How Students Can Observe the Bing Bang with an 11 Inch Telescope

Hans-Otto Carmesin*, Fabian Heimann, Jan-Oliver Kahl

*Gymnasium Athenaeum Stade, Harsefelder Straße 40, 21680 Stade

Studienseminar für das Lehramt an Gymnasien, Stade, Bahnhofstraße 5, 21682 Stade

Fachbereich 1, Institut für Physik, Universität Bremen, 28334 Bremen

Hans-Otto.Carmesin@t-online.de

URL: http://hans-otto.carmesin.org

Abstract

Students at the age of 12 to 18 observed the Bing Bang on their own with a telescope of the type C11.

Additionally, they evaluated their own observations, interpreted them and deduced the underlying

theories. Furthermore, they analyzed other observations of galaxies with a red shift of Δλ/λ greater

than 0.2, these observations were awarded with the Nobel Prize in Physics 2011. From these

observations they deduced quantitative conclusions about the cosmological curvature of the universe

as well as the density of the universe and of dark matter. These results were also presented in public.

In addition, students at the age of 10 evaluated these observations in a simplified form. In this article

we report on the experiences we gained from this project, which can be transferred to other classes.

1. Introduction

Many students would like to see on their own what it

means, when adults assert that there was the Big Bang

14 Billion years ago (Muckenfuß. 1999). Until now, this

is only possible with quite large telescopes. The Orange

Lutheran High-School from Orange in California used a

reasonably small telescope, when they observed

cosmological redshifts with a 14 inch telescope (La

Pointe, 2008). However they not determined the

distance of those galaxies.

Here we present a project, in which students at the age

of 12 to 18 observed the Big Bang at the observatory of

the Gymnasium Athenaeum in Stade with an 11 inch

telescope. They achieved measuring significant and

highly significant red shifts and distances of several

galaxies. Additionally, they interpreted them

cosmologically, calculated the age of the universe and

presented their results in public.

2. Aims of the project

The Big Bang is in some way notional from the point of

view of students, because they know that no human was

an eye witness. They also know that the Big Bang is

often questioned in public. Even professors cause a stir

with the argument the Big Bang is basically marketing

(Gast, 2012). One goal of this project is therefore to

enable as many students as possible to conduct an

independent observation and analysis of the Big Bang.

For this, a small telescope is beneficial.

This means we do not favor a huge telescope that

produces as accurate data as possible. We rather prefer a

small telescope that creates repeatable, clear and

significant data.

The observation of the Big Bang was developed and

conducted by students.

Thus, we pursue the goals to develop competences,

spark interest, motivate independent work including

evaluation and stimulate talents.

Fig. 1: Spectrum of the galaxy NGC 3516 (Beare, 2007,

Kennicutt, 1992). The thick emission line above 6563 Ȧ is the

H-Alpha-line. This line was often used to determine the red

shift.

3. Composition of the teams

Two students at the age of 17 and 18 took part in the

required extension of our observatory and developed

gradually an effective technique for observing galaxies

(Heimann, 2011). About 15 students from our working

group for astronomy took part in the observations,

developed model experiments, visualizations and

explanations. They presented them in public at several

suitable occasions. Meanwhile a third team was formed

with the aim to simplify the observations and to

improve the signal-to-noise ratio.

4. Used instruments

Our telescope is a C11 from Celestron. It is mounted

on a Gemini G40 in a dome with a diameter of 2 m. For

obtaining spectra we use the Deep Space Spectrograph

DSS-7 from SBIG. It is attached on a SBIG ST-402

camera. For the navigation we use a finder scope with a

focal length of 300 mm in combination with an EOS

camera by Canon plus the telescope drive unit FS2 by

Michael Koch.

More convenient would be an automatic mount as it

was used by the Orange Lutheran High School (La

Pointe, 2008). Moreover, a camera with less dead pixels

would improve the signal-to-noise ratio.

Fig. 2: Recording of the spectrum of the galaxy NGC 3516:

Slit widths from top to bottom: 400 µm, 100 µm, 50 µm,

200 µm und 400 µm. The horizontal bright line represents

the light of the galaxy. The other vertical lines mainly

represent the light pollution in Stade. The bright pixels are

caused by malfunctions of the camera.

5. Selection of the galaxies

Since our telescope is relatively small, it is difficult to

create significant spectra (s. Fig. 1) (University

Strasbourg, 2012) of distant galaxies at all. This is also

hindered by the fact, that light pollution can't be

neglected in Stade. Therefore, we choose galaxies with

as strong spectral lines as possible. These are galaxies,

in which many young stars emerging (Beare, 2007,

Unsöld, 1999). An example is the galaxy NGC 3516 (s.

Fig. 1) (University Strasbourg, 2012).

6. Observations

Altogether, the students conducted observations on

five galaxies (s. e.g. Fig. 2). These observations

contained substantial statistical dispersion. Here, we

present observations of three galaxies in this paper, in

which the dispersion seems to be acceptable based on

visual considerations and a statistical analysis.

Recording a single spectrum took 300 s in general, 222s

in one case. We also recorded and subtracted dark

frames to compensate for dead pixels. The camera was

cooled to a temperature of -9° C to decrease thermal

noise. In the spectrograph, we used a slit with a width of

100 µm. At several observation nights, different groups

of students took part so that most members of the

astronomy working group were able to experience an

observation of the Big Bang.

Fig. 3: Recording of the spectrum of the galaxy NGC 3516:

The part with the light of the galaxy was extracted. However it

still contains light pollution. The dark line at the right presents

the absorption of the oxygen in the earth’s atmosphere.

7. Extracting the spectrum of the galaxies

To separate the light of the galaxy as accurate as

possible from the light pollution, an interval of the raw

spectrum (see Fig. 2) is taken (see Fig. 3).

8. Calibrating the spectrograph

The spectrograph was calibrated with a common Neon

lamp at the start of each observation. For this purpose,

we placed the Neon lamp in front of the telescope and

recorded a spectrum. For the calibration, we used the

absolute maximum at a wavelength of 7032 Ȧ and the

left maximum at a wavelength of 5852Ȧ (s. Fig. 4). In

this manner, we identified a clear allocation of the

wavelength which is independent of atmospheric, stellar

and galactic features.

Fig. 4: Calibration with a Neon lamp: Lateral axis: Channels

of the spectrograph. Vertical axis: Recorded intensities of the

Neon lamp. The specifications of the wavelengths were taken

from literature.

9. Verifying the recorded spectra

Comparing the spectrum of the Neon lamp with the one

of the galaxy, there is a significantly lower noise in the

recording of the Neon lamp. This confirms that the

instrument works properly. In contrast, light from

distant galaxies is overlaid by the light pollution and the

statistical noise.

To evaluate our results we developed the following

procedure:

(a) Initially, a clear horizontal line should set apart from

the light pollution, as shown in Fig. 2.

(b) To ensure that the spectrum was taken correctly, we

determine the wavelengths of two known strong lines

and compare them with literature. So the lines of

mercury at 4358 Ȧ and oxygen at 7594 Ȧ were

confirmed (s. Fig. 5). This verification is necessary due

to the used Celestron telescope. Because it is possible,

that small shifts of the mirror might occur (La Pointe,

2008). For instance, averaging two spectra could

increase the signal-to-noise ratio in principle. However,

if the maxima are shifted apart, the mean signal value is

halved. As a consequence, the observed signal-to-noise

ratio of 3 (highly significant) would decrease to 1.5 (not

significant at all). Thus not verifying the spectra might

cause a severe problem.

Fig. 5: Spectrum of the galaxy NGC 3516. The light smog is

relatively bright, especially the three lines of mercury lamps.

The letter A marks the Fraunhofer – A - line of oxygen. The

hydrogen of the galaxy NGC3516 is marked by the H-Alpha-

line.

10. Analyzing the components of the spectrum

(a) 5300 Ȧ < λ < 6300 Ȧ: Even if no galaxy and no star

in shown in the raw data, a spectrum can be analyzed.

(s. Fig. 6) This spectrum is interpreted as the sky

background and mainly contains light pollution of near

street lamps. Because this light pollution is quite strong

between 5300 Ȧ and 6300 Ȧ, this interval of λ will not

be used any more.

Fig. 6: Background: From the spectrum (see Fig. 2), a

horizontal stripe was extracted below the stripe with the light

of the galaxy (see Fig. 3). The light pollution is clearly visible.

There is no H-Alpha-Line.

(b) 6300 Ȧ < λ: At these wavelengths the intensity

reduces approximately linear. We interpret this as a

systematic error for the analysis of individual lines.

Therefore we use a linear regression (see Fig. 7) which

offers the following expression for the intensity: 6837.4

– λ∙0.5991/Ȧ. This linear term was subtracted from the

raw spectrum. (see Fig. 8).

(c) λ < 5300 Ȧ: At these wavelengths we proceed

appropriate to the wavelengths greater than 6300 Ȧ (s.

Fig. 9).

Fig. 7: Linear Regression: For analyzing single spectral lines,

there is a systematic error which was identified by linear

regression and eliminated by subtraction.

11. Determining significant spectral lines

The observed data are a good example for an analysis of

statistical spread. Since empirical data is collected and

evaluated in several fields of activities (examples are

natural sciences, engineering sciences, election analysis,

psychology, medicine or sociology), the ability of

determining statistical parameters has a high importance

for the future lives of the students. Therefore, we

conduct such analyses in our working group for

astronomy.

Fig. 8: Spectral lines and statistical errors: Vertical axis:

Signal overlaid by statistical dispersion. The absolute

maximum is the H-Alpha-Line and has a signal-to-noise ratio

of 3.24. It is therefore highly significant.

To find significant spectral lines in the linear

corrected spectra, we first calculate the experimental

standard deviation σ. For this purpose, we first calculate

the empirical variance as mean value of the squared

intensity values. Then, the standard deviation is

obtained as the square of the variance. For wavelengths

greater than 6300 Ȧ we get σ> = 96 and for wavelengths

below 5300 Ȧ σ< = 115.

From the standard deviations we calculate the

signal-to-noise ratio as the quotient of the used signal

and the standard deviation as it is usual e.g. in image

processing. According to evaluating statistics the result

is significant if the signal-to-noise ratio is greater than

1.96 σ. Appropriate to this interval is a probability of

error of 5%. A result is highly significant if the signal-

to-noise ratio is at least 2.58 σ. This interval

corresponds to a probability of error of 1%. Here the

signal is the intensity of the H-alpha line. This has a

signal-to-noise ratio of 3.2. Therefore, we have a

probability of error of 0.14 %. In the appendix, one can

find all significant spectral lines of the observations

shown in figures 7 and 8 as well as their analysis and

interpretation.

The observations of the students are thus highly

significant according to the methods of evaluating

statistics. Nevertheless, there are many improvement

opportunities, which should not be discussed here. Our

data shows that we have achieved our main aim to

provide the significant observation of the Big Bang to

many students.

Fig. 9: Spectral lines and statistical errors: Vertical axis:

Signal overlaid by statistical dispersion. The absolute

maximum is the Hg-line with 4358 Ȧ. It has a signal-to-noise

ratio of 2.18 and is therefore significant.

12. Interpretation of the observed emission line

The students realized that the only observable

significant line caused by the galaxy is the emission line

at approximately 6590 Ȧ. (See also the appendix about

significant spectral lines.) The spectrum of NGC 3516,

which is known from the literature, suggests that this is

the H-alpha line of the galaxy (s. Fig. 1). But it is also

possible, that the line is caused by the oxygen (O-III) of

the galaxy at approximately 5050 Ȧ (s. Fig. 1). To find a

clear decision, we calculated the raw counts of both

lines. (See appendix about intensities of the lines.) We

determined an intensity of the H-alpha-line of 19.81,

while the oxygen line has only an intensity of 5.52. The

ratio is 3.6. Therefore, we consider the interpretation as

highly significant.

13. Observed redshift

We showed above, that students measured the H-alpha-

line in a highly significant way. The wavelength of the

maximum is 6590 Ȧ. As one can see in Fig. 1, the H-

alpha-line is relatively thick. Accordingly, we found a

second significant line at 6601 Ȧ with a signal-to-noise

ratio of 2.34 (s. Fig. 8). Since there are no strong atomic

lines in the surrounding, we calculated the mean value

and used the resulting 6595.5 Ȧ as the wavelength for

H-alpha. The mean value between both images is 6614

Ȧ. From this we get a redshift of z = Δλ/λ = (6614 Ȧ -

6563 Ȧ)/6563 Ȧ = 0.0077, literature: 0.0087 (University

Strasbourg, 2012).

Next we compared our wavelengths 6590 Ȧ and 6601 Ȧ

obtained for the H-alpha line with the corresponding

wavelength 6614 Ȧ contained in the data of Fig. 1. For

this purpose we determined the half width of the data of

Fig. 1 and obtained 25 Ȧ. So our result seems

reasonable. But can we expect our results with our

conditions of observation? In order to investigate this

question, we modeled the spectrum that we should

obtain based on the data of Fig. 1, the light pollution at

our observatory, the size of our telescope and the

electronic noise of our camera. As a result we obtain

maxima of the intensity typically ranging from 6580 Ȧ

to 6640 Ȧ. Thus we can explain our measurements also

by computer simulations.

The wavelength of the H-alpha line is λ = 6563 Ȧ when

it is not shifted. We conducted similar observations for

the galaxy M66 and got a wavelength for H-alpha of

6583 Ȧ. The corresponding redshift is z = 0,003;

literature 0.0024 (University Strasbourg, 2012). These

results were included in our distance-velocity-diagram

for evaluation.

Fig. 10: Determination of energy flux density: At the star GSC

4391 701, top left, the software displays 20 counts

(background subtracted). At the galaxy, top right, the software

displays 32 counts (background subtracted).

14. Determination of the distance

To get a rough value of the distance of the galaxy, we

introduce the approximation that the Milky Way

consists of 100 Billion stars that all have the same

intensity as the sun. This gives a power of P = 3.85∙1037

W. Furthermore, we assume that all observed galaxies

have the same power. With our camera we observed the

energy flux density of the galaxy with (s. Fig. 10).

According to the star map Guide 8 this star has an

apparent magnitude of m = 11.15. From this, we

calculate the energy flux density S = 1367 W/m2*10

-

0.4*(m+26.83) = 0,879pW/m

2 (Unsöld, 1999). Therefore, the

galaxy has an energy flux density of S = 0.879pW/m2 ∙

32/20 = 1.41 pW/m2. Because of that the distance of the

galaxy, is d = [P/(4πS)]0,5

= 0.156 Billion light years

(literature: 0,12 Billion light years (La Pointe, 2008);

discrepancy 30%). Using a survey, we investigated the

error of the distance that one should expect in general

and we obtained an error of 33.8 %, see worksheet in

the appendix.

In the same way, we estimated the distance for the

galaxy NGC 3227: d = 0.06 Billion light years. We also

included these in our Hubble diagram (Unsöld, 1999) (s.

Fig. 11).

Fig. 11: Velocity-Distance-Diagram: Milky Way (bottom left),

M66 (center left), NGC3227 (center right, SNR =1,55) and

NGC3516 (top right). The graph is nearly linear. The slope is

20 Gy (Gigayears) and corresponds to the so-called age of the

universe (Literature: 13Gy to 20Gy (Unsöld, 1999)).

15. Creating a distance-velocity-diagram

The redshift z = Δλ/λ is equal to the velocity v of the

galaxy in light years per year or in the units of c. This

was derived by students, see below. We plot the velocity

v against the distance d. The graph is almost a line

through the origin (s. Fig. 11). The proportionality

between the distance d and the velocity v is called

Hubble’s Law (Unsöld, 1999). The gradient d/v gives

the age of the universe. It is approximately 20 Billion

years (literature: 13Gy to 20Gy (Unsöld, 1999) or rather

13.72 Gy (Freedman, 2009)). As a comparison, students

determined the age of the universe with distances from

the literature and with self-measured redshifts, like it

was done by the students of the Orange Lutheran High

School (La Pointe, 2008). The result was 15.8 Gy.

As expected our distance determination is less accurate

than the determination of the redshift.

16. Conception of the astronomy evenings

Our public astronomy evenings address a broad

audience and a variety of themes. We held one

astronomy evening concerning the Big Bang only. The

students of the working group hold several lectures. In a

first section, a general understanding of the Big Bang

was established, whereas in a second section we

develop a mathematical and theoretical understanding.

17. Model experiment: Distance measurement

A model experiment for distance measurement starts

with a luxmeter. Attendant children were asked whether

it is brighter in front of a beamer or at the wall. Even 10

years old students supposed that the intensity of the

light is high in front of the beamer and decreases at

larger distances. The children also measured this with a

luxmeter and with the light sensor of a smartphone.

From this, one can see that you can calculate the

distance to the source of light after measuring the

intensity at an arbitrary point. For the older students, we

showed in the break at an experimental station that the

intensity is proportional to the inverse square of the

distance.

Fig. 12: Water waves spread behind a hole (TU Clausthal

2013).

18. Model experiment: Wave nature of light

In order to illustrate the wave nature of light, we

presented water waves behind a hole (s. Fig. 12) and

laser light behind a hole (s. Fig. 13). Both spread behind

a hole and this similarity suggests the wave nature of

light. Moreover Fig. 13 suggests that the wavelength

can be determined from the color of the light.

Fig. 13: Light spreads behind a hole.

19. Model experiment: Discrete atomic spectra

Next students investigated the spectra of several gas

lamps with a hand spectroscope. In particular they

investigated spectra of a neon lamp, an energy saving

lamp using mercury and a hydrogen lamp. So they

developed the competence to identify a material using

spectra. Conversely they predicted the spectrum

knowing the material emitting the light.

Students of class 7 or higher additionally took a

spectrum of the star Vega. They concluded by

comparison with the other spectra that in a star there is

rarely mercury but much hydrogen. In particular, they

asserted that the light of hydrogen contains the

distinctive H-alpha line and that it has a wavelength of

6563 Ȧ.

Fig. 14: Increase of the wavelength behind a swimming duck

(Carmesin, 2013).

20. Model experiment: Doppler shift

Next the students discovered the increase of the

wavelength behind a moving source from a photo of a

swimming duck (s. Fig. 14) or alternatively from a

swimming toy duck propelled by a motor.

Fig. 15: Worksheet for the development of the Doppler shift

formula v = c∙z.

21. Model experiment: Doppler shift formula

Next the students of class 7 or higher developed the

Doppler shift formula v = c∙z using a work sheet (s. Fig.

15).

22. Cosmology without forces

To get a simple general interpretation of the observed

data1, we roughly approximated the results for the

galaxy NGC 3516 to get simple numbers and units. The

galaxy departs from earth with a velocity 100 Zm/Gy.

That means the galaxy increases its distance by 100

Zetameter every Gigayear. The current distance is:

Distance today: d = 1400 Zm

At this step the 10 year old students calculated the

distance of the galaxy one Gigayear ago:

Distance one Gy ago: d = 1300 Zm

Thereupon the students calculated the distance of the

galaxy two Gigayears ago:

Distance 2 Gy ago: d = 1200 Zm

Afterwards they calculated the distance three Gigayears

ago:

Distance 3 Gy ago: d = 1100 Zm

Subsequent they calculated the distance of the galaxy 4

Gigayears ago:

Distance 4 Gy ago: d = 1000 Zm

This was continued in the same way. In the penultimate

step they calculated the distance of the galaxy 13

Gigayears ago:

Distance 13 Gy ago: d = 100 Zm

Finally they determined the distance of the galaxy 14

Gy ago:

Distance 14 Gy ago: d = 0 Zm

In this way the 10 year old students discovered that the

galaxy was here 14 Gigayears ago.

At this step already 10 year old students asked, what the

students of the astronomy working group found out

about the other galaxies. We regarded the galaxy NGC

3227 as another example and also used similar

simplified data. For this galaxy, we got a velocity of 50

Zm/Gy and a distance of 700 Zm. In the same way as

above, the 10 year old students quickly found out that

the galaxy was here 14 Gigayears ago. In this way the

10 year old students discovered that all galaxies moved

away from here at the same time, they discovered the

equality of start times.

1 See Carmesin 2012a for more details.

The 10 year old students liked most the model of a glass

that falls down on the floor and all cullets move away in

different directions with different velocities. The cullets

correspond to the galaxies. They also start at the same

time and the pieces with a higher velocity will have a

larger distance (s. Fig. 11).

Students from age 11 to 14 recognized without difficulty

that the distance is proportional to the velocity. This

proportionality is also very useful for Math lessons

(Carmesin 2002).

For the beginning of the expansion we introduced the

term Big Bang. Since we only have observations for the

time after the Big Bang, we call the time elapsed after

the Big Bang the age of the universe τ.

Fig. 14: Glass model fort the Big Bang: The picture sequence

presents a glass falling to bottom and brakes into pieces. Top:

the glass is far above the bottom. Second picture: the glass

approaches the bottom. Third picture: the glass just arrives at

the bottom. Bottom: the glass brakes into pieces.

23. Cosmology with gravitational forces

Initially, we considered a spherical volume with the

radius R, the mass M and an expansion velocity of the

universe of v=ΔR/Δt (Harrison 1990). For this, we used

the energy term for a sample mass m (s. Fig. 15). The

students recognized that a football shot from the earth

vertically has an energy term with an identical structure.

Here we have the mass of the ball m, the mass of the

earth M, the distance between the ball and center of

earth R and the velocity v of the ball. The students

concluded that there are generally three possibilities:

1) If the initial velocity is lower than the escape

velocity, the ball will return. This correlates to

a universe that first expands and then collapses.

2) If the initial velocity is higher than the escape

velocity, the ball will not return. This correlates

to a universe that expands continuously.

3) The third possibility is the borderline case that

the initial velocity equals exactly the expansion

velocity and the ball will not return.

Fig. 15: Text on blackboard: Cosmology with gravity.

24. Cosmology with curvature of space

The students analyzed the curvature of space using the

example of the earth. Here they examined the

consequences for the GPS. This is presented in another

article in detail (Carmesin, 2012b). The students were

able to transfer the results to cosmology:

They knew from the Schwarzschild Metric that

mass or energy curves the space hyperbolically.

Therefore, the space should be curved hyperbolically if

the energy is positive. If the energy is zero, the space

should be flat. If the energy is negative and therefore the

expansion restricted, the space should be curved

elliptically. This means a sphere like curvature. A

derivation for students is shown in the appendix.

Fig. 16: Text on blackboard: Cosmology with density of

vacuum.

25. Cosmology with a vacuum mass

In Mathematics, the properties of space are described

axiomatically. But the example of a curved space shows

that the properties of space must be measured. This

suggests that we also cannot assume the density of

space ρV, but have to measure it. Accordingly, we

extended the above cosmology with gravitational forces

in such a way that the mass of the vacuum MV is added

to the mass of the galaxies MG (Carmesin, 2002). We

deduced a term for the potential energy (s. Fig. 16). The

students also plotted this term. They conducted a

functional analysis discovering the local maximum and

calculated that at the maximum the density of matter ρM

= MG/(4/3πR3) is twice as large as the density ρV of the

vacuum. From this, they concluded that in the special

case of a vanishing velocity there is an unstable balance

in which the universe neither expands nor contracts.

Furthermore they concluded that the universe will

expand in an accelerated manner, if the density of matter

is less than twice the density of the vacuum. In contrast

the universe will contract in an accelerated manner, if

the density of matter is higher than twice the density of

the vacuum. They deduced that one can estimate the

density of vacuum by measuring the acceleration of the

galaxies relative to the earth.

26. Cosmology with a vacuum mass: Friedmann-

Lemaitre Equations

To get any demanded acceleration, the students

determined the force F = m∙R‘‘ that affects a sample

mass m as the negative derivative of the potential

energy that was calculated above:

m∙M∙G/R2 + 8πG/3 ∙ m∙ρV∙R = m∙R‘‘

Rewriting this equation gives one of the two Friedmann-

Lemaitre Equations (Unsöld, 1999):

R‘‘/R = 4πG/3 ∙ (2ρV – ρM)

The students instantly recognized at this step the above

conditions for the non-accelerated universe.

Additionally, they recognized from the algebraic sign

that the vacuum density accelerates the expansion, while

the density of matter decelerates it.

From the above cosmology with gravitational forces the

students know that they need the term for the energy of

a sample mass m for the curvature of space of the

universe and establish the energy term:

E = m∙(R‘)2/2 - m∙M∙G/R - 4πG/3 ∙ m∙ρV∙R

2

Rewriting this equation gives:

(R‘/R)2 = 8πG/3 ∙ (ρV + ρM) – k∙c

2/R

2

Here we substituted the normalized energy k = -

2E/(mc2). This is the second Friedmann-Lemaitre

Equation. Since the students knew that energy/mass

leads to a curvature of space, they interpreted it as a

quantity that describes the curvature of the universe.

They explained the 3 general cases shown above.

Fig. 17: Velocity-Distance-Diagram: Horizontal axis: Velocity

v in lightyears per year or v in c or redshift z of a galaxy.

Vertical axis: Distance d of a galaxy in Gly. The galaxies with

z below 0.01 have been observed by the students. The galaxies

with 0.01 < z < 0.3 have been investigated with infrared

radiation (Freedman, 2009). This includes the galaxy at z=0.2

with d = 2,8 GLy. The galaxy at the top right has a redshift of

0.46 and a distance of 11.15GLy (Riess, 2000).

27. Cosmology with a vacuum mass: evaluation

To get easier data we introduced the scaled density:

Ω = ρ/ρk with 4πG/3∙ρk = 0.0028/Gy2

This is equal to ρk = 10-26

kg/m3 because Gy means 1

Gigayear. So the Friedmann-Lemaitre Equations take

the following form:

R‘‘/R = 0.0028 ∙ (2ΩV – ΩM)/Gy2

(R‘/R)2 = 0.0056 ∙ (ΩV + ΩM)/Gy

2 – k∙c

2/R

2

The students wanted to estimate the three unknown

parameters: density of the vacuum ΩV, density of matter

ΩM and curvature parameter k. For this, they used recent

data of galaxies with high redshifts, which were

awarded with the Nobel Prize in Physics 2011 (s. Fig.

11).

Initially, the students recognized that the Hubble’s Law

is valid for redshifts less than 0.2. They highlighted

these as a straight line (s. Fig. 17). The galaxy at z=0.2

meaning v=0.2c has a distance of d=2.8 GLy. Therefore,

the slope of the line is:

d/v = 2.8/0.2 Gy = 14Gy = τ

The students set up an equation for the

accelerated motion:

R(t) = R0 + v∙t + 0,5∙v‘∙t2

Afterwards, they got the terms for R‘ and R‘‘ by taking

the derivative:

R‘ = v + v‘∙t and R‘‘ = v‘

To estimate R‘‘ = v‘ = Δv/Δt, the students accounted the

galaxy at z=0.46 (s. Fig. 17). According to Hubble’s

Law the redshift should have the following value:

v = d/τ = 0.80 c or z = 0.80

The deviation is:

Δz = -0.34 or Δv = -0.34c

Since the galaxy has a distance of 11.15 Gly and the

light came from the galaxy to the earth with the speed of

light, it was emitted at the following time:

Δt = -11.15Gy

Therefore the demanded parameter R‘‘ is:

R‘‘ = 0.34c/11.15Gy = 0.030c/Gy

Thus the quotient in the Friedmann-Lemaitre Equation

is

R‘‘/R = 0.03c/Gy/11.15GLy, thus

R‘‘/R = 0.0027/Gy2

The students divided the above term for R’ by R:

R‘/R = v/R+v‘/R∙t

Here they inserted the observed redshift for v. Further

they inserted the above estimated value 0.0027/Gy2 for

R‘‘/R = v’/R. Moreover they inserted t=d/c for the time.

For the galaxy at z = 0.2 they obtained the term:

R‘/R = 0.2c/2.8GLy+0.0027/Gy2∙2.8Gy

thus R’/R = 0.079/Gy

For the galaxy at z=0.46 they calculated accordingly:

R‘/R = 0.46c/11.15GLy+0.0027/Gy2∙11.15Gy

thus R’/R = 0.071/Gy

Since only the galaxy at z=0.46 shows a difference from

Hubble’s Law, the students set up the first Friedmann-

Lemaitre Equation only for this galaxy:

0.0027/Gy2 = 0.0028 ∙ (2ΩV – ΩM)/Gy

2

Simplifying gives the first equation for the

determination of the parameters:

0.96 = 2ΩV – ΩM

For the second Friedmann-Lemaitre Equation the

students inserted the data of the galaxy at z=0.2:

(0.079/Gy)2 = 0.0056 ∙ (ΩV + ΩM)/Gy

2 – k/(2.8Gy)

2

Simplifying gives the second equation for the

determination of the parameters:

1.1 = ΩV + ΩM – 23k

For the other galaxy (for z = 0.46) they get accordingly

the third equation for the determination of the

parameters:

0.89 = ΩV + ΩM – 1.4k

The students solved the linear system of three equations

and got the curvature parameter (literature value -0.0179

< k < 0.0081 (Riess, 2000, Freedman, 2009)):

k = -0.009

They got the density of the vacuum:

ΩV = 0.61

They also got the density of matter:

ΩM = 0.26

The students recognized that the curvature parameter is

relatively small and therefore the space as a whole can

be considered as not curved. Furthermore, the students

determined the relative ratio of the density of vacuum

(literature value 72.6 % (Riess, 2000, Freedman, 2009))

0.61/(0.61+0.26) = 70% ρV

as well as the relative ratio of the density of matter:

0.26/(0.61+0.26) = 30%. ρM

Knowing from dark matter lectures that 5/6 from the

30% of the density of matter is dark matter (literature

22.8 % (Hinshaw, 2009)) they calculated

ρ Dark Matter 25 %

The common matter described by the periodic table has

only the remaining part of (literature 4.56 % (Riess,

2000, Freedman, 2009)):

ρ Common Matter 5 %

They recognized that one does barely know anything

about 95 % of the energy or matter. Consequently there

remains much more to be discovered.

Fig. 18: Telescope with equipment.

28. Students evaluate cosmological models

The students evaluate the common cosmological models

by means of their interpretation of distant galaxies:

(a) In 1917, Einstein proposed a static universe, which

is characterized by the unstable equilibrium (Unsöld,

1999). The students disproved this with their own

observations.

(b) Between 1922 and 1924, Carl Wirtz discovered the

relation between distance and the redshift. In this way

he derived and interpreted a model of an expanding

universe (Wirtz, 1922, Wirtz, 1924, Appenzeller, 2009,

Unsöld 1999). The students confirmed this by

observation.

(c) In 1917 de Sitter introduced a model with a

vanishing density of matter (Unsöld, 1999). The

students disproved this with their own observation.

(d) In 1922 using the densities of matter and vacuum,

Friedmann introduced his well-known cosmological

equations. In 1927, Lemaitre proposed a corresponding

equation independently (Unsöld, 1999). This model was

confirmed by the students.

(e) From approximately 1930 to 1998, the so-called

standard model has been popular (Unsöld, 1999). This

assumed vanishing density of vacuum. The students

disproved this with their evaluations of observations

(Riess, 2000).

29. Experiences

The students from age 11 to 18 were able to observe the

Big Bang on their own with a telescope of the type C11

(s. Fig. 18).

Both the measured distances and the measured red shifts

are sufficiently accurate for the discovery of the

increasing distances of distant galaxies. Moreover, the

observations are highly significant. For comparison, the

signal-to-noise ratio of 3.2 achieved by the students is

comparable to the SNR of nearly 4 announced by the

CERN in July 2012 for its discovery of the Higgs

particle (Gast, 2012) (hereby the ‘look elsewhere effect’

is included). So the students obtained the principle of

the Big Bang on their own. Also, 10 year-old students

were able to comprehend the basic principles and

students of age 11 to 18 can explain the observations

with model experiments. For the 10 year old students it

was important to use units of the metric system rather

than light years, to use simple numbers rather than the

scientific notation of numbers and to use the equality of

start times rather than the equivalent Hubble law.

The students obtained theoretical explanations at four

levels of complexity:

(a) A cosmology without forces can already be

understood by 10 year-old students. They can evaluate

the results with rounded data. Additionally, students

from the age 11 to 15 discovered and analyzed the

proportionality between distance and velocity.

(b) A cosmology with gravitational forces can be

understood by students from age 16 or above.

(c) A cosmology with curvature of space can be

qualitatively understood on the basis of the

Schwarzschild Solution. The Schwarzschild Solution

can be deduced by students of age 16 or above on their

own with linear regression (Carmesin, 2012b).

(d) Students of the age 16 or older can deduce a

cosmology with a vacuum mass on their own on the

basis of Newtonian Mechanics.

All students can present their results to the public.

The subject of the Big Bang is of interest for many

people. For this reason the students of the astronomy

working group were dedicatedly concerned with

relatively difficult observations, model experiments and

theories. This is also the main reason why many people

came to our Astronomy-Evening and discussed

questions and ideas thoroughly with us in the break.

This immense interest was shown by a variety of

audiences at different events. Additionally, we noticed

that the participants learned many sophisticated skills

concerning Mathematics, Physics and science in

general.

30. Prospect

Currently, students conduct observations to decrease the

signal-to-noise ratio. Other students optimize our

equipment in order to enable as many people as possible

to observe the Big Bang on their own. Meanwhile,

Hans-Otto2 prepared an alternative approach in which

students discover the necessary physical laws with

model experiments and simulate the measurements

using Stellarium as well as the self-made software

Spectrarium for the simulation of astronomic

spectroscopy. Based on either of the two alternatives,

the students can independently establish their own

opinion on the origin of the universe.

31. Summary

In the project presented above, students from age 12 to

18 observed the Big Bang leading to highly significant

results. They interpreted their self-obtained results on

various levels of complexity. Even 10 year-old students

were able to analyze selected data both qualitatively and

quantitatively in the context of a cosmology without

forces. Students at the age of 16 or above were able to

develop a cosmology with gravitational forces, a

cosmology with curvature of space and one with a

density of vacuum. They were also able to review the

common cosmological models and evaluate up-to-date

observational data appropriately and quantitatively. In

particular, they discovered that matter which can be

described by the table of elements only amounts 5% of

the total matter and energy. They concluded that there

remains a lot to be discovered by future generations.

A largely independent work of the students was

possible because they deduced cosmological models on

various levels of complexity: These ranged from

Geometry over Newtonian Theory to results of the more

complicated Theory of General Relativity. So, each

student could pick his individually adequate level of

complexity. This focus to individually discover the

essential content progressively is favored due to reasons

of learning theory, cognition theory and epistemology

(Rosenstock-Huessy, 1968).

Literature

Appenzeller, I. (2009): Carl Wirtz und die Hubble-

Beziehung. Sterne und Weltraum, 44-52.

2 Lessons many worksheets and the software Spectrarium

have been prepared by Hans-Otto and can be requested.

Beare, R. (2007): Specimen Spectra for Bright Galaxies.

Retrieved from

http://www.docstoc.com/docs/14258744/Template-

spectra-for-galaxies-as-used-by-SDSS

Carmesin, H.-O. (2002): Urknallmechanik im

Unterricht. In: Nordmeier, V. (Ed.): Conference-CD

Fachdidaktik Physik. ISBN 3-936427-11-9.

Carmesin, H.-O. (2003): Einführung der Wellenlehre

mit Hilfe eines Kontrabasses. In: Nordmeier, V. (Ed.):

Conference-CD Fachdidaktik Physik. ISBN 3-936427-

71-2.

Carmesin, H.-O. (2012a): Schüler beobachten den

Urknall mit einem C11-Teleskop.

Internetzeitschrift: PhyDid B - Didaktik der Physik -

Beiträge zur DPG-Frühjahrstagung (ISSN 2191-379-

DD21p03).

Carmesin, H.-O. (2012b): Schüler entdecken die

Einstein-Geometrie mit dem Beschleunigungssensor.

Internetzeitschrift: PhyDid B - Didaktik der Physik -

Beiträge zur DPG-Frühjahrstagung (ISSN 2191-379-

DD15p06).

Carmesin, H.-O. (2013): Jugendliche beobachten den

Urknall in der Schulsternwarte. MINT Zirkel,

September/October 2013, p. 18.

Freedman, W. et al. (2009): The Carnegie Supernova

Project: The first Near-Infrared Hubble-Diagram to

z~0,7. Astrophys.J.704:1036-1058. Retrieved from

http://arxiv.org/abs/0907.4524v1

Gast, R. (2012). Hässliches wird passieren. ZEIT, 16,

38.

Gast, R. (2012): Das Gespenst von Genf wird greifbar.

Spektrum der Wissenschaft, Sonderausgabe Higgs Juli

2012, 1-4.

Harrison, E. (1990): Kosmologie. 3rd Ed. Darmstadt,

Verlag Darmstätter Blätter.

Heimann, F & Kahl, J. O. (2011). Beobachtung der

Urknalldynamik mit einem 11-Zoll-Teleskop. Jugend

forscht Thesis.

Hinshaw, G.. et al. (2009): Five-Year Wilkinson

Microwave Anisotropy Probe (WMAP) Observations:

Data Processing, Sky Maps, & Basic Results.

Astrophys.J.Suppl.180:225-245. Retrieved from

http://lanl.arxiv.org/abs/0803.0732v2

Kennicutt, R. (1992): A Spectrophotometric Atlas of

Galaxies. The Astrophysical Journal Supplement Series,

79, 255-284.

La Pointe, R. et al. (2008). Measuring the Hubble

Constant Using SBIG’s DSS-7. Society for

Astronomical Sciences, 137-141. Retrieved from

http://adsabs.harvard.edu/full/2008SASS...27..137L

Muckenfuß, H. (1995). Lernen im sinnstiftenden

Kontext. Berlin, Germany, Cornelsen.

Riess, Adam G. et al. (2000): Tests of the Accelerating

Universe with Near-Infrared Observations of a High-

Redshift Type Ia Supernova. Astrophys. J. 536, 62,

Retrieved from http://lanl.arxiv.org/abs/astro-

ph/0001384v1.

Rosenstock-Huessy, E. (1968): William Ockham. In:

Grolier (Ed.): The American Peoples Encyclopedia Vol.

19. New York: Grolier.

TU Clausthal: URL: http://www2.pe.tu-

clausthal.de/agbalck/biosensor/wellen-le-g-005.jpg.

Retrieved 2013.

University Strasbourg (2012). Astronomical Database

SIMBAD. Retrieved from http://simbad.u-

strasbg.fr/simbad/

Unsöld, A. & Baschek, B. (1999). Der neue Kosmos.

6th Edition, Berlin, Springer.

Wirtz, C. (1922): Die Radialbewegungen der Gasnebel.

Astronomische Nachrichten 215, 19.

Wirtz, C. (1924): De Sitters Kosmologie und die

Radialbewegungen der Spiralnebel, Astronomische

Nachrichten 222, 21. Retrieved from

http://articles.adsabs.harvard.edu/cgi-bin/nph-

iarticle_query?1924AN....222...21W&amp;

data_type=PDF_HIGH&amp;whole_paper=YES&amp;

type=PRINTER&amp;filetype=.pdf

Acknowledgements

We are grateful to the EWE-foundation and its von

Klitzing-award. The money of the award was used to

buy the equipment necessary for our observation of the

Big Bang. We are grateful to the pupil Marvin Ruder

who took part in observations and investigated noise

sources of out equipement.

with

P = 13 quadrillion YW

Dmeasured Dtheoretical Error

Nr. F in fW/m^2 in Zm in Zm in %

1 180,07 3113 2397 23,0

2 5,82 32805 13327 59,4

3 4,50 11882 15170 27,7

4 3,79 19490 16511 15,3

5 2,95 34900 18724 46,3

6 2,61 31037 19915 35,8

7 2,20 37701 21670 42,5

8 1,96 46868 22973 51,0

9 1,85 35459 23625 33,4

10 1,64 32756 25099 23,4

11 1,45 40048 26722 33,3

12 1,46 66121 26616 59,7

13 1,21 31105 29281 5,9

14 1,17 49863 29722 40,4

15 1,11 44772 30500 31,9

16 1,02 35010 31912 8,8

17 0,95 51606 32973 36,1

18 0,91 46852 33756 28,0

19 0,89 26715 34049 27,5

20 0,81 25132 35641 41,8

21 0,76 53544 36844 31,2

22 0,73 45672 37542 17,8

23 0,69 61605 38709 37,2

24 0,70 61490 38348 37,6

25 0,67 74472 39360 47,1

26 0,65 47206 39852 15,6

27 0,65 56496 40037 29,1

28 0,63 39849 40389 1,4

29 0,58 28565 42149 47,6

30 0,60 50445 41396 17,9

31 0,58 50306 42376 15,8

32 0,53 50468 44082 12,7

33 0,47 58323 46985 19,4

34 0,44 53009 48349 8,8

35 0,42 55370 49369 10,8

36 0,46 58114 47258 18,7

37 0,43 65951 48909 25,8

38 0,45 39508 47754 20,9

39 0,39 80315 51529 35,8

40 0,41 53429 50261 5,9

41 0,41 50468 50522 0,1

42 0,34 52125 55346 6,2

43 0,34 47300 55506 17,3

44 0,34 46925 55063 17,3

45 0,33 68811 56013 18,6

46 0,32 76774 56650 26,2

47 0,29 55686 59994 7,7

48 0,27 46368 61882 33,5

49 0,28 24517 61320 150,1

50 0,28 58332 60432 3,6

51 0,28 62698 60997 2,7

52 0,22 50182 68567 36,6

53 0,21 61555 70319 14,2

54 0,24 84931 65429 23,0

55 0,19 27170 74355 173,7

56 0,21 80281 70423 12,3

57 0,17 76787 77525 1,0

58 0,16 85419 79911 6,4

59 0,15 55612 83896 50,9

60 0,13 66369 90245 36,0

61 0,10 39021 102068 161,6

62 0,07 46723 124751 167,0

Means 49217 46827 33,8

Appendix

Worksheet, Astronomy Group,

Dr. Carmesin, 2013

Table:

Columns 1-3: Galaxy Survey [1].

Column 4:

Dtheoretical = (P/(4πF))0,5

with:

P = 13 quadrillion YW or

P = 13∙1036

W

Column 5: |Dmeasured – Dtheoretical|∙100%

Exercise:

Control Dtheoretical for Nr. 1.

[1](Yee, H. K. C. u. a.: The CNOC2 Field

Galaxy Redshift Survey. I. The Survey and

the catalog for the Patch CNOC 0223+00.

The Astrophysical Journal Supplement Series,

129, 475-492, 2000.