1. 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

2. 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,

3. 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

4. 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/m2
(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

5. 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

6. 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.

7. 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

8. 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∙R2
Rewriting this equation gives:
(R‘/R)2
= 8πG/3 ∙ (ρV + ρM) – k∙c2
/R2
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)/Gy2
– k∙c2
/R2
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)/Gy2
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)/Gy2
– k/(2.8Gy)2
Simplifying gives the second equation for the
determination of the parameters:
1.1 = ΩV + ΩM – 23k

9. 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

10. 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.

11. 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.

12. 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.