How%20Far%20is%20a%20Light%20Year?

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How Far is a Light Year?

• Claire Hodgin Science Instructional Coach
• University of Texas University Charter Schools
• Armosky and Hodgin ? University of Texas at
  Austin, 2009

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Engage

• Powers of Ten
• About the Relative Size of Things in the Universe
• What was the smallest to the largest distance on
  the video?

1040 10,000,000,000,000,000,000,000,000,000,000,0
00,000,000 m
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Explore
messagesfromearth.wordpress.com

• If we could shrink the Sun to the size of this
  balloon, how big would the Earth be?

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Our Solar System
kiroastro.com
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What is one way to measure a planet or star?

• By the Diameter of the sphere

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Diameter of a planet
Diameter of a sphere

• The distance from one edge to the opposite edge

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It would take 108 Earths laid side-by-side to go
across the Suns diameter
messagesfromearth.wordpress.com
findfreeclipart.com
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Finding the Earth/Sun Diameter Ratio
The Earths diameter is 12,756,000 meters or
1.3 X 107 m
The Suns diameter is 1,400,000,000
meters or 1.4 X 109 m The ratio of the Earth
Sun diameter is 1.3 X 107 m 1.4 X 109
m Simplify the ratio...
1.3 X 107 m 1 m 1.4 X 109 m 108
m Earth to Sun Diameter ratio is
1 108
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Actual Distance from the Sun to the Earth
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If we use the same scale as we used for the SIZE
of Sun and Earth

• How far apart would the Sun and Earth be in our
  model?

Sun Diameter Sun Diameter Sun to Earth Distance Sun to Earth Distance
Model .45 m X Model
Actual 1.4 x 109 m 1.5 x 1011 m Actual
Cross multiply and x 4.8 x 101 m (48 m) or 50
m
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Distance from the Sun to the Earth in our model
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Lets take a field trip

• To build a model to scale
• the Sun will be a 450 mm balloon
• the Earth will be a 4 mm lentil
• and they will be 50 meters apart

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Explain
The Milky Way Galaxy is about 100,000 light years
across
Powersof10.com
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One light-year is the DISTANCE that light travels
in one year

• If we are going to find out
• HOW FAR is a Light Year,
• we need to know two things
• The speed of light, measured in meters per second
  and
• The number of seconds in a year

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What is the fastest speed in the universe?

• The Speed of Light
• What is the speed of light?
• (abbreviated c)
• 300,000,000 meters per second or
• 3 X 108 m/s
• (remember the line in Powers of Ten?)

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How Many Seconds in a Year?

• 60 seconds per minute
• X 60 minutes per hour
• X 24 hours per day
• X 365.25 days per year
• the number of seconds per year

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On the Graphing Calculator

• Turn on and press Mode
• At the top row are the words
• Normal Sci Eng
• And the Normal is highlighted in black
• Arrow right to Sci until it is highlighted, and
  press Enter
• Quit (2nd Mode), and now all of your calculations
  are in Scientific Notation (Powers of Ten)

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In science we call this Dimensional Analysis,
in math Unit Conversion
60 s 60 min 24 hr 365.25 days 3.2 x 107 s
1 min 1 hr 1 day 1 yr 1 yr

Lets try this on the graphing calculator
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So How Far is a Light Year?

• Multiply the Speed of light (m/s) by the number
  of seconds per year (s/yr)
• number of m/yr
• 3 x 108 m/s X 3.2 x 107 s/yr
• 3 2nd LOG 8 ) X 3.2 2nd LOG 7 ) Enter
• 9.5 x 1015 m/yr
• Or 9,500,000,000,000,000 meters
• Thats Nine Quadrillion, Five Hundred Trillion
  Meters

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• How long does it take light to get from the Sun
  to the Earth?
• 8 minutes

It takes 16 minutes to go there and back
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If we use the same scale as we used for the SIZE
and DISTANCE of Sun and Earth

• How long would a light year be in the model?

Sun Diameter Sun Diameter Light Year Light Year
Model .45 m X Model
Actual 1.4 x 109 m 9.5 x 1015 m Actual
Cross multiply and x 3.1 x 106 m
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3.1 x 106 meters

• Thats 3.1 x 103 kilometers!
• Thats 3 times wider than Texas!
• Thats too much tape!

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Lets change the scale of our model.

• What is the new scale factor so that 1 light year
  fits inside a 50 meter paper strip?

Light Year Distance Light Year Distance Sun Diameter Sun Diameter
Model 50 m X Model
Actual 9.5 x 1015 m 1.4 x 109 m Actual
Cross multiply and x 7.4 x 10-6 m
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