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1445 Introductory Astronomy I

1445 Introductory Astronomy I. Chapter 0b Scientific Notation & Measurements R. S. Rubins Fall, 2010. Scientific Notation 1. Positive powers of ten T (tera) = 10 12 = 1,000,000,000,000 = one trillion (US)

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1445 Introductory Astronomy I

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  1. 1445 Introductory Astronomy I Chapter 0b Scientific Notation & Measurements R. S. Rubins Fall, 2010

  2. Scientific Notation 1 • Positive powers of ten T (tera) = 1012 = 1,000,000,000,000 = one trillion (US) G (giga) = 109 = 1,000,000,000 = one billion (US) M (mega) = 106 = 1,000,000 = one million k (kilo) = 103 = 1000 = one thousand 102 = 100 = one hundred 101 = 10 = ten, 100 = 1 = one • Examples: 3.842 x 102 = 384.2 , 3.842 x 104 = 38,420 .

  3. Scientific Notation 2 • Negative powers of ten c (centi) = 102 = 0.01 = one hundredth m (milli) = 103 = 0.001 = one thousandth m (micro) = 10-6 = 0.000,001 = one millionth n (nano) = 109 = 0.000,000,001 = one billionth (US) p (pico) = 1012 = 0.000,000,000,001 = one trillionth (US) • Examples: 384.2 x 102 = 3.842 , 384.2 x 104 = 0.03842 .

  4. Scientific Notation: Simple Operations • Multiplication 105x 10–2= 10(5– 2) = 103. • Inverse 1/103= 10–3, 1/10–3= 103. • Division 105/104= 10(5– 4) = 101 =10. 105/10–4= 10(5+ 4) = 109. • Powers (105)3= 105x 105x 105 = = 10(5+5+5) = 10(5x3) = 1015. • Square roots 106= 10(6/2) = 103.

  5. Multiplication, Division, and Square Roots • (2.0 x 106)(3.5 x 102) = (2.0 x 3.5) x 10(6 – 2) = 7.0 x 104. • (9.0 x 107)/(2.0 x 104) = (9.0/2.0) x 10(7 – 4) = 4.5 x 103. • 1/(2.5 x 102)3 = 1/[(2.5)3 x 10(2 x 3)] = 1/(15.6 x 106) = 0.064/10–6 = 0.064 x 106 = 6.4 x 104. • [(3.0 x 104)(7.5 x 107)] = (22.5 x 10(4+7)) (22.5 x 103) = (2.25 x 104) = 1.5 x 102.

  6. Units of Distance • SI unit: m (meter). 1 km = 1000 m = 103 m, 1 mm = 103 m, 1 m = 106 m, 1 nm = 109 m. • 1 mi (mile) = 1.6 km or 5 mi  8 km. 1 AU (astronomical unit) = 1.5 x 108 km. 1 ly (light year) = 63,000 AU. 1 pc (parsec) = 3.26 ly or 30 pc  100 ly.

  7. Distance Definitions 1 • Astronomical unit (AU)is the average distance of the Sun from the Earth. 1 AU = 93 million miles (= 1.50 x 108 km). • Light-year (ly)is the distance that light travels through space in 1 year. 1 ly = 63,000 AU ≈ 6 trillion miles. • Parsec (pc) , defined in the next slide, is just over three times larger than the light-year; i.e. 1 pc = 3.26 ly ≈ 20 trillion miles.

  8. Parsec Parsec (pc)is the distance from the Earth at which a length of 1AU subtends an angle of 1 arcsec.

  9. Things smaller than we are

  10. Things larger than we are

  11. Speed and Velocity • Speed (is a scalar) SI unit: m/s (meter/second); 1 km/s = 1000 m/s = 2236 mph (miles per hour). • Velocity(is a vector) Velocity = speed + direction; e.g. the wind velocity is 45 mph from the north.

  12. Speed of Light • Light (and all electromagnetic radiation) travels through space at the speed c, where c = 300,000 km/s = 3.00 x 108 m/s = 186,000 mi/s. • The distance x traveled by light in a time t is given by x = ct , so that t = x/c and c = x/t . • Example: the time taken by light to travel 6 km is t = x/c = 6 km / 300,000 km/s = (2/100,000) s = 2 x 105 s = 20 x 106 s = 20 µs.

  13. Acceleration Accelerationis the rate at which the velocity changes. It is a vector quantity, with the SI unit: m/s2. Since velocity contains both speed and direction, a change of either produces an acceleration.

  14. Centripetal acceleration • An object moving in a circle has a centripetal acceleration. • This acceleration is directed towards the center of the circle; e.g. i. a satellite orbiting the Earth ; ii. a child riding a merry-go-round.

  15. Temperature Scales 1 • Fahrenheit to Celsius TC= (5/9)(TF – 32). • Celsius to Fahrenheit TF = (9/5)TC + 32. • Celsius to Kelvin TK = TC + 273.15. • Example: if TC = ̶40 oC, then, TF = [(9/5) x ( ̶ 40)] + 32 = ̶ 72 + 32 = ̶ 40 oF.

  16. Temperature Scales 2

  17. Angular Measure 1 • An angle is a measure of the opening between two straight lines, which meet at a point. The two stars furthest from the handle of the Big Dipper subtend an angle of about 5o at the eye.

  18. Angular Measure 2 • Angles are used to measure the sizes that objects appear to us. • The full Moon has an angular diameter or angular size of almost ½ o, roughly the same as that of the Sun, which is both much larger and much further away. • 1 arcdegree (o) = 60 arcminutes (‘); arcminute = 60 arcsec (“).

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