Orbital period Main Page | See live article | Alphabetical index Orbital period The orbital period is the time it takes a planet (or another object) to make one full orbit . There are two main kinds of orbital periods of objects orbiting the sun : The sidereal period is the time that it takes the object to make one full orbit around the sun, relative to the stars . This is considered to be an object's true orbital period. The synodic period is the time that it takes for the object to reappear at the same spot in the sky, relative to the sun , as observed from Earth . This is the time that elapses between two successive conjunctions with the sun and is the object's apparent orbital period. The synodic period differs from the sidereal period since Earth itself revolves around the sun. Relation between sidereal and synodic period Copernicus devised a mathematical formula to relate a planet's sidereal period with its synodic period. Using the abbreviations ASTRONOMY FINAL 3 Flashcards - Course Hero rock/planetoid- most in belt orbiting between mars and jupiter gravity force primarily responsible for the formation of a galaxy Size most obvious difference between the terrestrial and Jovian planets What two things effect gravity?

Mass and Distance the interactive movements of the moon and the earth relative to the sun Hipparchus gave us the modern magnitude system for measuring the brightness of a star Sun The largest object in the solar system. It dominates all aspects of the solar system. galactic halo material in a spherical distribution around our galaxy Galaxy Clumps of stars randomly scattered in space solar system system of nine planets, including Earth, and other objects that revolve around the Sun precession very slow earth movement, direction in which earth's axis points changes Diurnal having a daily cycle or occurring every day which comes closer to jupiter: earth or saturn earth a rapidly spinning neutron star that produces radio waves Open Clusters Have a loose, disorganized apperance and contain no more than a few thousand stars. the actual period of revolution relative to the stars, 27-1/3 days sidereal month Frequency Number of complete wave cycles that pass a point each second. Measured in waves (or cycles) per second.

Penumbra Outer lighter regions of the shadows of the Earth and Moon Brightness the amount of energy striking per unit area per unit time of some light sensitive surface (how it appears to us- affected by distance) can be measured directly waning getting smaller (as does the moon from full moon to new moon) Temperature The spectral type of a star is primarily a measure of its visible Moon phases describe the part of the moon that is ______ to us on earth orbits in clusters galaxies orbit each other faster because of dark matter Radiation Era Heliocentric Model of the Universe Sun in the center the visible surface of the sun lying just below the chromosphere. plate tectonics plates in constant motion with respect to each other Betelgeuse A red super-giant that has a magnitude of 0.5.

nuclear fusion the subatomic bonding of hydrogen to form helium at immense densities, resulting in the release of massive amounts of energy north pole faces the sun during the summer solstice spring tides tides that have the greastest tidal range due to the alignment of the earth-moon-sun system, due to gravitational pull greatest elongation farthest from the sun in our sky Richter scale measures the magnitude or strength of an earthquake coma The glowing head of a comet. (p. 464) Mars Atmosphere 3000 km long canyon system 8 km deep at points formed by deep crust fracture CONSTELLATION A group of stars that forms a pattern in the sky that looks like a familiar object. day the amount of time that it takes a body to rotate once on its axis Jupiter and Saturn are only jovians with high enough pressure for ____ and ____ to exist in liquid and metallic states. Hydrogen and Helium loops occur when the planets get near the sun-conjunction (mars, jupiter, and saturn) Cometary impact site Strange chains of craters have been seen on the Moon.

Once thought to be due to a line of volcanic vents ecliptic apparent path of the sun in the sky throughout the year the type of fusion occuring at the core of a red giant no fusion sunspots areas of gas on the sun's surface that are cooler than the gases around them, they appear as dark spots meteoriod large rock moving in an orbit in the soar system The chemical makeup of the central core of Earth is considered to be almost pure iron. Galaxies that have very little gas and dust are called How close is the closest star? 4 light years away annular eclipse A solar eclipse in which the solar photosphere appears around the edge of the moon in a bright ring, or annulus. The corona, chromosphere, and prominences cannot be seen. (p. 37) vernal equinox the time when the sun crosses the plane of the earth's equator, making night and day of approximately equal length all over the earth and occurring about March 21 Visible light from a distant star can be spread into a spectrum by using a glass prism or A diffraction grating. Spring and Neap Tides You get exceptionally low "neap" tides when the tidal forces from the Sun and the Moon interfere with each other.

Differential rotation the rotation of a star or planet at different speeds at its equator and poles absolute magnitude brightness a star would have if it was 32.6 light-years away (standardizes brightness) astronomer's obstacles in observing stars light pollution from cities, effects of twinkling from earth's atmosphere Sidereal period the time that it takes the object to make one full orbit around the Sun, relative to the stars. This is considered to be an object's true orbital period. What is the 1st stage in a star life cycle? main sequence Clocks on board a rapidly moving space ship will run slow. Celestial Sphere A sphere of the night sky used to used to locate objects in space with a grid system. Newton's Laws of Motion number one, an object at rest will stay at rest. and a object in motion will stay in motion unless something interferes within its path. (inertia) number two, the relationship between force, mass, and acceleration. number three, every action has a opposite and equal reaction.

how a star is born 1- hydrogen gas cloud shrinks due to gravity 2- pressure of gasses heat up cloud 3- fusion begins three principles of special relativity speed of light is same for all observers, there is no absolute frame of reference, space and time are not independent but are unified as spacetime Approximately where is it currently high tide on Earth? On the portion of Earth facing directly toward the Moon and on the portion of Earth facing directly away from the Moon stage 3 of a stars life is hydrogen and dust heat upfrom banging against each other,it creates nuclear reactions. this is the begining of a star Accurately measured light? when & how? Olaus Roemer in 1673 by observing the moons of Jupiter What are some problems that could harm scientisits from gathering information during an eclipse - some things they have to worry about??? Weather, Human Error, for the Hawaii one (clouds and volcanic dust) Which region of the early universe was most likely to become a galaxy? A region whose matter density was higher than average The Sun's apparent path among the stars is ____ South of the celestial equator part of the time and north of the celestial equator part of the time.

• Which of the following statements about lunar phases is true?  It is possible to have two full Moons during January, but not during February how can you see what a star is made up of? only certain wavelengths get absorbed, so if you look through a prism, you can see which wavelengths show through, and therefore which elements the star is composed of. each element has a unique spectrum, like a fingerprint planetoid the most explosive eruptions on the sun solar eclipse occurs when the moon phases between eath and the sun, blocking the sunlight going to earth. (can only happen during a new moon phase) Full Moon sunlit side faces Earth, entire lit side visible About how many hours of daylight would there be on June 21st in Australia? 9hrs. a small solid body that enters a planet's atmosphere Autumnal Equinox Sept 23 Point when the ecliptic crosses the equator with the sun moving south Oort cloud A spherical region of comets that surrounds the solar system.

What is Mercury's largest impact Caloris Basin 800miles across the movement of one object follows as it revolves around another object angular resolution Is the minimum angular separation that the telescope can distinguish gravitational force the force of attraction between all masses in the universe True or False: Earth rotates from west to east, or counterclockwise. True A planet moving in a constant direction (east) Chaldeans Believed that an eclipse was a display of the Moon's anger. Doppler effect The change in the wavelength of radiation due to relative radial motion of source and observer. (p. 115) galileo first person to use a telescope to examine heavens Spiral galaxy a galaxy where the arms form a pinwheel shape Groups of stars which seem to form a picture are called constellations aphelion the point in its orbit where a planet or other solar system body is farthest from the sun Yuri Gagarin Soviet cosmonaut who in 1961 was the first person to travel in space inferior conjunction when an inferior planet and Earth (or a superior planet) are lined up on the same side of the sun Open Is the local group an open or closed cluster?

apparent magnitude of a star at 10pc from earth absolute magnitude summer solstice the point on the ecliptic where the sun is at its northernmost point above the celestial equator nuclear bulge a distribution of stars in the shape of a flattened sphere that surrounds the nucleus of a spiral galaxy like the Milky Way Gas Giant any of the four outermost planets in the solar system Solstice either of the two times of the year when the sun is at its greatest distance from the celestial equator Some of the following features of the solar system overlap. But which objects, on average, are the farthest from the Sun? Oort-cloud objects the band in a narrow zone around the ecliptic in which the planets move tide the rise and fall of the level of water in the ocean What is aperigee? when the moon is furthest from earth The moons of Mars are believed to be captured by asteroids tells us how fast their peaks travel across the pond Planetary Nebula A shell of gas ejected by a low-mass star late in its evolutionary lifetime. appear as a glowing gas ring around a central star. radiation zone A region of very tightly packed gas in the sun's interior where energy is transferred mainly in the form of light.

Conservation of energy energy cannot appear out of nowhere or disappear into nothingness What is the smallest in size part of the spiral galaxy? The bulge Type of rocks: basalts, anorthosites, breccia, and regolith Density A ratio of the mass of an object to its volume what is the average live span of a star 10 billion years ★ Do black holes suck? Black holes do NOT suck. That assumption is bad astronomy. It is just an object with mass. And as long as you stay at least 1000 km away from the black hole, you could safely orbit the black hole. what are four main periods of western astronomy in order?

prehistoric, classical, renaissance, modern how long dose it take the sun to orbit arround the milky way 225million years The cosmic background radiation comes from a time in the evolution of the universe when electrons began to recombine with nuclei to form atoms electromagnetic wave: what it is, electron spectral lines -transitions from high to low orbits causes center of electron cloud to oscillate about the nucleus -causes electromagnetic wave (light wave) to be emitted-photon that carries away energy difference btw two orbits - when waves pass by other charges those charges will move also -each element has own set of states for its electrons, each element has a set of "spectral lines" or wavelengths that it can emit or absorb, can be used to ID elements in stars from stars light what is th diameter and depth of copernicus 56 mi and 2 mi D. Cepheid variables in its spiral arms. For finding the distance to M31, Hubble relied upon A. RR Lyrae stars in its globular clusters. B. Type I supernova in its core. C. Type II supernova in its spiral arms. D. Cepheid variables in its spiral arms. E.

planetary nebulae near its core. Mars' atmosphere is 100 times less dense than Earths', but yet dense enough to create what? enough to support a weather system that includes clouds and winds Jupiter and the other Jovian planets are noticeably oblate because C. they are mostly fluid bodies that are spinning rapidly Jupiter and the other Jovian planets are noticeably oblate because A. they all have strong magnetic fields that deform their shape B. their powerful gravity acts more strongly on the poles than at the equator C. they are mostly fluid bodies that are spinning rapidly D. they are tidally distorted by the pulls of their satellite systems E. all of the above are correct Potential energy stored in mass may be converted into... radiant energy, for example this is how a star shines. The X-ray emission from a neutron star in a binary system comes mainly from: Heated material in an accretion disk around the neutron star Why do we need Einsteins Theory of Relativity to understand black holes? a)limits the speed of light. b) the fact that light is affected by gravity What does the universe look like from Earth?

With the naked eye, we can see more than 2,000 stars as well as the Milky Way. Constellations stage of large star dying irregular no shape, near collisions or collisions made them, our satellite galaxies are the Magellan clouds and are irregular Absolute zero the coldest possible temperature, 0K what will the sun be next red giant any natural or artificial object that revolves around another object latitude angular distance from the horizon to the north celestial pole Satallite any object, natural or man-made that revolves around another object a scientific model must make a testable prediction true the outer later of the sun's atmosphere accretion This process of assembly from small parts is called...

Irregular Galaxies galaxies that have an irregular shape Supernova An enormous explosion of a supergiant star when it runs out of fuel evidence for big bang Irregular rocky bodies that orbit the sun Enceladus - Saturn moon, second closest to planet - made of pure water ice - surface reflects almost 100% of sunlight that hits it - nearly crater free, has cracks and grooves - its orbit is produced by Dione's (moon) gravity - tidal flexing by Saturn heats interior causing active ice volcanoes the unit of work is a newton-meter, otherwise known as a ______ joule Dying star, cooling, lower left of H-R, collapsed to Earth's mass size TRUE or FALSE; SETI does not produce any scientific data FALSE A tide with the least difference between low and high tides.

Astronaut a person trained to travel in a spacecraft Neptune planet that is blue due to methane gas light-year the distance traversed by light in one mean solar year observatory A building with an automated roof that opens to expose the night sky to its one or more telescopes Black Hole Massive, and you cannot see the light Thomas Young Discovered that light works as a particle (Double Slit Experiment) astronomy the study of the moon, stars, and other objects in space Random walk in the radiation zone, photons bounce around randomly trying to escape super nova Brilliant burst of light that follows the collapse of the iron core and explosion of a massive star craters the large round pits that mark the moon's surface heliocentric The theory where Earth and the other planets revolve around the sun. This theory is being used today.

distance of moon and earth at perigree 221,000 miles the distance that light travels in a vacuum in 1 year Galileo Galilei created the telescope, found 4 of the largest moons of Jupiter-Europa, Gannymede, Callisto, Io) scientific theory an idea about the natural world that is subject to verification and refinement Astronomical Unit the average distance from the Earth to the Sun James Webb Space Telescope will give scienctists with the oppertunity to study many things Low Mass Stars 0.1 solar masses- last trillions of years. Lunar Eclipse the blocking of sunlight to the moon that occurs when Earth is directly in between the moon and the sun Kirchoff's third law A dark line or absorption line spectrum is seen when a source of a continuous spectrum is viewed behind a cool gas under pressure. the sun is directly overhead the tropic of what on june 21? tropic of cancer force of gravity the strenght of the _________ ___ ___________ between 2 objects depends on the masses of the objects and the distance between the, Scale of Astronomy 1.) Astronomy is the science of the entire study of the entire universe.

Regular fish = on meter and there are 40 scales of magnitude in the unverise. Stars are the size of a billion fishes, galaxies are 100 billion times bigger than stars and galaxy clusters are 1000 times bigger than that. Humans are in the middle. synodic month the cycle of the moon through all of its phases Geocentric model The idea that Earth is at the center of the solar system. Sometimes referred to as the Ptolemaic model (Greek scientist named Ptolemy). equinox the 2 days of the year on which either hemisphere is tilted toward or away from the sun. The coolest stars are dull _____, and the hottest stars are _____ red and blue Which planet has a Red Spot that is a storm? Jupiter greater the distance of galaxy away from earth the greater the recessional velocity and so what is greater the observed red shift A measure of the size of the event horizon of a black hole.

Red Giant A large, reddish star late in its life cycle stronger magnetic fields cause sunspots are in the photosphere Kepler's 1st Law the orbit of each planet is an ellipse with the Sun at one focus The End of Fusion When the core becomes iron, the core cannot generate any more energy thus is collapses. Triangulation to Calculate Stellar Distances 1.) D=1/p;Distance in parsecs is the reciprocal of its parallax in arcseconds 2.) 1 arc second=1/3600th of 1° 2.)parsec2.) As earth moves from one side of its orbit to the other, it creates a 2 AU baseline 3.)1 arcsecond means star is one pc away--no stars are this close but the sun 4.)The smaller the parallax the larger the distance 5.) 0.1 arcsecond would mean the star is 10 pc away What is considered the "direct motion" early planetary observers saw? Normal eastward movement across the sky. Similar properties of Uranus and Neptune Blue-green color due to methane.

The temps are too cold for the chemicals that give orange color to Jupiter and Saturn.` What states that every object in the universe attracts every other object? Newton's law of universal gravitation First Law of thermal radiation Each square meter of a hotter objects surface emits more light at wavelengths . Stefen-Boltzmann's theory metallic hydrogen swirling in its interior What is the source of Jupiter's large magnetic field? Death of a low mass star dies as a carbon oxygen. a star becomes a red giant by running out of hydrogen What is thought to cause Io's volcanism? C. tidal stresses from both Jupiter and Europa What is thought to cause Io's volcanism? A. Jupiter's magnetosphere Astronomy in Ancient India - Crystalinks Astronomy in Ancient India Tool for keeping track of the constellations Sun Dial Jantar Mantar in Jaipur The Jantar Mantar in Jaipur is actually one of six major observatories built by the Maharajah. The one in Jaipur not only follows the movements of the sun and the moon to help determine auspicious dates for events, it also helps map out the position of the stars in the sky.

Although no telescopic instruments were available at the time, the precise observation of the stars was greatly facilitated by observatories such as Jantar Mantar. It should also be noted that such an endeavor (six major observatories, a staff of full-time priests etc.) did not come to a small cost. This is further evidence of the importance placed on the study of the stars. As mentioned earlier, both astrology and astronomy were reasons to build these structures. Unlike the "west", astrology did not become as pseudo-science as astronomy became more factual and experimental. Instead, both were considered an integral part of society. Ancient India's contributions in the field of astronomy are well known and well documented. The earliest references to astronomy are found in the Rig Veda, which are dated 2000 BC. During next 2500 years, by 500 AD, ancient Indian astronomy has emerged as an important part of Indian studies and its affect is also seen in several treatises of that period. In some instances, astronomical principles were borrowed to explain matters, pertaining to astrology, like casting of a horoscope.

Apart from this linkage of astronomy with astrology in ancient India, science of astronomy continued to develop independently, and culminated into original findings, like: The calculation of occurrences of eclipses Determination of Earth's circumference Theorizing about the theory of gravitation Determining that sun was a star and determination of number of planets under our solar system There are astronomical references of chronological significance in the Vedas. Some Vedic notices mark the beginning of the year and that of the vernal equinox in Orion. This was the case around 4500 BC. Fire altars, with astronomical basis, have been found in the third millennium cities of India. The texts that describe their designs are conservatively dated to the first millennium BC, but their contents appear to be much older. Yajnavalkya (perhaps 1800 BC) advanced a 95-year cycle to synchronize the motions of the sun and the moon.A text on Vedic astronomy that has been dated to 1350 BC, was written by Lagadha.

In 500 AD, Aryabhata presented a mathematical system that took the earth to spin on its axis and considered the motions of the planets with respect to the sun (in other words it was heliocentric). His book, the Aryabhatya, presented astronomical and mathematical theories in which the Earth was taken to be spinning on its axis and the periods of the planets were given with respect to the sun. In this book, the day was reckoned from one sunrise to the next, whereas in his Aryabhata-siddhanta he took the day from one midnight to another. There was also difference in some astronomical parameters. Aryabhata wrote that 1,582,237,500 rotations of the Earth equal 57,753,336 lunar orbits.

This is an extremely accurate ratio of a fundamental astronomical ratio (1,582,237,500/57,753,336 = 27.3964693572), and is perhaps the oldest astronomical constant calculated to such accuracy.Brahmagupta (598-668) was the head of the astronomical observatory at Ujjain and during his tenure there wrote a text on astronomy, the Brahmasphutasiddhanta in 628. Bhaskara (1114-1185) was the head of the astronomical observatory at Ujjain, continuing the mathematical tradition of Brahmagupta. He wrote the Siddhantasiromani which consists of two parts: Goladhyaya (sphere) and Grahaganita (mathematics of the planets). The other important names of historical astronomers from India are Madhava and Nilakantha. On April 19, 1975, India sent into orbit its first satellite Aryabhatta. In 1984, Rakesh Sharma became the first Indian to go to outer space.

Kalpana Chawla, later a US citizen, became the first woman of Indian origin to go to space. Early cultures identifed celestial objects with gods and spirits. They related these objects (and their movements) to phenomena such as rain, drought, seasons, and tides. It is generally believed that the first "professional" astronomers were priests (Magi), and that their understanding of the "heavens" was seen as "divine", hence astronomy's ancient connection to what is now called astrology. Ancient constructions with astronomical alineations (such as Stonehenge) probably fulfilled both astronomical and religious functions. Calendars of the world have usually been set by the Sun and Moon (measuring the day, month and year), and were of importance to agricultural societies, in which the harvest depended on planting at the correct time of year. The most common modern calendar is based on the Roman calendar, which divided the year into twelve months of alternating thirty and thirty-one days apiece. In 46 BC Julius Caesar instigated calendar reform and created the leap year. There are astronomical references of chronological significance in the Vedas.

Some Vedic notices mark the beginning of the year and that of the vernal equinox in Orion - this was the case around 4500 BC. Fire altars, with astronomical basis, have been found in the third millennium cities of India. The texts that describe their designs are conservatively dated to the first millennium BC, but their contents appear to be much older. Yajnavalkya (perhaps 1800 BC) described the motions of the Sun and the Moon in his book Shatapatha Brahmana, and also advanced a 95-year cycle to synchronize the motions of the Sun and the Moon. The Vedanga Jyotisha, a text on Vedic astrology that has been dated to 1350 BC, was written by Lagadha. It describes rules for tracking the motions of the Sun and the Moon, and also develops the use of geometry and trigonometry for astronomical uses. Aryabhata In Indian languages, the science of astronomy is called Khagola-shastra. The word Khagola perhaps is derived from the famous astronomical observatory at the University of Nalanda which was called Khagola.

It was at Khagola that the famous 5th century Indian Astronomer Aryabhatta studied and extended the subject. Around 500 BCE, Aryabhata presented a mathematical system that took the Earth to spin on its axis and considered the motions of the planets with respect to the Sun. He also made an accurate approximation of the Earth's circumference and diameter, and also discovered how the lunar eclipse and solar eclipse happen for the first time. He gives the radius of the planetary orbits in terms of the radius of the Earth/Sun orbit as essentially their periods of rotation around the Sun. He was also the earliest to discover that the orbits of the planets around the Sun are ellipses. He is the first known astronomer on that continent to have used a continuous system of counting solar days. His book, The Aryabhatiya, published in 498 AD described numerical and geometric rules for eclipse calculations. Indian astronomy at that time was taking much of its lead from cyclic Hindu cosmology in which nature operated in cycles, setting the stage for searching for numerical patterns in the expected time frames for eclipses. Aryabhatta is said to have been born in 476 A.D.

at a town called Ashmaka in today's Indian state of Kerala. When he was still a young boy he had been sent to the University of Nalanda to study astronomy. He made significant contributions to the field of astronomy. He also propounded the Heliocentric theory of gravitation, thus predating Copernicus by almost one thousand years. Aryabhatta's Magnum Opus, the Aryabhattiya was translated into Latin in the 13th century. Through this translation, European mathematicians got to know methods for calculating the areas of triangles, volumes of spheres as well as square and cube root. Aryabhatta's ideas about eclipses and the sun being the source of moonlight may not have caused much of an impression on European astronomers as by then they had come to know of these facts through the observations of Copernicus and Galileo. But considering that Aryabhatta discovered these facts 1,500 years ago, and 1,000 years before Copernicus and Galileo makes him a pioneer in this area too.

Aryabhatta's methods of astronomical calculations expounded in his Aryabhatta-Siddhatha were reliable for practical purposes of fixing the Panchanga (Hindu calendar). Thus in ancient India, eclipses were also forecast and their true nature was perceived at least by the astronomers. The lack of a telescope hindered further advancement of ancient Indian astronomy. Though it should be admitted that with their unaided observations with crude instruments, the astronomers in ancient India were able to arrive at near perfect measurement of astronomical movements and predict eclipses. Indian astronomers also propounded the theory that the Earth was a sphere. Aryabhatta was the first one to have propounded this theory in the 5th century. Another Indian astronomer and mathematician, Brahmagupta estimated in the 7th century that the circumference of the earth was 5000 yojanas. A yojana is around 7.2 kms. Calculating on this basis we see that the estimate of 36,000 kms as the Earth's circumference comes quite close to the actual circumference known today.

There is an old Sanskrit Sloka (couplet) which is as follows: "Sarva Dishanaam, Suryaha, Suryaha, Suryaha." This couplet means that there are suns in all directions. This couplet which describes the night sky as full of suns, indicates that in ancient times Indian astronomers had arrived at the important discovery that the stars visible at night are similar to the Sun visible during day time. In other words, it was recognized that the sun is also a star, though the nearest one. This understanding is demonstrated in another Sloka which says that when one sun sinks below the horizon, a thousand suns take its place. This apart, many Indian astronomers had formulated ideas about gravity and gravitation. Brahmagupta, in the 7th century had said about gravity that "Bodies fall towards the Earth as it is in the nature of the Earth to attract bodies, just as it is in the nature of water to flow". About a hundred years before Brahmagupta, another astronomer, Varahamihira had claimed for the first time perhaps that there should be a force which might be keeping bodies stuck to the Earth, and also keeping heavenly bodies in their determined places.

Thus the concept of the existence of some attractive force that governs the falling of objects to the Earth and their remaining stationary after having once fallen; as also determining the positions which heavenly bodies occupy, was recognized. It was also recognized that this force is attractive force. The Sanskrit term for gravity is Gurutvakarshan which is an amalgam of Guru-tva-akarshan. Akarshan means to be attracted, thus the fact that the character of this force was of attraction was also recognized. This apart, it seems that the function of attracting heavenly bodies was attributed to the sun. The term Gurutvaakarshan can be interpreted to mean, 'to the attracted by the Master". The sun was recognized by all ancient people to be the source of light and warmth. Among the Aryans the sun was defiled. The sun (Surya) was one of the chief deities in the Vedas. He was recognized as the source of light (Dinkara), source of warmth (Bhaskara). In the Vedas he is also referred to as the source of all life, the center of creation and the center of the spheres.

The last statement is suggestive of the sun being recognized as the centre of the universe (solar system). The idea that the sun was looked upon as the power that attracts heavenly bodies is supported by the virile terms like Raghupati and Aditya used in referring to the sun. While the male gender is applied to refer to the sun, the Earth (Prithivi, Bhoomi, etc.) is generally referred to as a female. The literal meaning of the term Gurutvakarshan also supports the recognition of the heliocentric theory, as the term Guru corresponds with the male gender, hence it could not have referred to the earth which was always referred to as a female. Many ancient Indian astronomers have also referred to the concept of heliocentrism. Aryabhata has suggested it in his treatise Aryabhattiya. Bhaskaracharya has also made references to it in his Magnum Opus Siddhanta-Shiromani. But it has to be conceded that the heliocentric theory of gravitation was also developed in ancient times (i.e. around 500 B.C.) by Greek astronomers.

What supports the contention that it could have existed in India before the Greek astronomers developed it, is that in Vedic literature the Sun is referred to as the 'center of spheres' along with the term Guru-tva-akarshan which seemingly refers to the sun. The Vedas are dated around 3000 B.C. to 1000 B.C. Thus the heliocentric idea could have existed in a rudimentary form in the days of the Rig Veda and was refined further by astronomers of a later age. Indian Astronomers like Aryabhatta and Varahamihira who lived between 476 and 587 A.D. made close approaches to the concept of Heliocentrism. In the Surya-Siddhanta, an astronomical text dated around 400 A.D., the following appellations have been given to the sun. "He is denominated the golden wombed (Hiranyagarbha), the blessed; as being the generator". He is also referred to as "The supreme source of light (Jyoti) upon the border of darkness - he revolves. bringing beings into being, the creator of creatures".

The Surya-Siddhanta also says that "Bestowing upon him the scriptures (Vedas) as gifts and establishing him within the egg as grandfather of all worlds, he himself then revolves causing existence". Thus we can see that what ancient Indian astronomers say comes close to the heliocentric theory of gravitation, which was a thousand years later articulated by Copernicus and Galileo inviting severe reactions from the clergy in Rome. Brahmagupta (598-668) was the head of the astronomical observatory at Ujjain and during his tenure there wrote a text on astronomy, the Brahmasphutasiddhanta in 628. He was the earliest to use algebra to solve astronomical problems. He also develops methods for calculations of the motions and places of various planets, their rising and setting, conjunctions, and the calculation of eclipses of the Sun and the Moon. Bhaskara (1114-1185) was the head of the astronomical observatory at Ujjain, continuing the mathematical tradition of Brahmagupta.

He wrote the Siddhantasiromani which consists of two parts: Goladhyaya (sphere) and Grahaganita (mathematics of the planets). He also calculated the time taken for the Earth to orbit the sun to 9 decimal places. Other important astronomers from India include Madhava, Nilakantha Somayaji and Jyeshtadeva, who were members of the Kerala school of astronomy and mathematics from the 14th century to the 16th century. They were responsible for founding calculus and modern mathematical analysis, along with a number of other developments. Hindu Astronomy The Hindu Astronomy is one of the ancient astronomical systems of the world. It is sometimes considered a controversial subject, because some scholars argue that it shows a higher antiquity of the Vedic culture as generally assumed. The astronomy and the astrology of India are based upon sidereal calculations. The sidereal astronomy is based upon the stars and the sidereal period is the time that it takes the object to make one full orbit around the Sun, relative to the stars.

This is considered to be an object's true orbital period.In Hindu Astronomy, the vernal equinox (the First Point of Aries) is often calculated at 23� from 0� Aries (1950 CE), i.e. about 7� Pisces (Frawley 1991:148). The constellation that marks this vernal equinox is the Uttarabhadra. In the time of the Puranas, the vernal equinox was marked by the Ashwini constellation (beginning of Aries), which gives a date of about 300-500 CE. The Vishnu Purana (2.8.63) states that the equinoxes occur when the Sun enters Aries and Libra, and that when the sun enters Capricorn, his northern course (from winter to summer solstice) commences, and the southern course when he enters Cancer. In the Suryasiddhanta, the rate of precession at 54" (it actually is 50.3"), which is much more accurate than the number calculated by the Greeks (Frawley 1991:148).

The Hindus use a system of 27 or 28 Nakshatras (lunar constellations) to calculate a month. Each month can be divided into 30 lunar tithis (days). There are usually 360 or 366 days in a year. The Hindu astronomer Varahamihira, Garga (quoted by Somakara), the Mahabharata and the Vedanga Jyothish refer to the constellation Dhanishta (Shravishta) and thus to an ancient calendar that would have been used in 1280 BCE (see Frawley 1991: 152 ff.). The Kaushiktaki Brahmana and possibly the Atharva Veda refer to a similar calendar (Frawley 1991). The Atharva Veda, the Tandya Mahabrahmana and Laughakshi (quoted by Somakara) may show knowledge of an earlier calendar, but still in the Magha constellation (Frawley 1991). In still earlier Hindu calendars, the vernal equinox was in the Krittika constellation.

There are additionally references to the summer solstice in the Magha constellation. This could indicate a date around 2000 BCE. The Atharva Veda, the Taittiriya Brahmana, the Shatapahta Brahmana, the Maitriyani Upanishad and the Vishnu Purana show such a constellation in the Krittika (Frawley 1991). In the working out of horoscopes (called Janmakundali), the position of the Navagrahas, nine planets plus Rahu and Ketu (mythical demons, evil forces) was considered. The Janmakundali was a complex mixture of science and dogma. But the concept was born out of astronomical observations and perception based on astronomical phenomenon. In ancient times personalities like Aryabhatta and Varahamihira were associated with Indian astronomy. It would be surprising for us to know today that this science had advanced to such an extent in ancient India that ancient Indian astronomers had recognized that stars are same as the sun, that the sun is center of the universe (solar system) and that the circumference of the Earth is 5,000 Yojanas.

One Yojana being 7.2 kms., the ancient Indian estimates came close to the actual figure. Copy URL Embed / Widget The orbital period is the time taken for a given object to make one complete orbit around another object. When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars . There are several kinds of orbital periods for objects around the Sun , or other celestial objects. Varieties of orbital periods Orbital period is an approximated term, and can mean any of several periods , each of which is used in the fields of astronomy and astrophysics : The sidereal period is the temporal cycle that it takes an object to make a full orbit, relative to the stars . This is the orbital period in an inertial (non-rotating) frame of reference . The synodic period is the temporal interval that it takes for an object to reappear at the same point in relation to two or more other objects, e.g. when the Moon relative to the Sun as observed from Earth returns to the same illumination phase. The synodic period is the time that elapses between two successive conjunctions with the Sun–Earth line in the same linear order.

The synodic period differs from the sidereal period due to the Earth's orbiting around the Sun. The draconitic period, or draconic period, is the time that elapses between two passages of the object through its ascending node , the point of its orbit where it crosses the ecliptic from the southern to the northern hemisphere. This period differs from the sidereal period because both the orbital plane of the object and the plane of the ecliptic precess with respect to the fixed stars, so their intersection, the line of nodes , also precesses with respect to the fixed stars. Although the plane of the ecliptic is often held fixed at the position it occupied at a specific epoch , the orbital plane of the object still precesses causing the draconitic period to differ from the sidereal period. The anomalistic period is the time that elapses between two passages of an object at its periapsis (in the case of the planets in the solar system , called the perihelion ), the point of its closest approach to the attracting body. It differs from the sidereal period because the object's semimajor axis typically advances slowly.

Also, the Earth's tropical period (or simply its "year") is the time that elapses between two alignments of its axis of rotation with the Sun, also viewed as two passages of the object at right ascension zero. One Earth year has a slightly shorter interval than the solar orbit (sidereal period) because the inclined axis and equatorial plane slowly precesses (rotates in sidereal terms), realigning before orbit completes with an interval equal to the inverse of the precession cycle (about 25,770 years). Small body orbiting a central body According to Kepler's Third Law , the orbital period T (in seconds) of two bodies orbiting each other in a circular or elliptic orbit is: T {displaystyle a={sqrt[{3}]{frac {GMT^{2}}{4pi ^{2}}}}} where: G is the gravitational constant , M is the mass of the more massive body, T is the orbital period in seconds. For instance, for completing an orbit every 24 hours around a mass of 100 kg , a small body has to orbit at a distance of 1.08 meters from its center of mass .

Orbital period as a function of central body's density When a very small body is in a circular orbit barely above the surface of a sphere of any radius and mean density ρ (in kg/m3), the above equation simplifies to (since M = Vρ = 4/3πa3ρ): T ρ {displaystyle T={sqrt {frac {3pi }{Grho }}}} So, for the Earth as the central body (or any other spherically symmetric body with the same mean density, about 5,515 kg/m3) [2] we get: T = 1.41 hours and for a body made of water (ρ ≈ 1,000 kg/m3) [3] T = 3.30 hours Thus, as an alternative for using a very small number like G, the strength of universal gravity can be described using some reference material, like water: the orbital period for an orbit just above the surface of a spherical body of water is 3 hours and 18 minutes.

Conversely, this can be used as a kind of "universal" unit of time if we have a unit of mass, a unit of length and a unit of density. Two bodies orbiting each other In celestial mechanics , when both orbiting bodies' masses have to be taken into account, the orbital period T can be calculated as follows: T {displaystyle T=2pi {sqrt {frac {a^{3}}{Gleft(M_{1}+M_{2}right)}}}} where: a is the sum of the semi-major axes of the ellipses in which the centers of the bodies move, or equivalently, the semi-major axis of the ellipse in which one body moves, in the frame of reference with the other body at the origin (which is equal to their constant separation for circular orbits), M1 + M2 is the sum of the masses of the two bodies, G is the gravitational constant . Note that the orbital period is independent of size: for a scale model it would be the same, when densities are the same (see also Orbit#Scaling in gravity ). In a parabolic or hyperbolic trajectory, the motion is not periodic, and the duration of the full trajectory is infinite.

Synodic period When two bodies orbit a third body in different orbits, and thus different orbital periods, their respective, synodic period can be found. If the orbital periods of the two bodies around the third are called P1 and P2, so that P1 < P2, their synodic period is given by 1 Kepler's Laws and Newton's Laws Kepler's Laws and Newton's Laws Kepler's Laws Johannes Kepler (1571-1630) developed a quantitative description of the motions of the planets in the solar system. The description that he produced is expressed in three ``laws''. Kepler's First Law: The orbit of a planet about the Sun is an ellipse with the Sun at one focus. Figure 1 shows a picture of an ellipse. It is constructed by specifying two focus points, F1 and F2, of the ellipse. All points on the ellipse, such as P in Figure 1, have the property that the sum of the distance between P and F1 and the distance between P and F2 is a constant. The dimension of an ellipse is often described by giving its major axis and minor axis.

In descriptions of orbits in the solar system, however, it is more common to use the semi-major axis to describe the size of the orbit, and the eccentricity of the ellipse to describe its shape. The eccentricity is given by the ratio of the distance between the two focus points to the length of the major axis of the ellipse. The periapsis, or the shortest distance between the orbiting body and the central mass, is determined by the product of the semi-major axis and the complement of the eccentriciy (1 - e): if the body is orbiting the sun, this is the perihelion, symbolized by q): q = a (1 - e). A circle is a special case of an ellipse, with an eccentricity of 0, or so that q = a. Kepler's Second Law: A line joining a planet and the Sun sweeps out equal areas in equal intervals of time. Figure 2 illustrates Kepler's Second Law. Consider the line between the Sun and point A on the elliptical orbit. After a certain amount of time, the planet will have moved along the orbit to point B, and the line between the Sun and the planet will have swept over the cross hatched area in the figure.

Kepler's Second Law states that for any two positions of the planet along the orbit that are separated by the same amount of time, the area swept out in this manner will be the same. Thus, suppose that it takes the planet the same amount of time to go between positions C and D as it did for the planet to go between positions A and B. Kepler's Second Law then tells us that the second cross hatched area between C, D, and the Sun will be the same as the cross hatched area between A, B, and the Sun. Kepler's Second Law is valuable because it gives a quantitative statement about how fast the object will be moving at any point in its orbit. Note that when the planet is closest to the Sun, at perihelion, Kepler's Second Law says that it will be moving the fastest. When the planet is most distant from the Sun, at aphelion, it will be moving the slowest. Kepler's Third Law: The squares of the sidereal periods of the planets are proportional to the cubes of their semimajor axes. We have defined the semimajor axis of the orbit above, in our discussion of Kepler's First Law.

The sidereal period of a planet's orbit is the time that it takes a planet to complete one orbit around the Sun. Kepler discovered a quantitative relationship between these two properties of the orbit. If P is the period of the orbit, measured in years, and a is the semimajor axis of the orbit, measured in Astronomical Units, then P2 = a3 Newton's Laws Kepler's Laws are wonderful as a description of the motions of the planets. However, they provide no explanation of why the planets move in this way. Moreover, Kepler's Third Law only works for planets around the Sun and does not apply to the Moon's orbit around the Earth or the moons of Jupiter. Isaac Newton (1642-1727) provided a more general explanation of the motions of the planets through the development of Newton's Laws of Motion and Newton's Universal Law of Gravitation. Newton's Laws of Motion One way to describe the motion of an object it to specify its position at different times. Consider the car in Figure 3. We can tell where it is at different times as it travels down a road. It starts at milepost 0.

One minute later it is between mileposts 1 and 2 at a distance of about 1.3 miles from the start. Two minutes later, the car has gotten to a distance of about 3.3 miles from the start. In general, we could specify a unique position for the car at any time. For example, we might have written down where the car was at a time 1.5 minutes after the start, and even if we hadn't, we're pretty sure that the car was, in fact, somewhere. Mathematicians call this kind of a relationship a function. When we say that the position of the car is a function of time, it just means that there is a unique location for the car for any time. For a planetary orbit, we can describe the orbit in the same way, by providing the position of the planet along the orbit for all times. Another useful property for describing motion is the velocity of the object. Velocity is defined to be the change of position with change in time. Thus, for our car moving along the road, we can find the velocity by dividing the distance travelled by the time it takes to travel that distance.

In our example, during the first minute, the car travels 1.3 miles along the road. Thus, the car's velocity would be 1.3 miles per minute (or about 78 miles per hour!) on the average during that first minute. It is important to note that physicists are very particular about the definition of velocity, and when we state a velocity we always make a statement about the direction of the motion. In our one dimensional case, this corresponds to my statement that the the car moved along the road. In general, if we were looking at a road map, we might say that the velocity was 1.3 miles per minute towards the East -- if the street ran towards the East. Velocity always is specified by both a value and a direction. A final useful property for describing motion is the acceleration of the object. Just as the velocity describes the rate of change in the position of the object, the acceleration describes the rate of change of the velocity. In our example, the car moved farther during its second minute of travel than it did during its first minute.

The average velocity during the second minute would be 2 miles per minute (120 miles per hour), since the car covered two miles from 1.3 to 3.3 during the one-minute time interval from 1 minute after the start to 2 minutes after the start. The velocity increased a lot (0.7 miles per minute) between the first minute of travel and the second minute of travel, and we describe this change by the acceleration. In this case, the car's velocity increased by 0.7 miles per minute in a time interval of one minute. Thus, we'd say that the average acceleration of the car during this time was 0.7 miles per minute PER MINUTE --- acceleration is the rate of change of the velocity. Like velocity, acceleration has both a value and a direction implied. In our example, the direction was ``along the road'', but in a more general case, the acceleration is not necessarily in the same direction as the velocity. An especially good example for understanding the solar system is the case of uniform circular motion. Lets consider the case below of a car moving around a circle.

The speed is constant in this motion, but the direction is changing continuously -- note the arrows showing the direction of motion in the figure -- so there must be an acceleration here. The acceleration in this special case of circular motion is called the centripetal acceleration. It is always in the direction of the center of the circle, as indicated in the figure, and it has a value, A, of A = v2 / R where v is the speed of the object along its circular path, and R is the radius of the circle. Newton's First Law of Motion: A body remains at rest or moves in a straight line at a constant speed unless it is acted upon by an outside force. If you look back at the definition of acceleration, you will see that: (1) a body at rest is not accelerating; and (2) a body moving in a straight line at a constant speed is not accelerating either. Thus, the first law of Newton says that objects do not accelerate unless they are acted upon by an outside force.

Newton's Second Law of Motion: If a force, F, works on a body of mass M, then the acceleration, A, is given by F = M A The first law said that if there is acceleration, then there is a force. Newton's second law gives a quantitative relationship between the force and the acceleration that is observed. The relationship depends on a new property of the object, its mass. The mass is simply a measure of the amount of material in the object; mass is conventionally measured in grams or kilograms. Note that the second law implies that, for a given force, a less massive body will accelerate more than a more massive body. This is consistent with the world you are familiar with. Shove your kid brother, he might move a long way; shove Shaquille O'Neal with the same force and he won't move that far... Newton's Third Law of Motion: If one body exerts a force on a second body, the second body exerts an equal and opposite force on the first. This law is sometimes called the ``Action-Reaction'' law. Consider what happens if you are in one row boat and you pull on a line attached to a second row boat.

When you pull the line, you exert a force on the second boat. But, by the third law, the other boat exerts an equal and opposite force back on you. Thus, if the second row boat has a large shipment of bricks in it so it is very heavy, your lighter boat may do all the moving even though you are doing all the pulling. Implications for the Planets The elliptical orbits of the planets have such small eccentricities that, to a very good approximation, we can think of them as circles. (Only very precise measurements, like those available to Kepler, are able to detect the difference.) This means that we can use the idea of uniform circular motion to analyze planetary motion. In that section, we revealed that a body in uniform circular motion was constantly accelerating towards the center of its circular track. Thus, according to Newton's first law of motion, there must be a force acting on the planet that is always directed toward the center of the orbit -- that is toward the Sun! Newton's second law of motion allows us to state what the magnitude of that force must be. The required force is just the mass of the Earth times its acceleration.

We know that the acceleration of an object moving in uniform circular motion is A = V2/R. Thus, we can calculate the force that is required to keep the Earth on its circular path and compare it to physical theories about what that force might be. This is what Newton later did, although he did it first for the Moon rather than the Earth, to learn about the force of Gravity. Finally, let us consider an implication of the ``action-reaction'' law. If there is a force that attracts the Earth toward the Sun, then there must be an equal and opposite force attracting the Sun towards the Earth. Why, then, doesn't the Sun move? The answer is that it does move, but by a very small amount since the mass of the Sun is about half a million times that of the Earth. Thus, when subjected to the equal and opposite force required by the third law, it accelerates about half a million times less than the Earth as well. For this reason, to a very good approximation, we can treat the Sun as stationary in our studies of planetary motion.

Newton's Universal Law of Gravitation By now you must be wondering: ``What is the Force that keeps the Earth going around the Sun?'' Newton's great discovery was the force of {\sl gravity}, which is an attractive force that occurs between two masses. The Universal Law of Gravitation is usually stated as an equation: Fgravity = G M1 M2 / r2 where Fgravity is the attractive gravitational force between two objects of mass M1 and M2 separated by a distance r. The constant G in the equation is called the Universal Constant of Gravitation. The value of G is: G = 6.67 X 10-11 meters3 kilograms-1 seconds-2 Newton's great step was developing this law and using it, with his laws of motion, to explain the motion of lots of different things --- from falling objects to planets. Amazingly, out of these simple and general rules, Newton was able to show that all of Kepler's descriptive laws for orbits followed as a direct consequence. When you combine Newton's gravitation and circular acceleration, which must balance in order for the object to remain in orbit, you get a nice relation between the period, distance, and mass of the central body.

It beings by equating the centripetal force (Fcent) due to the circular motion to the gravitational force (Fgrav): Fgrav = Fcent Fgrav = G m1 m2 / r2 Fcent = m2 V2 /r Let the Earth be m1 and the Moon be m2. For circular motion the distance r is the semi-major axis a. The orbital velocity of the Moon can be described as distance/time, or circumference of the circular orbit divided by the orbital period: V = 2 pi r /P so setting the forces equal yields G m1 m2 / a2 = m2 V2 /a note that the m2 will cancel, so that circular orbital motion is independent of the mass of the orbiting body! G m1 / a2 = ((2 pi a)2/P2)/a which we rearrange to place all the a-terms on the right and all the P-terms on the left: G m1/(4 pi2) P2 = a3 which should look startlingly like Kepler's third law, but this time for the Earth's mass (or any other) instead of the sun's mass.

To use a and P to solve for mass, manipulate once more so that m1 = a3 (4 pi2/G) / P2

Question: What is the term for the time that it takes an object to make one full orbit around the Sun, relative to the stars?
Answer: Sidereal period