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Angle, distance, and Powers of Ten Lecture 2 by Inseok Song In this class, you will learn 1-5 How astronomers measure the positions and sizes of celestial objects 1-6 How to express very large or very small numbers in convenient notation 1-7 Why astronomers use different units to measure distances in space 1-8 What astronomy can tell us about our place in the universe Before we begin these, let’s first get realized how vacant the space truly is! Solar System Overview Put it on a tangible scale about 1/3 miles away If we scale down everything by 100 million times… Sun = a small truck at the Physics Building at UGA Mercury = a quarter at the Stegeman Coliseum So much of empty space… about a mile away If we scale down everything by 100 million times… Sun = a small truck at the Physics Building at UGA Earth = an apple at the intramural field So much of empty space… ~3 miles away If we scale down everything by 100 million times… Sun = a small truck at the Physics Building at UGA Asteroids = millions of planktons scattered around the Loop 10 (perimeter road) So much of empty space… ~5 miles away If we scale down everything by 100 million times… Sun = a small truck at the Physics Building at UGA Jupiter = a classroom desk near the west-end of Athens So much of empty space… ~10 miles away If we scale down everything by 100 million times… Sun = a small truck at the Physics Building at UGA Saturn= a classroom desk near Bogart on highway 316 So much of empty space… ~20 miles away If we scale down everything by 100 million times… Sun = a small truck at the Physics Building at UGA Neptune = a basketball near the Gwinnett county airport (Lawrenceville) So much of empty space… ~30 miles away If we scale down everything by 100 million times… Sun = a small truck at the Physics Building at UGA Pluto = a penny at the I-85 / GA-316 intersection So much of empty space… ~40-60 miles away If we scale down everything by 100 million times… Sun = a small truck at the Physics Building at UGA K-B objects = millions of microbes + small insects scattered around northern Georgia So much of empty space… ~200,000 miles away If we scale down everything by 100 million times… Sun = a small truck at the Physics Building at UGA Nearest Star = another truck at the distance to the Moon Angles in astronomy circumference = 2π × radius for a given radius, the length of an arc will be proportional to an angle. Astronomers use angles to denote the positions and apparent sizes of objects in sky. angular distance angular size a complete circle = 360° 1° = 60’ 1’ = 60” d=α×R Small angle formula when the angle is small, we can approximate that the length (A) is equal to the arc length (B) A Linear size of an object (D), α in arcseconds. D d 206265 B Figure 1-11a Vertical Moon 90° 1/2° Horizontal The angular diameter of the full moon in the sky is about 1/2°. Complete circle = 360° (a) Measuring angles in the sky The angular distance between the Figure 1-11b,c two pointer stars at the front of the Big Dipper is about 5°, roughly 10 times the angular diameter of the Moon. 5° 6° The angular distance between the stars at the top and bottom of the Southern Cross is about 6°. (b) Angular distances in the northern hemisphere (c) Angular distances in the southern hemisphere Powers of Ten notation From atoms to the entire Universe, astronomy is a subject of extremes. If we express the size of a Hydrogen atom and the Universe in meters… Universe = 100,000,000,000,000,000,000,000,000 meters = 1026 meters atom = 0.0000000001 meter = 10-10 meters To efficiently express a wide range of numbers, astronomers use the power-of-ten notation 1 giga bytes = 1 billion bytes Study box 1-2 : arithmetic with powers-of-ten Astronomical distances Although we could express all sizes and distances in astronomy using one unit (e.g., meter), it is oftentimes more convenient to use different units scale of planetary systems A.U. average distance between stars parsec or light-year AU = astronomical unit = average distance between Earth and the Sun 1 AU = 1.496×108 km light-year = the distance that light travels in one year 1 ly = speed of light × (365 days × 24 hours × 60 minutes × 60 seconds) = 300,000 km/sec × (3.156×107 seconds) = 9.46 × 1012 km Yet, another distance unit 1 AU The parsec (pc), a unit of length most commonly used by astronomers, is defined by the apparent size of the Earth orbit. Sun At 1pc away from the solar system, the angle between the Sun and Earth is 1 arcsec. Earth’s orbit 1 kiloparsec = 1 kpc = 103 pc 1 megaparsec = 1Mpc = 106 pc Distance: 1 parsec (3.26 light-years) Angle: 1 arcsec" = 1 At a distance of 1 parsec, a length of 1 AU subtends an angle of 1 arcsec. Observer Sizes in the Universe Cosmic connection (SWF animation) In summary… Important Concepts Important Terms Angular Measure: Astronomers use angles to denote the positions and sizes of objects in the sky. The size of an angle is measured in degrees, arcminutes, and arcseconds. Powers-of-Ten Notation is a convenient shorthand system for writing numbers. It allows very large and very small numbers to be expressed in a compact form. Units of Distance: Astronomers use a variety of distance units. These include the astronomical unit (the average distance from Earth to the Sun), the light-year (the distance that light travels in one year), and the parsec. arcsec = arc seconds = second of arc armin = arc minutes Astronomical Unit (AU) Parsec (pc) Chapter/sections covered in this lecture : sections 1.5-1.8