!”
The sky is ‘she’.
She felt a pain in her heart,
but she did not cry,
because if she did,
her tears would fall down to earth
and make the day a rainy day.

Dulshi Ranaweera

Mars’ Closest Approach October 6, 2020

On October 6, 2020 (today), Mars comes to its closest distance from earth which is only 62.07 million kilometers (38.6 million miles)! You’ll be able to see it in your eastern sky as a red bright ‘star’ when the dark falls (For most of the countries including Sri Lanka) and it will come to its highest position in the sky at about 00 : 00. It is so bright and you can easily recognize it. Don’t miss this, because Mars won’t be this bright until 2035!

[Don’t worry if you couldn’t observe it when it was in its closest approach (on October 6th). It will be brighter on the 13th of October than on October 6th, because the opposition of Mars is on the 13th of October 2020!]

Why is it brighter on October 13th?

Mars comes to its opposition with earth on the 13th of October. When the Earth is exactly between Sun and Mars, it is known as the opposition of Mars. The Sun, Earth and Mars lie nearly on a straight line as shown in the following figure.

figure 1

Earth may not be exactly between Sun and Mars as in an opposition when it is in its nearest position to Mars. (I’ll tell you more about that later in the article.) So, when mars is in its closest distance from earth, it does not reflect the light it gains from the Sun directly to earth. When Mars is in its opposition, it reflects more light directly to earth and because of that we can see it brighter.

Why aren’t we closest to Mars on the (opposition) day we pass between it and the sun? If both the Earth and Mars circled the sun in perfect circles, and on the same exact plane, the distance between Earth and Mars would always be least on the day of Mars’ opposition. But we don’t live in such a symmetrical universe. All planets have elliptical orbits and a perihelion (closest point) and aphelion (farthest point) from the sun.

Mars’ orbit around the sun takes 687 days in contrast to 365 days for Earth. It has a year nearly twice as long as ours. Earth’s farthest point from the sun comes yearly, in early July. Mars was at its closest to the sun on August 3, 2020. Ever since July 4, 2020, Earth has been moving closer to the sun; and ever since August 3, 2020, Mars has been edging away from the sun.

At its opposition on October 13 – when Earth will be directly between Mars and the sun – Mars will be farther from than sun than on October 6, 2020. On the other hand, Earth will be closer to the sun (and therefore farther from Mars) on October 13 than on October 6. That all adds up to Earth being slightly closer to Mars on October 6 than October 13.[1]

Mars Closest Approaches

“At its 2003 close approach – on August 27, 2003 – Mars was 34.65 million miles (55.76 million km) away.

At the 2018 close approach – on July 31, 2018 – Mars was 35.78 million miles (57.59 million km) away.

Mars won’t beat its 2003 performance until until August 28, 2287, when the red planet will be 34.60 miles (55.69 million km) away.”[1]

Earth and Mars are closer on October 6, 2020 than they will be again for another 15 years, or until September 2035; I say again, Don’t miss this!

You can observe Mars throughout this month (October), so turn off all the lights, go out and enjoy the sky!! Thanks for reading!



Basics for Astronomy Olympiads and Quizzes: Introduction to Spherical Trigonometry (Part 2)

As I said in my previous article on spherical trigonometry, spherical triangles are made out of 3 parts of 3 great circles. Now we will discuss about great circles.

Great circles and small circles.

figure 1

Great circles of a sphere are circles that are drawn on a sphere with the same diameter of the sphere. If we say it in another way, radius of a great circle is equal to the radius of its sphere.

But the radii of small circles are smaller than that of the radius of the sphere.

There can be an infinite number of great circles and small circles on a sphere.

I say again, the three sides of a SPHERICAL TRIANGLE must belong to three great circles of the same sphere, which means that every spherical triangle formed by three great circular arcs intersecting pairwise.

For an example, as shown in figure 2.1 and 2.2, if a triangle is made from the observer’s meridian, celestial equator and the azimuth line (vertical circle), that triangle is a spherical triangle, because all the above mentioned circles are great circles. See my previous articles under Astronomy Category if you don’t know what Meridian, Azimuth and Celestial Equator are.

figure 2.1
figure 2.2

Spherical triangles are not like plane triangles. The sum of the interior angles of a spherical triangle is always greater than 180 degrees and less than 540 degrees.

Main formulas related to spherical triangles

There are 2 main simple formulas used in spherical trigonometry. Of course there are more. If you understand these two properly you can learn and apply other formulas by yourself easily.

Trigonometric ratios can be applied for sides of spherical triangles too, because they are also angles originated from the center of the sphere.

Consider the following images for the cosine and sine formulas below the image.

figure 3
figure 4

Cosine formula for spherical triangles

cos a = cos b.cos c + sin b.sin c.cos A

same formula applies for other sides as below.

cos b = cos a.cos c + sin a.sin c.cos B

cos c = cos a.cos b + sin a.sin b.cos C

Sine formula for spherical triangles

sin a / sin A = sin b / sin B = sin c / sin C

sin A / sin a = sin B / sin b = sin C / sin c

I’ll come up with some examples in my next article.

Thank you SO MUCH! Click this if you want to listen!

Dear adults,

Thank you so much for contributing to ruin our future. You’ve taken a very good decision this time. You took the same decision over the past years since we got independence from Britain and that idea you have to ruin your children’s lives have grown much bigger this time. You’ve sent the most precious, selfless, intelligent and patriotic people to the parliament. Thank you so much. Now, all the drug addicts will be sent to the prison, and people who bring drugs to the country will rule the country sitting on thrones; this is you idea: “well, although they bring drugs here to ruin the country, they send the drug addicted people to the prison, no? And also, although they try to destroy people by selling them drugs, they develop the country, no? So we should vote them. They will save the Sinhalese community, the most treacherous Sinhalese-Buddhist culture and all that, by destructing ancient monuments like “Bhuwanekabha Raja Sabhawa” to build casino-playing places. Although they sell the country part- by part to China, India, etc. they develop the country, no? ” The people whom you sent will talk for you at the parliament. HAHAHA..! Wait for it. YOU KNOW they won’t! YOU KNOW they won’t talk for your children! YOU KNOW THEY WON’T MAKE LAW FOR THE SRI LANKANS’ BENEFIT and still you vote them!

I want to express my heartfelt gratitude to the minority of people who voted for the true benefit of the country although it didn’t go well this time because they were the minority-people who voted the compass (and the majority was ‘foolish and “වහල්”-minded’ as every day). I know. This is so rude to talk like this as a 16-year old. But how can I stay without talking?! It is my future you are destroying!

We are debtors to the whole world. Rulers of the country spend luxurious lives while the majority of the people suffer economically, mentally and physically. Do the rulers have the problems normal people have? Each one of us have been debtors. Is it our fault? Do you think it is because of your fault? It is not the rulers who are responsible for this. But you ! You are the ones who are responsible for this! You are the ones who made them to rule the country. As our country is democratic , the power to assign leaders of the country is in the hands of people.

It is our Educational system which fits our little brains to think within this frame. Each one of us has a little bit of racism germinated deep within. I don’t know about others, but when considering me, I don’t even notice a single racist idea within me, because I don’t let that racist seed to grow in my mind. If there is a racist idea in a text book or if one of my teachers talks about a racist idea, I notice it, but I reject it. My mind rejects it. But most of the students absorb it and that is the reason for the present majority to be racist and vote those people who fertilize racism in the country. When racism rises, it is easy for them to get the votes and get the power.

You have brains to think. Do you know that Nigeria takes our country as an economically failed country and that they are being careful not to be like our country? This is how your rulers have developed the country over the past years. Try to think out of the frame. Thank you for reading.

Basics for Astronomy Olympiads and Quizzes: Introduction to Spherical Trigonometry (part 1)

Spherical Trigonometry is the subject related to Spherical Triangles. Simply, spherical triangles are triangles that are drawn on a sphere, but to be a spherical triangle, the sides of the triangle should be made out of great circles of the sphere. I will explain more about Spherical Triangles and great circles in my next article. In this article, I will introduce you the background of Spherical Trigonometry used in Astronomy.

Mainly, we use spherical trigonometry to locate an object in a sky. For an example, if we have the equatorial coordinates of an object (RA and Dec), we can say where that object is in our sky (Altitude and Azimuth of the object) at the current time. We can also find things like distances between stars by determining the angular distance between them. To find the angular distance, Spherical Trigonometry might be helpful.

To make spherical triangles in the celestial sphere, we combine both Alti-azimuth and Equatorial coordinate systems. In that, we assume that the observer is near the center of the Earth, because when comparing with the distances between objects in the universe, radius of the Earth is relatively negligible. See figure 1.

figure 1

The latitude of the observer is denoted by the Uppercase or Lowercase Greek letter phi (ϕ or φ). The angle measured from the horizon to the North Celestial Pole always takes the value of the latitude (ϕ) of the observer if the observer is in the Northern Hemisphere. If the observer is in the Southern Hemisphere, he sees the South Celestial Pole |ϕ|° (angle corresponds to the absolute value of the latitude) above the horizon in the direction of South. If the latitude(ϕ) = 0°, South Celestial Pole is at the horizon in the direction of South and North Celestial Pole is at the horizon in the direction of North. What is the reason for this? See figure 2.

figure 2

Latitude is the angle measured from the equator to the location of the person along the longitude. In the figure 2, the observer’s latitude is 50°. So the angle measured from the equator to the observer is 50°. When the straight line drawn from the center of the earth to the observer is produced to the celestial sphere, it meets the zenith of the observer. Therefore, angle between the Celestial equator and the Zenith of the observer is also 50° which is the latitude of the observer. Rotational axis of the celestial sphere is perpendicular to the Celestial Equator and because of that, the angle between the NCP and the Zenith of the observer becomes 90°- 50°= 90 – ϕ =40°. Since the straight line joining the Zenith and the center of the sphere is perpendicular to the horizon, angle between horizon and the NCP becomes 90°-(90°- 50°) = 50° = ϕ.

When we locate a celestial object in an alti-azimuth and equatorial combined celestial sphere, we mark its altitude and azimuth as well as its Right Ascension and Declination. I hope to include more about it in the next article.

Hour Angle (HA)

There’s another special angle called Hour Angle which we use to locate a celestial object in the sky. Imagine that, you only have the equatorial coordinates of a star and you want to find where that star is in your sky at the current moment. If you have the altitude and azimuth of the star, you can easily find it, right? So, it is essential to know the Hour Angle of that star to find its altitude. First I’ll tell you what an Hour Angle is. There are some simple calculations to find the hour angle and if you want to know them all, stay tuned! I will include them in my future articles.

Hour angle is the angle measured westwards from the meridian of the observer to the Right Ascension of the star. Meridian is the line joining the observer’s North, Zenith and South respectively. Hour angle is measured in hours, minutes and seconds as we measured Right ascensions. See figure 3.

figure 3

That’s it for today. Stay Tuned for the next article! Thank you for reading!

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