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3. Time-scale and Distance (시간 척도와 거리) SI 단위계에서 사용하는 접두어 Cosmic Calendar Cosmic Calendar: Scale 12 Billion year History of Universe into one year. 1 month = 1 Billion years. 우주의 달력 : 우주의 탄생에서 현재까지를 1년으로 두었다 • • • • • • • • • Jan 1: The Big Bang Feb. : The Milky Way forms August 13: The Earth Forms December 13: Invertebrate (무척추) Life Evolves December 25: Rise of Dinosaurs December 30: Dinosaurs Extinct December 31: 9:00 pm Earliest Human Ancestors December 31: 11:59:47 pm Pyramids are Built December 31: 11:59:58.4 pm King Sejong was born Chronology of the Universe 우주의 연표 (연대기) 13.7 Gyr 13.4 Gyr 12 Gyr 4.567 Gyr 4.5 Gyr 4.45 Gyr 4.4 Gyr 4.2 Gyr 4 Gyr >3.5 Gyr >3.5 Gyr 2.3 Gyr 0 Gyr Big bang; formation of the elements H and He First stars and galaxies; first supernova explosions produce the heavy elements (C,N,O,Si,Fe,…) Formation of the milky way Formation of the solar system; at this point in time the interstellar medium has been enriched with 1% heavy elements Formation of the earth and the moon Layer structure of the earth Solid earth crust Early ocean Plate tectonics Earth’s magnetic field Origin of life Formation of oxygen-rich atmosphere; formation of ozone Today 원소의 주기율표 Distance and Size of the Moon 달까지의 거리와 달의 크기 • In the 3rd Century B.C., a Greek, Aristarchus of Samos, figured out a way to measure the relative sizes and distances of the Moon and Sun. • He noticed that when the Moon was eclipsed by the Earth (월식) we can see the Earth's shadow creep across the face of the Moon. Earth's shadow is circular, and if we assume that the Sun's rays are roughly parallel to one another. • From the arc of Earth's shadow we can estimate the size of it's full circle, then you measure the size of the Moon's circle. This tells us the relative size of the Earth to the Moon. What you are measuring is the angular size of the Earth's shadow and the Moon. • Aristarchus measured a ratio of Earth's size to the Moon's size to be 2.9 (real ratio=3.7). • Using the angular size of the Moon (=0.5 degree) we can estimate its distance as shown below: tan = D/d (when <<1, in radian) where D and d denote the diameter of the moon and distance between the Earth and the moon. • The angular size of the Moon is about 0.5° ( = 0.5°). Thus we have a distance to the Moon of about 40 Earth Diameters (actually 30). Distance and Size of the Sun 태양까지의 거리와 크기 • In addition, Aristarchus considered that when the Moon was seen to be exactly in either 1st or 3rd Quarter Phase (exactly half lit up as seen from Earth), we can draw a right triangle between Earth, Moon, and Sun. • The legs of the right triangle are the distance from the Earth to the Moon (d1) and the distance between the Moon and the Sun (d2). The hypotenuse is then the distance between the Earth and Sun (d). We can measure the angle between d1 and d (A), it's the angular separation between the Sun and Moon in the sky. We derive the distance d by the Pythagorean theorem. d2 d1 d • Aristarchus measured A= 87°. This corresponds to a distance to the Sun of d = 573DE. Now, the angular size of the Sun is also about 0.5° so by the same method as for the Moon Aristarchus estimated that the Sun was 5.33 times bigger than the Earth. • This measurement is a difficult one to make, and the real answer is A= 89.9°. This corresponds to a distance to the Sun of d = 11,700DE and a size of the Sun, DS = 109DE. • Either way, Aristarchus was able to establish that the Sun was bigger than Earth. Aristarchus of Samos, the ancient Copernicus • Earth radius 6400 km • Moon-Earth distance 3.8105 km • Sun-Earth distance 1.5108 km 1 AU (astronomical unit) Parallax시차 (視差) • Parallax = angle subtended (i.e., covered) by 1 A.U., the distance from Earth to the Sun. (1/2 of the diameter of Earth's orbit). • As distance increases the parallax angle decreases. Ultimately limited by the smallest angles measurable (resolved). • The distance at which 1 A.U. subtends 1" (one arc second) is called 1 parsec (pc). (parallax arc second). • dpc = 1/p(") • 1 pc = 3.26 Light-years. Distance to nearest star, Centauri p = 0.762" ---> d = 1.31 pc = 4.27 light-years 1 parsec = 3.26 light year