Angle, distance, and Powers of Ten

1. Angle, distance, andPowers of Ten Lecture 2 by Inseok Song

2. 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!

3. Solar System Overview

4. 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

5. 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

6. 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)

7. 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

8. 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

9. 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)

10. 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

11. 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

12. 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

13. 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

14. Small angle formula • when the angle is small, we can approximate that the length (A) is equal to the arc length (B) • Linear size of an object (D), α in arcseconds. A B

16. Figure 1-11a The angular diameter of the full moon in the sky is about 1/2°. Vertical Moon 90° 1/2° Horizontal Complete circle = 360° (a) Measuring angles in the sky

17. Figure 1-11b,c The angular distance between the two pointer stars at the front of the Big Dipper is about 5°, roughly 10 times the angular diameter of the Moon. The angular distance between the stars at the top and bottom of the Southern Cross is about 6°. 6° 5° (b) Angular distances in the northern hemisphere (c) Angular distances in the southern hemisphere

19. 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

20. 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

21. Yet, another distance unit 1 AU Sun The parsec (pc), a unit of length most commonly used by astronomers, is defined by the apparent size of the Earth orbit. At 1pc away from the solar system, the angle between the Sun and Earth is 1 arcsec. 1 kiloparsec = 1 kpc = 103 pc 1 megaparsec = 1Mpc = 106 pc Earth’s orbit 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

22. Sizes in the Universe

24. Cosmic connection (SWF animation)

25. In summary… Important Concepts Important Terms arcsec = arc seconds = second of arc armin = arc minutes Astronomical Unit (AU) Parsec (pc) • 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. • Chapter/sections covered in this lecture : sections 1.5-1.8