2. NUMBERS IN ASTRONOMY See Appendix 4 & 5

3. Hydrogen Atom Proton Electron NUMBERS in ASTRONOMY.00000001 cm.0000000000001 cm Some numbers are very small Some numbers are very small äE.g. Diameter of Hydrogen Atom is about 0.00000001 cm

4. NUMBERS in ASTRONOMY l Other numbers are very large  E.g. size of galaxy 100,000,000,000,000,000,000,000 cm Some numbers are very small Some numbers are very small äE.g. Diameter of Hydrogen Atom is 0.00000001 cm

5. 100,000,000,000,000,000,000,000 cm

6. NUMBERS in ASTRONOMY ä The number of zeros is denoted by an exponent of 10. ä This exponent is positive if the number is larger than 1. ç10 N is 1 followed by N zeros ç E.g. 100,000,000,000,000,000,000,000 is written as 10 23 äThe exponent (power) is negative if the number is smaller than 1. ç10 -N represents a 1 in the N th place after the decimal çE.g. 0.00000001 is written as 10 -8 Some numbers are very small Some numbers are very small äE.g. size of Hydrogen Atom (GS) is 0.00000001 cm Other numbers are very large Other numbers are very large äE.g. size of galaxy 100,000,000,000,000,000,000,000 cm Powers of 10 Notation Powers of 10 Notation

7. POWERS OF 10 NOTATION l 10 N is 1 followed by N zeros l 10 -N is a 1 in the N th decimal place after the decimal point l More complicated numbers are represented by a combination of a power of 10 and a multiplying factor ä10 3 is 1000 ä10 8 is 100,000,000 ä10 -3 is 0.001 ä10 -8 is 0.00000001 ä0.000000025 is 2.5 x 10 -8 ä64,000 is 6.4 x 10 4

8. NUMBERS IN ASTRONOMY l Rule for Multiplication l Rule for Division äMultiply the factors and add the powers  E.g. 2 x 10 4 times 3 x 10 5 is (2x3) x 10 (4+5) = 6 x 10 9 äDivide the factors and subtract the powers çE.g. 5 x 10 6 divided by 2 x 10 4 is (5  2) x 10 (6-4) = 2.5 x 10 2

9. TEST YOURSELF l The mass of the Sun is: 1,989,000,000,000,000,000,000,000,000,000 kg. Write this mass in the powers-of-ten notation. l Answer: 1.989 x 10 30 kg

10. FLASHCARDFLASHCARD The Gross National Product of Canada in 2000 was 7.6 x 10 11 Canadian Dollars. There are 3 x 10 7 people in Canada. What is the amount of GNP per person? A) 2.5 x 10 3 A) 2.5 x 10 3 B) 2.5 x 10 4 C) 2.5 x 10 5 D) 2.5 x 10 6

11. FLASHCARDFLASHCARD The centre of our Galaxy is 7 x 10 16 km from us. UNBC (in Prince George) is about 5 x 10 2 km away from us. How many times farther (in powers of 10 notation) is the Galactic centre from us compared to UNBC? A) 3.5 x 10 19 B) 1.4 x 10 8 C) 1.4 x 10 14 D) 7.1 x 10 -15

12. FLASHCARDFLASHCARD The mass of our Galaxy is about 7 x 10 11 times the mass of our Sun. There are about 10 11 galaxies in the Universe. If an average star weighs about half that of our Sun, about how many stars are there in the Universe? A) 7 x 10 121 B) 14 x 10 22 C) 7 x 10 22 D) 7

13. POWERS of TEN EXAMPLES Sizes in Meters

14. UNITS in ASTRONOMY l Mass: kilograms (kg) l Time: seconds (s) or years (y) äA light year is the distance light travels in one year çSpeed of light = 3 x 10 5 km/s çThere are 3 x 10 7 seconds in a year çThus a lightyear is (3 x 10 5 ) x (3 x 10 7 ) = 9 x 10 12 km l Distance: meters (m), kilometers (km), light years (ly), or Astronomical Units (AU) äAn Astronomical Unit is the mean distance between Earth and the Sun (1.5 x 10 8 km)

15. UNITS in ASTRONOMY l Light year: l Astronomical Unit: l Solar Mass äThis is the distance which light will travel in the period of 1 year äThe speed of light (c) is 3 x 10 5 km/s äThere are 3 x 10 7 seconds in a year äThus, a light year is (3 x 10 5 ) x (3 x 10 7 ) = 9 x 10 12 km äNote: the star nearest the Sun (Proxima Centauri) lies at a distance of 4.26 ly (or 38 million million km!) äThis is a convenient unit to use for mass and is equal to the mass of our own Sun (1.9891 x 10 30 kg) äYour instructor weighs in at a hefty 4 x 10 -29 solar masses äThis is the mean Earth-Sun distance, and is about 1.5 x 10 8 km ( 150 million km)

16. UNITS in ASTRONOMY l Temperature: äUse Degrees Kelvin (K) äK = C + 273 äC water freezes at 0C boils at 100C äK water freezes at 273K boils at 373K äRoom Temperature about 300K ä0K = - 273C is absolute 0

17. ANGULAR MEASUREMENT 0° 360 degrees 90 degrees 180 degrees 270 degrees

18. ANGULAR MEASUREMENT 360 degrees in a full circle 1 degree = 60 minutes 1 minute = 60 seconds

19. ANGULAR MEASUREMENT

20. FLASHCARDFLASHCARD WHAT IS THE ANGULAR SIZE OF THE MOON AS SEEN FROM THE EARTH? A) 0.5 degree B) 5 degrees C) 10 degrees D) 50 degrees