Models to visualize size and distance in the universe

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

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

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. {
Click here if you want to cheat, that is if you want to see what the diagram with those 'tracking' lines would look like, before doing the tracking yourself.}
         Could the fragments have all come from the same place? Even if the answer is Yes, they could, it doesn't mean they actually were once all the same common point together.
         Whether they actually were all together depends on whether they were all at the common location at the same time, meaning, the same amount of time back from Now.

To get the answer to that, fill in the table below.

2. Length of
3. Speed of
4. Distance to
common point
5. Time from
common point

First, in the diagram, number the streaks from 1 to 13.
COLUMN 2: LENGTH OF STREAK Then, for each streak, measure the length of the streak. Multiply by the scale factor, and enter the result (preferably in meters) in column 2, "Length of streak."
COLUMN 3: SPEED OF FRAGMENT Since this is how far the firecracker fragment traveled in 1/50 of a second (0.02 sec), divide your entry in column 2 by 0.02sec, and you will get the speed of the fragment. Enter that into column 3, "Speed of fragment". You will find that some fragments traveled with much greater speed than others.
COLUMN 4: DISTANCE FROM COMMON POINT Now measure in the same way you did for column 2, the length of the dotted line from the crossing point to the beginning of the streak. Multiply by the scale factor, and enter the result in column 4, "Distance from common point."
COLUMN 5: TIME FROM COMMON POINT If you divide the distance from the common point by the speed of the fragment (use your value from column 3), you will find how long the fragment had been on its way since it was at the common point when the camera began to record the streak. Enter that value in column 5, "Time from common point."

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?

(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?

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

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