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An equinox is an astronomical event in which the plane of Earth’s equator passes through the centre of the Sun. It occurs twice each year around 20 March and 23 September.On an equinox, days and nights are of approx equal duration, all over the planet, due to the angular size of the Sun and atmospheric refraction.

The motion of the Earth around the Sun is called a revolution. It revolves around the sun at a distance of 150000000 km (app.) in a nearly circular orbit. It takes 365.25 days to complete one revolution around the Sun. Earth spins about its own imaginary axis like a top, from west to east. This motion of the Earth about its own axis, is called rotation. Earth completes one rotation about its own axis in 24 hours. Days and nights are formed due to the rotation of Earth about its own axis, in 24 hours. Seasons are caused due to the revolution of Earth around the Sun and the tilting of its axis of rotation.

Rashi: Moon sign at the time of the birth is known as Rashi. Moon sign is the name of the zodiac in which the moon was located at the time of the birth are affected due to the revolution of Earth around the Sun, as well as the by the preception of Sun moving along elliptical path along the space occupied by 12 reshis and 27 nakrashtra (or constellations).

The answer is (C) Both (A) and (B)

Varahmihira was born in 499 A.D., in a family of Brahmins, settled at Kapittha, a village near Ujjain. His father, Adityadasa was a worshipper of the god Sun and it was he, who taught Varahamihira, astrology. On a visit to Kusumapura (Patna), young Varahamihira met the great astronomer and mathematician, Aryabhatta. The meeting inspired him so much, that he decided to take up astrology and astronomy as a lifetime pursuit. At that time, Ujjain was the centre of learning, where many schools of arts, science and culture were flourishing, in the prosperity of the Gupta reign. Varahamihira therefore, shifted to this city, where scholars from distant lands were gathering.

In due course, his astrological skills came to the notice of Vikramaditya Chandragupta II, who made him, one of the Nine Gems of his court. Varahamihira’s mathematical work included the discovery of the trigonometric formulas. He improved the accuracy of the sine tables of Aryabhata-I. He defined the algebraic properties of zero as well as that of negative numbers. Furthermore, he was among the first mathematicians, to discover a version of what is now known as Pascal’s triangle. He used it to calculate the binomial coefficients.

His treatise such as Pancha Siddhantika (Five Principles), Brihatsamhita (Master collection), Brahjataka (Astrological work) have put him on as high a pedestal in Astrology, as Kautilya’s in Political philosophy, Manu’s in Law or Panini’s in Grammar.

Varahamihira’s main work is the book Pancha Siddhantika (“Treatise on the five Astronomical Canon’s which gives information about old Indian texts, which are now lost). The work seems to be a treastise on mathematical astronomy and it summarises five earlier astronomical treatises, namely, the Surya Siddhanta

Romaka Siddhanta, Paulisa Siddhanta, Vasishtha Siddhanta and Paitama Siddhanta. Panch Siddhanta holds a prominent place, in the realms of astronomy.

Varahamihira was learned in the Vedas, but he was not a blind believer in the supernatural. He was a scientist. Like Aryabhatta before him, he declared that the earth was spherical. In the history of science, he was the first to claim that some “Force” might be keeping bodies stuck to the round earth. The force is now called gravity.

Bhaskara was born in 1114, near Vijjadavida (believed to be Bijjaragi of Vijayapur in modern Karnataka).

Bhaskara II, also known as Bhaskara or as Bhaskaracharya, was a 12th-century Indian mathematician. He was also a renowned astronomer, who accurately defined many astronomical quantities, including the length of the sidereal year. A brilliant mathematician, he made the significant discovery of the principles of differential calculus and its application to astronomical problems and computations centuries before European mathematicians, like Newton and Leibniz made similar discoveries.

It is believed that Bhaskara II was the first to conceive the differential coefficient and differential calculus. Bhaskara II wrote the first work with full and systematic use of the decimal number system and also wrote extensively on other mathematical techniques and on his astronomical observations of planetary positions, conjunctions, eclipses, cosmography, and geography. In addition, he also filled many of the gaps, in his predecessor, Brahmagupta’s work. In recognition of his invaluable contributions, to mathematics and astronomy, he has been called the greatest mathematician of medieval India.

Scientific work and achievements:

1. He made many significant contributions to mathematics, throughout his career. He is credited to have given a proof of the Pythagorean theorem, by calculating the same area in two different ways, and then cancelling out terms, to get a₂ + b₂ = c₂ .

2. His work on calculus was groundbreaking and much ahead of his times. He not only discovered the principles of differential calculus and its application to astronomical problems and computations but also determined solutions of linear and quadratic indeterminate equations (Kuttaka). The works in calculus performed by the European mathematicians of the 17th century is comparable to the rules he had discovered, way back in the 12th century.

3. His major work ‘Siddhanta Siromani’(“Crown of treatises”) was completed in 1150 when he was 36 years old. Composed in the Sanskrit Language, the treatise consists of 1450 verses. The work is divided into four parts called “Lilavati, “Bijaganita’, and ‘Goladhyaya’, which are also sometimes considered four independent works. The different sections deal with different mathematical and astronomical fields.

4. The first part “Lilavati’ consists of 13 chapters, mainly definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions, plane geometry and solid geometry and many others aspects of mathematics. It also has a number of methods for computing numbers, such as multiplication, squares, and progression.

5. His work “Bijaganita’(“Algebra”) was a work in 12 chapters. This book covered topics like positive and negative numbers, zero, surds, determining unknown quantities, and elaborated the method of ‘Kuttaka’for solving indeterminate equations and Diophantine equations. He also filled many of the gaps in his predecessor, Brahmagupta’s work.

6. The sections ‘Ganitadhyaya’ and ‘Goladhyaya’ of ‘Siddhanta Shiromani ’ are devoted to astronomy. He used an astronomical model developed by Brahmagupta, to accurately define many astronomical quantities, including the length of the sidereal year. These sections covered topics such as mean longitudes of the planets, true longitudes of the planets, solar and lunar eclipses, cosmography, geography etc.

7. Bhaskara II was especially known for his in-depth knowledge of trigonometry Discoveries first found in his works, including computation of sine of angles of 18 and 36 degrees. He is credited to have discovered spherical trigonometry, a branch of spherical geometry, which is of great importance for calculations, in astronomy, geodesy and navigation.

8. Bhaskara-II major work was the treatise-‘Siddhanta Siromani’, which was further divided into four parts, each of them dealing with diverse topics on arithmetic, algebra, calculus, trigonometry, and astronomy. He is considered to be a pioneer in the field of calculus, as it is probable that he was the first to conceive the differential coefficient and differential calculus.

Aryabhatta: Aryabhatta was an acclaimed mathematician astronomer. He was born in Kusumapura (Patna) in Bihar, India. His contribution to mathematics, Science and astronomy is immense and yet he has not been accorded the recognition in the world history of science. At the age of 24, he wrote his famed “Aryabhatiya”. He was aware of the concept of zero, as well as the use of large numbers up to 1018. He was the first to calculate the value for ‘pi’ accurately, to the fourth decimal point. He devised the formula for calculating areas of triangles and circles. He calculated the circumference of the earth as 62832 miles, which is an excellent approximation, and suggested that the apparent rotation of the heavens was due to the axial rotation of the earth on its axis.

He was the first known astronomer to devise a continuous counting of solar days, designating each day with a number. He asserted that the planets shine, due to the reflection of sunlight, and that eclipses occur due to the shadows of the moon and earth. His observations account for the ‘flat earth concept and lay the foundation for the belief that earth and other planets orbit the Sun.

Scientific works and achievements:

Direct details of his work are known only from the Aryabhatiya, His disciple Bhaskara I, calls it Ashmakatantra (or the treatise from the Ashmaka). The Aryabhatiya is also occasionally referred to as Arya-shatas-ashta (literally, Aryabhata’s 108), because there are 108 verses in the text. It also has 13 introductory verses, and is divided into four or chapters.

Aryabhatiya’s  first chapter, Gitikapada, with its large units of timc-Kalpa, manvantra, and Yuga-introduces a different cosmology. The duration of the planetary revolutions during a mahayuga is given as 4.32 million years.

Ganitapada, the second chapter of Aryabhatiya has 33 verses, covering mensuration, arithmetic and geometric progressions, gnomon or shadows, simple, quadratic, simultaneous, and indeterminate equations. Aiyabhatiya’s third chapter, Kalakriyapada explains different units of time, a method for determining the positions of planets for a given day, and a seven – day week with names for the days of week.

The last chapter of the Aryabhatiya, Golapada describes Geometric/ trigonometric aspects of the celestial sphere, features of the ecliptic, celestial equator, shape of the earth, cause of day and night and zodiacal signs on the horizon.

(i) It is speculated that Aryabhata used the word (approaching), to mean that not only is this an approximation but that the value is incommensurable or irrational.

(ii) In Ganitapada, he gives the area of a triangle as: “for a triangle, the result of a perpendicular with the half-side is the area. He discussed sine, by the name of ardha-jya or half-chord.

(iii) Like other ancient Indian mathematicians, he too was interested in finding integer solutions to Diophantine equations, with the form – + by = c; he called it the (meaning breaking into pieces) method.

(iv) His contribution to the study of Algebra is immense. In Aryabhatiya, Aryabhata provided elegant results for the summation of series of squares and cubes through well-tried formulae.

(v) He correctly believed that the earth rotates about its axis daily.

(vi) In Aryabhatiya, he writes that ‘setting and rising of planets’ is a perception, similar to that of Someone in a boat going forward sees an object going backwards.

(vii) He correctly, asserted that the planets shine, due to the reflection of sunlight, and that the eclipses occur due to the shadows of moon and earth, and not caused by a demon called ‘Rahu’.

(viii) He correctly deduced that the orbits of the planets are ellipses.

Other Achievements:

The gave the knowledge of Algebra, Intermediate equations, Trigonometry, Place value system and zero and also the motions of the Solar system.

The phases of moon occurs due to relative change in the position of the earth and moon, while revolving around the Sun.

Tithis: In Vedic timekeeping, a tithi (also spelled thithij is a lunar day or the time it takes for the longitudinal angle between the Moon and the Sun to increase by 12°. Tithis begin at varying times of day and vary in duration from 19 to approximately 26 hours. Thithi plays an important role along with nakshatra in Hindu’s daily as well as special activities, in selecting the muhurta. There are good tithis, as well as bad tithis. 

The good tithis are called shulkla paksha (bright fortnight) and the bad tithis are called Krishna Paksha (dark fortnight), when fast moving moon gives an interval of 12° from Sun, then that time interval is called Pratipada Tithi.

Asteroids are the small piece of rocks or metals which revolve around the Sun, between the orbits of Mars and Jupiter.

The answer is (D) new moon

Mercury, Mars, Venus, Earth, Neptune, Uranus, Saturn, Jupiter.

The bright shiny star-like objects with a long tail, approaching the sun in a highly elliptical orbit are comets.

The answer is (A) Cancer

Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune.

The answer is (C) comet

The answer is (A) Sky

The heavenly bodies found outside the earth’s atmosphere, either small or massive in size are called celestial bodies. For example, stars, Sun, Moon, planets etc.

The answer is (B) hydrogen

Constellation has the following characteristics: 

1. It is a group of a few stars. 

2. A constellation appears to resemble an animal or a human being or some other known object in shape.

The answer is (B) 4

The answer is (C) constellation

The answer is (D) All of these

The answer is (C) Bhaskara II

The answer is (A) comet

The answer is (B) After 2 years

The complexity of the Indian calendar system is not just in the plethora of available calendar, but also in the manner in which they link up with one another. A principal point of linkage of most Indian calendars is their name of the months, As we shall see, the similar set of month names are used in more than one calendar. We aim to formulate the rules, determining the name of months. Our motivation is not just taxonomic, month names, as we shall see, are critical for understanding the Indian calendar system.

The set of month names named after nakshatras is used by both solar and lunisolar calendars, adding to the complexity of the Indian calendar system. Indeed, as we shall see, this type should actually called months initially named after nakshatras; there has been an infusion of solar rules into an essentially lunar convention. The motion of the moon is related to lunar months.

Let us then, first consider the original rule. Saha and Lahiri mention that Pakshas or fortnights were differentiated based on the nakshatra. That is to say, if a particular full moon occurs near, say, the lunar asterism, Visakha, the full moon would be called as Vaisakha Pumimasi, and the month would be Vaisakha. The earliest lunisolar months, then, were pumimanta, that is, the name of the full moon corresponded to the name of the month. Of course, the full moon occurs at all nakshatras. Fifteen were taken into account for the naming of the month, spaced more or less equally. We thus have the following set of names along with their respective nakshatras:

Bhaskaracharya.

Rashi contains Nine charans.

The first Indian Satellite was named on Aryabhatta.

Terrestrial planets are:– Mercury, Venus, Earth, Mars.

Phobos and Deimos.

Aryabhatta gave the relation between circumference and diameter of circle

The answer is (A) Jupiter

West to East.

Venus, Mars, Mercury, Jupiter Saturn, Uranus, Neptune.

Panchami occurs after chaturdashi of Shukla paksh

Life is discovered on Mars planet, except Earth

Y is greater than X, so Y has the larger revolution time.

The answer is (A) Pluto

The answer is (A) 12 – 24

(a) Largest planet- Jupiter 

(b) Smallest planet- Mercury.

Saturn, having 30 satellites.

Asteroids the bodies of the solar system that have failed to assemble into a planet

The answer is (B) Sun

The answer is (C) Both (A) and (B)

Marga Shirsh.

A solid heavenly body which revolves around the Sun in a closed circular orbit is called a planet. 

Star: 

1. Stars have their own light. 

2. Stars produce their own energy, due to the fusion of hydrogen. 

3. Stars appear to twinkle at night. 

4. Stars have enormous mass. 

5. Stars do not change their relative position in the sky, every day. 

6. Stars appear to move from east to west in the sky. 

Planet: 

1. Planets do not have their own light. 

2. Planets do not produce their own energy. They have to depend upon the Sun for energy. 

3. Planets do not twinkle at night. 

4. Planets have insignificant mass, compared to the stars.

5. Planets change their position in the sky, on a daily basis. 

6. Planets appear to rotate from the west to east in the sky.

The answer is (B) Venus

A Hindu muhurta (forty-eight-minute duration) can be represented in five attributes of Hindu astronomy, namely, vara the weekday, tithi, nakshatra the Moon’s asterism, yoga. The angular relationship between Sun and Moon and /carana-half of a tithi.