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