Answers for Models to visualize size and distance in the universe

Answers

JOB 2: The Earth a grain of fine sand

Step 1. Establish a scale for your JOB 2 model
SCALE = [1.2x10⁷m] / [0.25 x 0.001m] = [4.8x10¹⁰] : [1]

The SCALE of this model is: [4.8x10¹⁰] : [1]
The Scale factor is 4.8x10¹⁰

Question (A): How large will the sun be in your JOB 2 model?
Solution: Diameter of the sun in your model is: 1.5x10⁹m / 4.8x10¹⁰m = .03125m

In your JOB 2 model, the sun's diameter will be .0312m or 3.125cm.
or about the size of sphere _H_ pictured on page 1.

Question (B): How far will the Earth be from the Sun in your JOB 2 model?
Solution: Sun-Earth distance in your model is: 1.5x10¹¹ / 4.8x10¹⁰m = 3.125m

In your JOB 2 model, the distance from the Sun to the Earth will be 3.125m.

Question (C): What will be the diameter of the solar system in your JOB 2 model?
Solution: Diameter of the solar system in your model is: 9.6x10¹²m / 4.8x10¹⁰ = 200m

In your JOB 2 model, the diameter of the solar system will be
200 meters, or 2 times the length of a football field.

Question (D): How far is it to Alpha Centauri in your JOB 2 model?
Solution: Distance to Alpha Centauri in your model is: 4.3x10¹⁶m / 4.8x10¹⁰ = 896,000m

In your JOB 2 model, the distance to Alpha Cenaturi, the nearest star (other than the sun), will be 896,000m or 560 miles.
Name a place that is about that far from your home town
_Chicago to Kansas City_

JOB 3: The Sun a grain of fine sand

Step 1. Establish a scale for your JOB 3 model
Make a ratio of the actual diameter of the sun to the diameter of the model of the sun
(Be sure units are the same in the numerator and denominator before canceling them)
SCALE = 1.5x10⁹m / 0.00025m = [ 6x10¹² ] : [1]

The SCALE of this model is: [ 6x10¹² ] : [1]
The Scale factor is 6x10¹²

Question (A): How far will the Earth be from the Sun in your JOB 3 model?
Solution: Sun-Earth distance in your model is: 1.5x10¹¹m / 6x10¹² = 0.025m

In your JOB 3 model, the distance from the Sun to the Earth will be 0.025m or 2.5cm.

Question (B): What will be the diameter of the solar system in your JOB 3 model?
Solution: Diameter of the solar system in your model is:9.6x10¹²m / 6x10¹² = 1.6m

In your JOB 3 model, the diameter of the solar system will be 1.6 meters.

Question (C): How far is it to Alpha Centauri in your JOB 3 model?
Solution: Distance to Alpha Centauri in your model is: 4.3x10¹⁶m / 6x10¹² = 7,200m

In your JOB 3 model, the distance to Alpha Cenaturi, the nearest star (other than the sun), is 7,200m or 4.8 miles.

Question (D): What is the diameter of our Milky Way galaxy in your JOB 3 model?
Solution: Diameter of the Milky Way galaxy in your model is: 1x10²¹m / 6x10¹² = 1.67x10⁸m

In your JOB 3 model, the diameter of the Milky Way galaxy is 1.67x10⁸m or 100,000 miles.

JOB 4: A scale for the whole Universe: The Milky Way galaxy a size E ball

Step 1. Establish a scale for your JOB 4 model
SCALE = 1x10²¹m / 0.004m = [ 2.5x10²³ ] : [1]

The SCALE of this model is: [ 2.5x10²³ ] : [1]
The Scale factor is 2.5x10²³

Question (A): How far is it to the Andromeda galaxy in your JOB 4 model?
Solution: The distance to Andromeda in your model is: 2x10²²m / 2.5x10²³ = 0.08m

In your JOB 4 model, the distance to the Andromeda galaxy will be 0.08m or 8 cm.
Name an object that is approximately this big _an apple_

Question (B): The farthest object observed so far (a quasar) is over 12 billion light years away. How far is it to that quasar in your JOB 4 model?
Solution: Distance to the quasar in your model is: 1.2x10²⁶m / 2.5x10²³ = 480m

In your JOB 4 model, the distance to the farthest object ever observed
is 480m; or about 5 times the length of a football field.

JOB 5: The exploding firecracker: What Hubble saw

A student was pointing her camera upward in a park during a Fourth of July firecracker show. She took a snap shot just after a firecracker had exploded. During the camera exposure the lens was open 1/50 second.
Her photo (below) shows the pattern of streaks made by the burning fragments of the firecracker during the 1/50 sec exposure.
The scale shows a line of actual length 10 meters as it would appear in the photo if it had been actually at the same height as the firecracker fragments.

Step 1. Determine the scale
Make a ratio of the actual length (10.0 meters) of the 10 meter line, to the length, "S", of the 10m line in the picture (measure "S" in cm, and convert to meters)

Note: The length "S" that you will obtain will depend on the printer used, or the screen on which you may make the measurements.

     A typical printer produces an output in which the SCALE line measures an actual length of 7.0cm. The following answers were produced using that value for the SCALE line length.
     Of course, all other measured lengths will also be affected by the output used.

     The results in column 5, however will be unaffected by the value of the SCALE line length, because the time calculated there comes from calculations in which scaled distances cancel.

(Be sure units are the same in the numerator and denominator before canceling them)
SCALE = [10m] / [length "S"] = [ 10m / 0.07m ] : [1]

The SCALE of this model is: [ 143] : [1]
The scale factor is _143_

Did all the fragments come from one place?
To answer that question, extend each fragment streak backward (with a dotted line made by a straightedge) toward where the fragment presumably originated.

Note: We designated:
     the track at 0^o as that of fragment #1
     the track at 20^o as that of fragment #2
     the track at 45^o as that of fragment #3

Fragment #	2. Length of streak	3. Speed of fragment	4. Distance to common point	5. Time from common point
1	1.29m	64.5m/s	7.72m	0.119sec
2	0.60m	30.0m/s	3.72m	0.124sec
3	1.86m	93m/s	11.44m	0.123sec
4
5
6
7
8
9
10
11
12
13

The numbers in column 5, the time from the moment when the streak was observed, back to when the fragments were all at the common point, tell a very very important story.

How long ago was the "Big Bang" of this firecracker?

the numbers in column 5 should all be about the same

(Your answer should be about 0.12 seconds)

And what does all this have to do with Edwin Hubble and the history of the Universe?

1. Did your drawing of the dotted extensions of the streaks all seem to come from a common point?
2. Did you notice that the fastest fragments (Column 3) are also those that had traveled the farthest from the common point (Column 4), and that these two quantities are roughly proportional?
3. Did it occur to you that this means that all the fragments came from a common original location, and that the time that it took each of them to get to the location at which their streaks were photographed is related to Hubble's calculation of the "age of the universe"?

Permission is hereby granted to reproduce the contents of this section for use in teaching, provided no charge or fee is accepted and provided credit is given to Cavendish Science Organization

Return to 'Scale Models of the Universe' home page.
Return to 'JOB 0' Get started on scales and models.
Return to 'JOB 1' The Earth a size E ball.
Return to 'JOB 2': The Earth a grain of fine sand.
Return to 'JOB 3' The Sun a grain of fine sand.
Return to 'JOB 4' A scale for the whole Universe.
Return to 'JOB 5' The Universe an exploding 4^th of July firecracker.

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