How Far is a Light Year? Claire Hodgin – Science Instructional Coach University of Texas – University Charter Schools
Mar 28, 2015
How Far is a Light Year?
Claire Hodgin – Science Instructional CoachUniversity of Texas – University Charter Schools
Armosky and Hodgin University of Texas at Austin, 2009
Engage
Powers of TenAbout the Relative Size of Things in the Universe
What was the smallest to the largest distance on the video?
1040
10,000,000,000,000,000,000,000,000,000,000,000,000,000 m
Explore
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
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What is one way to measure a planet or star?
By the Diameter of the sphere…
Diameter of a planet…
The distance from one edge to the opposite edge
Diameter of a sphere
It would take 108 Earths laid side-by-side to go across the Sun’s diameter
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Finding the Earth/Sun Diameter Ratio
The Earth’s diameter is12,756,000 meters or ~ 1.3 X 107 m
The Sun’s 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
Actual Distance from the Sun to the Earth
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 DiameterSun Diameter Sun to Earth Sun to Earth DistanceDistance
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
Distance from the Sun to the Earth
in our model
Let’s 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
Explain
The Milky Way Galaxy
is about 100,000
light years across
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One light-year is the DISTANCEDISTANCE that light travels in one year
If we are going to find out
HOW FAR is a Light YearHOW 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
What is the fastest speed in the universe?
The Speed of LightThe Speed of Light
What is the speed of light?(abbreviated “c”)
300,000,000 meters per second300,000,000 meters per second or
3 X 103 X 1088 m/s m/s
(remember the line in Powers of Ten?)
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
On the Graphing Calculator…
• Turn on and press “Mode”
• At the top row are the words:
NormalNormal 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)
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
Let’s try this on the graphing calculator
=
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 23 2ndnd LOG 8 ) X 3.2 2 LOG 8 ) X 3.2 2ndnd LOG 7 ) Enter” LOG 7 ) Enter”
9.5 x 1015 m/yr
Or 9,500,000,000,000,000 meters
That’s Nine Quadrillion, Five Hundred Trillion Meters
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
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 DiameterSun Diameter Light YearLight 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
3.1 x 103.1 x 1066 meters meters
That’s 3.1 x 103 kilometers!
That’s 3 times wider than Texas!
That’s too much tape!
Let’s 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 Light Year DistanceDistance Sun DiameterSun 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