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
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
10,000,000,000,000,000,000,000,000,000,000,000,000,000 m
Explore
messagesfromearth.wordpress.com
If we could shrink the Sun to the size of this
balloon, how big would the Earth be?
Our Solar System
kiroastro.com
What is one way to
measure a planet or star?
By the Diameter of the
sphere…
Diameter of a planet…
Diameter of a sphere
The distance from one edge to the opposite edge
It would take 108 Earths laid side-byside to go across the Sun’s diameter
messagesfromearth.wordpress.com
findfreeclipart.com
Finding the Earth/Sun Diameter Ratio
The Earth’s diameter is
12,756,000 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
1.4 X 109 m
: 1m
: 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 to Earth
Distance
Sun Diameter
Model
.45 m
Actual 1.4 x 109 m
=
X
Model
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 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
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
3X
8
10
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:
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)
In science we call this
“Dimensional Analysis,”
in math “Unit Conversion”
60 s
1 min
60 min 24 hr 365.25 days 3.2 x 107 s
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 2nd LOG 8 ) X 3.2 2nd 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 Diameter
Model
.45 m
Actual 1.4 x 109 m
Light Year
=
X
Model
9.5 x 1015 m Actual
Cross multiply and x = 3.1 x 106 m
3.1 x
6
10
That’s 3.1 x
meters
3
10 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
Distance
Model
50 m
Actual 9.5 x 1015 m
Sun Diameter
=
X
Model
1.4 x 109 m Actual
Cross multiply and x = 7.4 x 10-6 m