**Ideas for Astronomy in A Level Physics**

Hayley Flood of the National Space Academy

http://nationalspaceacademy.org/

To get across the idea of the relative size of the Earth and Moon use a basketball for Earth and a tennis ball for the Moon.

The distance between the Earth and the Moon is 9.5 times the circumference of the Earth. Use string wound around the basketball to get this across. Students nearly always get the distance wrong so unwinding the string to the desired length gets the point across. The average distance to Mars is 600 times the circumference of the Earth.

**A model to Explain Hubble’s Law**

Can a balloon model of an expanding Universe explain Hubble’s Law.

Apparatus: balloon; 30cm ruler; 20cm piece of string; stop watch/clock; permanent marker pen.

1) Blow up a balloon so that it is 10cm across. It should not be fully inflated. Put a clip on the balloon so that it holds its air.

2) Use a marker pen to draw some galaxies onto the balloon. Each galaxy can be about 1 cm across. They should be separated by about 4 times their size.

3) Put a number from 0 to 9 on ten of the galaxies.

4) Make a table like this for your results.

5) Measure the distance from galaxy 0 to each of the other galaxies. Record your results in the second column of the table labelled “At the start”.

6) Undo the clip and hold the balloon.

7) Start the stop clock and inflate the balloon a bit more using one large, slow puff. Stop the clock and clip the balloon again.

8) Record the time it took to inflate the balloon.

9) Complete the table by:

Measuring the distance from galaxy 0 to each of the other galaxies;

Calculating (D – d), how much each galaxy moved away from galaxy 0;

Working out the speed of the galaxy during inflation.

10 ) Plot a graph of speed against distance for the galaxies.

11) Draw a best fit line through your points.

12) Describe what your graph shows.

13a) Calculate the gradient of your graph, this gives a value for the Hubble constant of your balloon Universe. What are the units?

13b) You can use this to calculate the age of your balloon Universe using:

Age = 1/Hubble constant

What is the age of your balloon Universe? How does this compare with the time it took you to inflate the balloon?

13c) Compare your balloon Universe to the real Universe. Is it a good model? What are the good and bad points of the model?

13d) The fabric of the balloon is two dimensional (although it occupies three dimensions). How is this different from the fabric of space?

14) Use a Value of H = 75 km/s/Mpc to determine the age of the Universe.

Data: 1 pc = 3.1 x 10^{13}km; 1 y = 3.2 x 10^{7}s

Hints:

We first need the value of 1 Mpc in km.

We then need to change the unit of H from km/s/Mpc to km/s/km so that the km will cancel. To do this, we divide by the number of km in 1 Mpc.

We now need to invert this to give the estimated age of the Universe in seconds, and then convert this into years.

**My results**

Time for inflation = 4.9 seconds

My Universe’s Hubble constant is the gradient of the above graph. It equals (1.02- 0.2)/(5-1) = 0.205 s^^{-1}

The age of my Universe is 1/H = 1/0.205 = 4.88s which is in good agreement with time of inflation of 4.9 seconds.

The real Hubble constant (at the moment) is 75 km/s/Mpc

1 Mpc = 3.1 x E^{19}km

75km/s/3.1 x E^{19} km = 2.42 x E^{-18}s^^{-1}

Age of the actual Universe is therefore believed to be 1/2.42 x E^{-18}

= 4.13 x E^{17} seconds = 1.29 x E^{10} years