A Bit Of Geodesy
Surveying means to correlate many (protruding) points in a certain
terrain. Starting from an (arbitrary) origin point, distances,
angles and differences in elevation are measured. This is how each
country is covered with a net of surveying points (TP,
trigonometric point) forming a framework of triangulars and fitting
perfectly to the form of the earth's surface. One of the nets
existing in Germany is the "Deutsche Hauptdreiecksnetz" (German
Basic Triangular Net, DHDN) providing the basis for surveying in
Germany. The centre (origin) of the DHDN is (was) Rauenberg TP in
Berlin-Tempelhof.
This reticule might be very useful for land registry offices.
However in a global context you can't derive much from it, as the
definition of a position in geographic coordinates is not possible
ad hoc. To do this you have to find a relation between this net of
triangulars and its position and orientation on the earth.
Traditionally, information about the position was derived from
correlating the earth's rotation to star positions. This is why the
Rauenberg TP had close ties to the former Berlin observatory: The
position measured in the observatory was transferred
trigonometrically to the TP. For the correct orientation of the
DHDN ("How do I have to turn the reticule around its origin to get
the correct results?") the azimuth (angle to the North) to another
fixed point in Berlin was exactly defined. Also this point had been
arbitrarily chosen, probably it is the church spire of St. Mary's
(Marienkirche).
Geodatic Datum
The earth is not a disk. However the earth is not a globe either,
sad but true. But what on earth it is then? The answer "A potato!"
would probably be closest to reality. This potato is called
"geoid". A part of the surface of this potato is e.g. Germany. To
survey this part one looks for a geometric body, an ellipsoid (kind
of "flat egg"), that fits best to this part of the geoid. The
parameters defining such an ellipsoid (length of axis, oblateness,
deviation of its centre from the earth's centre) is generally
called a "(map) datum". In the case of Germany the Bessel ellipsoid
is used, defined by the surveying mentioned above and providing a
good approximation. This is (was) called the "Rauenberg Datum".
Another datum known to every geocacher is e.g. WGS 84. It is
possible to convert the coordinates given in a certain datum to
another datum. Converted to the Rauenberg datum the cache
coordinates stated above would be N 52° 27,200' E 13° 22,082'.
When the marking of the Rauenberg TP was destroyed after 1910, it
was intended to define the Helmertturm TP situated in the West on
the Telegrafenberg close to Potsdam as the new German origin point.
However in the end it was decided only to allocate the geographic
coordinates in the Rauenberg system to this point, what meant that
a laborious conversion of all TPs to the new system was avoided and
that this step did not have any practical consequences. However it
brought about the not completely correct name "Potsdam Datum" in
the postwar period.
Your Task
Go to Rauenberg in Tempelhof (don't forget to bring a calculator).
Next to the coordinates stated above you will find the memorial
tablet for the Rauenberg TP. To find the coordinates of the cache
do the following calculations:
- Distance: Calculate the Western longitude of the Ferro
Observatory (Sternwarte). If the earth had a diametre of
247 m, which distance (in m) would
correspond to this angle on the equator?
- Azimuth: Look to St. Mary's church (Marienkirche). Add
1,25°.
The task is set in a way that you can solve it at Rauenberg TP
using a calculator that features the number pi. Alternatively you
know pi by heart ;-). You don't have to search the internet, but of
course also there all relevant information can be found.