1446 Introductory Astronomy II

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1446 Introductory Astronomy II

• Appendices A D
• Scientific Notation Measurements
• R. S. Rubins
  Fall, 2009

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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.

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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 .

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Scientific Notation Simple Operations

• Multiplication 105 x 102 10(5 2) 103.
• Inverse 1/103 103,
• 1/103 103.
• Division 105 /104 10(5 4) 101
  10.
• 105 /104 10(5
  4) 109.
• Powers (105)3 105 x 105 x 105
• 10(555)
  10(5x3) 1015.
• Square roots ?106 10(6/2) 103.

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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 x 106 6.4 x 104.
• ?(3.0 x 10?4)(7.5 x 107) ?(22.5 x 10(?47))
  
• ?(22.5 x 103) ?(2.25 x 104) 1.5 x 102.

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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.
• 
  

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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.
• Parsec (pc) is the distance from the Earth at
  which a length of 1AU subtends an angle of 1
  arcsec.
• 1 pc 3.26 ly.

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Parsec

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

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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.

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Speed of Light

• Light (and all electromagnetic radiation) travels
  through space at the speed
• c 300,000 km/s.
• or c 3.00 x 108 m/s or 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.

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Acceleration

• Acceleration is the rate at which the velocity
  changes.
• SI unit m/s2.
• Since velocity contains both speed and direction,
  a change of either produces an acceleration.

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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.

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Centripetal Force 1

• A centripetal force Fc , which is a force
  towards the center
• of the circle, is needed to produce a centripetal
  acceleration
• ac i.e.
• Fc m ac .
• For astronomical objects, this force is gravity.

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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.

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Temperature Scales 2
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Angular Measure 2

• The two stars furthest from the handle of the
  Big Dipper subtend an angle of about 5o at the
  eye.

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Angular Measure 1

• Hold hand at arms length to estimate angles,
  which are given in arcdegrees (or degrees of
  arc).
• Note 1 arcdegree (o) 60 arcminutes ()
• 1 arcminute 60 arcsec ().