Chapter 1: Astronomical Numbers © BRIEF 20141

Astronomical Numbers Overview: 1.What are Astronomical Numbers? 2.The Metric System 3.Scientific Notation 4.Putting things into perspective (measuring by a measurement that makes sense to us) Astronomical Numbers © BRIEF 20142

ASTRONOMICAL: Astronomy uses A LOT of numbers and they are ASTRONOMICAL: Age of the Earth: 4,550,000,000 years (4.55 Billion years) Average distance of the Earth from the Sun: 149,597,900 kilometers 1 LY = 9,460,000,000,000 kilometers 1 PC = 30,900,000,000,000,000 meters Mass of the Sun: 1,989,000,000,000,000,000,000,000,000,000 kilograms Small numbers: Diameter of a Hydrogen Atom m What are Astronomical Numbers © BRIEF 20143

Other examples of large numbers: Highest numerical bank note ever printed: 1 sextillion pengõ or 1x10 21 in Hungary in Zimbabwe printed a 100 trillion (10 14 ) Zimbabwean dollar worth about $30 Astronomical Numbers © BRIEF 20144

Astronomical So now what? How do we express those Astronomical numbers? We invented numbers that make these more tangible: Astronomical Unit Parsec Light Year Astronomical Numbers © BRIEF 20145

The standard unit of length in science: Meter Metric system is the exclusive Global standard. Only 3 nations still use other than the meter system: Myanmar (Burma), USA, Liberia. Astronomical Numbers: Metric System © BRIEF 20146

Historical Perspective: Traditional definition comes from the French Enlightenment Prior, units of length were manipulated locally, and by the current power structure: “He who has the Gold makes the rules!” Standardization was sought and this needed to be useful everywhere The Meter: Physically based Defined as 1 ten millionth of the distance from the North Pole to the Equator of the earth. Then was divided by an even power of 10 Thus based on powers of 10 Since the sphere of the earth is uneven, there was an updated definition provided as: The distance traveled by light in a vacuum in 1/299,792,458 th of a second. Astronomical Numbers: Metric System © BRIEF 20147

How it works: Encodes the powers of 10 within the name. Powers of 10 to the 3 are the main divisors. Keeps things roughly in the 1,000s frame of mind. Same for negative numbers except for Centi. Centi is about the width of a human finger and therefore is often kept as the derivation from the powers of 3 rule. Nano is about as low as we go in Astronomy Nano is common in light Astronomical Numbers: Metric System * * * * * * Most Common in Astronomy © BRIEF 20148

HOWEVER: HOWEVER: Astronomical numbers are SO LARGE, even the metric system become impractical: Metric System Metric System At 1000km (start to see curvature of the earth, and major geographical structures) 10,000km (greater than continents or large sections of planets) 100,000km (1/4 way from earth to the moon. Scales of planets and their moons) Astronomical Numbers © BRIEF m 100m 1000m 1km 10,000km 1,000km

HOWEVER: HOWEVER: Astronomical numbers are SO LARGE, even the metric system become impractical: Astronomical Unit: Astronomical Unit: The mean distance of the Earth from the Sun 1.498x10 8 km 10AU to Saturn Kuiper Belt 40AU 1000AU very outskirts of solar system Past the solar system we get to 100,000 and need to reset length measurement Astronomical Numbers © BRIEF Source: JPL

HOWEVER: HOWEVER: Astronomical numbers are SO LARGE, even the metric system become impractical: Light Year: Light Year: Time it takes light to travel in one year Used for distances between the stars 4LY to closest star: Alpha Centauri 26,000LY to center of galaxy 13B to the most distant object 100,000LY diameter of Milky Way Parsec: Parsec: 3.26LY Astronomical Numbers © BRIEF

© BRIEF 2014 Pasachoff_uFig. 1.1a Astronomical Numbers: A Sense of Scale 12

© BRIEF 2014 Pasachoff_uFig. 1.1b Astronomical Numbers: A Sense of Scale 10cm= 10x10 -2 m 13

© BRIEF 2014 Pasachoff_uFig. 1.1c Astronomical Numbers: A Sense of Scale 10m= 10x10 1 m 14

© BRIEF 2014 Pasachoff_uFig. 1.1d Astronomical Numbers: A Sense of Scale 1km= 1x10 3 m 15

© BRIEF 2014 Pasachoff_uFig. 1.1e Astronomical Numbers: A Sense of Scale 100km= 1x10 5 m 16

© BRIEF 2014 Pasachoff_uFig. 1.1f Astronomical Numbers: A Sense of Scale 17

© BRIEF 2014 Pasachoff_uFig. 1.1g Astronomical Numbers: A Sense of Scale NOTE: NOTE: At these distances the “yardstick” usually changes to AU or Light Orbit of Moon around the Earth 18

© BRIEF 2014 Pasachoff_uFig. 1.1h Astronomical Numbers: A Sense of Scale 19

© BRIEF 2014 Pasachoff_uFig. 1.1i Astronomical Numbers: A Sense of Scale Entire Solar System 20

© BRIEF 2014 Pasachoff_uFig. 1.1j Astronomical Numbers: A Sense of Scale 21

© BRIEF 2014 Pasachoff_uFig. 1.1k Astronomical Numbers: A Sense of Scale At this distance only a few stars are enclosed 22

© BRIEF 2014 Pasachoff_uFig. 1.1l Astronomical Numbers: A Sense of Scale 1,000LY Cube 23

© BRIEF 2014 Pasachoff_uFig. 1.1m Astronomical Numbers: A Sense of Scale Size of a typical Galaxy 24

© BRIEF 2014 Pasachoff_uFig. 1.1n Astronomical Numbers: A Sense of Scale 10M LY Across 25

© BRIEF 2014 Pasachoff_uFig. 1.1o Astronomical Numbers: A Sense of Scale 1B LY would only show our local group of galaxies as part of a local super-cluster 26

Questions? © BRIEF