Answers for Models to visualize size and distance in the universe

# 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] : 

 The SCALE of this model is: [4.8x1010] :  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 ] : 

 The SCALE of this model is: [ 6x1012 ] :  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 ] : 

 The SCALE of this model is: [ 2.5x1023 ] :  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 observedis 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 ] : 

 The SCALE of this model is: [ 143] :  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 0o as that of fragment #1      the track at 20o as that of fragment #2      the track at 45o 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 1.29m64.5m/s7.72m0.119sec
20.60m30.0m/s3.72m0.124sec
31.86m93m/s11.44m0.123sec
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