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Vaisakhan Thampi D S AASTRO-Kerala • The stars move in the sky but not with respect to each other • The planets (or “wanderers”) move differently from stars – They move with respect to the stars – They exhibit strange retrograde motion • What does all this mean? • How can we explain these movements? A flash back of Astronomy… Aristotle (BC 384-322) Earth is round Earth is the center of Universe Stars are all stationary Celestial bodies are made up of immortal aether Universe above moon is different from Universe below moon First Heliocentric theory Aristarchus (BC 310-230) A flash back of Astronomy… Ptolemy (AD 90-168) Earth is the centre A flash back of Astronomy… Earth is thrown out from the throne! Concluded that Earth is a planet. Proposed a model of the solar system with the sun at the center Copernicus 1473-1543 Heliocentric model De revolutionibus Orbium Celestium A flash back of Astronomy… Along the way of Copernicus Many objects in the sky like earth Sun is just one among many other stars Giordano Bruno (1548-1600) All other stars are just like our sun Burned alive for what he said! A flash back of Astronomy… Designed and built instruments to measure the locations of the heavenly bodies. Observations, especially of Mars, were far more precise than any made previously. Tycho Brahe 1546-1601 Father of Observational Astronomy A flash back of Astronomy… Planetary laws Johannes Kepler 1571-1630 1. The orbit of every planet is an ellipse with the Sun at one of the two foci. 2. A line joining a planet and the Sun sweeps out equal areas during equal intervals of time. 3. The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. A flash back of Astronomy… Described the behavior of moving objects. Developed his own telescope and made important discoveries: Galileo Galilei 1564-1642 1. Four satellites, or moons, orbit Jupiter. 2. Planets are circular disks, not just points of light. 3. Venus has phases just like the moon. 4. The moon’s surface is not smooth. 5. The sun has sunspots, or dark regions. In the year Galileo died, On a Christmas day…. Isaac Newton (1642-1727) The legendary Apple! The Apple & The Moon Isaac Newton realized that the motion of a falling apple and the motion of the Moon were both actually the same motion, caused by the same force - the gravitational force. Centripetal force Newton’s deductions from Kepler’s laws Law of areas is a consequence of force acting towards sun Third law is a consequence of the fact that farther the object, weaker the force When two planets at different distances are compared, the force is inversely proportional to the square of its distance Newton’s laws of Motion • 1st Law – A body at rest, or in uniform motion, will remain so unless acted upon by an unbalanced force. • 2nd Law – The change in motion (acceleration) is proportional to the unbalanced force • 3rd Law – For every action there is an equal and opposite reaction 1. Earth’s circumference, originally estimated by Eratosthenes (about 200BC), and improved by French surveyors during Newton’s lifetime. Their best value, in today’s units, 69.2miles/degree = 69.2 x 360 miles = 24900miles = 40 100km. This implies a radius (Re) of 6380km. Fact 2 The Moon’s distance from Earth(radius of Moon’s orbit, Rmo) Estimated by Aristarchus and Hipparchus Using the size of the shadows during a lunar eclipse, they found the Moon’s distance, Rmo to be about 60 x Earth’s radius, 60Re. i.e., about 60 x 6380 = 383000km = 3.83 x 108m Fact 3 Length of a lunar month (time taken for Moon to make one complete orbit) =27.32 days = 27.32 x 24 x 3600 sec = 2.36 x 106seconds. This is easily measured by counting the number of days taken for several lunar months. Fact 4 Acceleration of falling objects on Earth = 9.8m/s2 Estimated by Galileo Idea 1 The force used to keep an object rotating in a circle depends on the object’s speed and the circle’s radius in this way:F = m v2 / r This implies that the centripetal acceleration (directed towards the centre on the circle) is equal to v2 / r. This was proved in Newton’s Principia. This is his own copy. Possibly the first proof. Idea 2 The Moon is in orbit around the Earth because gravity supplies this centripetal force. Why doesn’t moon fall to earth? • Of course it does! • But the surface of earth falls down as the moon falls down • So it never reaches the ‘ground’ There are two places where we can compare the Earth’s gravitational field: One at the Earth’s surface and the other at the orbit of the Moon. This uses idea 3. Idea 3 The force is inversely proportional to the square of the distance from source and force is proportional to acceleration 1 / (radius of Earth)2 1/ (radius of Moon’s orbit) 2 ge = gm = (radius of Moon’s orbit) 2 (radius of Earth) 2 = Rmo2 / Re2 Rearranging slightly ge = Rmo2 x centripetal accn of Moon(gm) Re2 To get a numerical value for ge, all we need to do is to insert the centripetal acceleration from Idea 1 and the known value of the ratio of the orbital sizes (60/1). Idea 1 Centripetal accn of Moon = v2 / Rmo First - the Moon’s velocity, v, = circumference of Moon’s orbit time for one revolution = 2πRmo / 2.36 x 106 = 1019m/s and, second, the accn of Moon, gm = v2 Rmo = 10192 = 1.038x106 Rmo Rmo = 1.038x106 / (60 x Re) = 1.038x106/(60 x 6.38 x 106) gm = 0.00271m/s2 Now we can substitute this into our expression for ge ge = Rmo2 x gm Re2 where Rmo2 / Re2 = 602 and so, finally, ge = 602 x 0.00271m/s2 ge = 9.8m/s2 Universal Gravitation Newton realized that gravity was a universal force acting between any two objects. It has become the ‘Universal Law of Gravitation’ The Universal Law of Gravitation is formulated as F = Gm1m2/r2 G = 6.67 x 10-11 N m2/kg2 Gravity is too weak a force that the entire mass of earth is required to pluck a ripened apple from the tree! Occurrence of tides Spherical Shape of Earth Prediction of Neptune Binary Stars Globular Star Cluster Shape of Galaxies Star formation The universe is so beautiful, you just have to look at it.