Astronomical Measurements

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Astronomical Measurements

• 8/26/08

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Measuring distances

• The universe is really really really big.
• Even small parts of the universe are really big.
• Our usual units of distance are simply inadequate
  (m, km)

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Examples

• The distance from the Earth to the Sun is
  approximately 150,000,000 km
• If the sun were a basketball, earth would be 110
  feet away and the size of a BB
• The distance to the nearest star is approximately
  40,000,000,000,000 km
• If the entire solar system fit inside a
  basketball, the nearest star is over ¾ mile away
• The diameter of the milky way galaxy is around
  1,240,000,000,000,000,000 km
• If the solar system fit inside a basketball, our
  galaxy would stretch for 26,000 miles (about the
  circumference of Earth)

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Measuring distances, contd

• We need to use units that represent much larger
  distances so our numbers are easier to work with
• New Unit 1 The Astronomical Unit (AU)
• The distance from the earth to the sun
• 1.5x108 km (about 93 million miles)
• The solar system has a radius of about 30 AU
• The nearest star is 268,170 AU away

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Measuring distances, contd

• New Unit 2 The light year (ly)
• The distance light travels in one year
• The speed of light is 300,000 km/s
• In one year, light can travel 9,500,000,000,000
  km
• The nearest star is about 4.2 light years away
• The milky way is about 130,400 ly across
• Relationship between units
• One light year is about 63,300 AU

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The Size of Objects as Seen From Earth

• Although the literal size of an object is
  important, often all we need to know is how much
  of the sky does it take up?
• This is done through angular measurement
• Degrees (There are 360? in complete circle)
• Minutes of Arc (There are 60 in one degree)
• Seconds of Arc (There are 60 in one minute)

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30 degrees
15 degrees
90 degrees
45 degrees
180 degrees
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Hold your hand at arms length
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2
20
10
3
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These are, of course, only approximations
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• The moon has an angular diameter of 0.5

• The sun has an angular diameter of 30

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Perspective

• The further away an object is, the smaller it
  appears.
• We only need measure the apparent size of an
  object, then
• If we know its true size, we can calculate how
  far away it is
• If we know how far away it is, we can calculate
  its true size

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But first, one last distance unit

• The distance to most stars is measured using
  STELLAR PARALLAX
• Parallax is the apparent displacement of an
  object due to the motion of the observer
• To illustrate parallax, hold your thumb out and
  view it with your right eye, then your left
• Your thumb moves with respect to the background

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q
q is the parallax angle
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q
The further away an object is, the smaller its
parallax angle
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New Distance Unit 3

• The parsec (pc)
• The distance at which an object displays a
  parallax of one second of arc
• One parsec is 3.3 ly
• When parallax is in arcseconds and distance is in
  parsecs
• d 1/p

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Summary of distance units

• 1 AU 150,000,000 km
• The distance from Earth to the Sun
• 1 ly 9.5x1012 km
• The distance light travels in one year
• 1 pc 3.3 ly
• The distance at which an object has a parallax of
  one second of arc

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Triangulation

• 8/27/08

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Right-Triangle Geometry

• Relationships in right triangles can be used to
  calculate the distance to an object knowing its
  size
• OR
• Calculate the size of an object knowing how far
  away it is

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Geometric Relationships

• Tan q opposite/adjacent

Opposite side
q
Adjacent side
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h
q
d
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h
35? 15
1500 ft
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When completed at the end of this year, the
worlds tallest building will be the Burj Dubai
at 2650 ft. How long will its shadow be when the
sun is 15 degrees above the horizon?
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Using parallax to determine distance
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30 feet
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Applications in Astronomy

• Lets say we want to know how far away the moon
  is
• Theoretically, all we need to know is how big the
  moon is (which was first found by finding how
  long it took the moon to pass through Earths
  shadow during a total lunar eclipse)
• The diameter of the moon is 3,480 km
• We can use simple right triangles, or make use of
  a simple proportion known as the SMALL ANGLE
  EQUATION

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The diameter (D) is to the circumference of the
circle (2p d) as The angular diameter (?) is to
360
D
d
D ? 2p d 360
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Now apply a similar calculation to find the
diameter of the sun

• Distance to the sun 1 AU (150,000,000 km)
• Angular diameter of the sun 0.5 degrees

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The Small Angle Equation

• Can only be used when the angle is small
• Works great for objects in our solar system
• Objects further away cannot be resolved into a
  disk, no matter how large your telescope is.
  Therefore we cannot measure the angular diameter
  of objects (such as stars) outside our solar
  system