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"Eine halb
astronomische, halb
geografisch-geodätische Aufgabe" von Arno
Schmidt >>Peter rüttelte
herrscherlich sein Gabelzepter über die
Flämmchen, die sogleich gefällig
zischelnd höher wucherten; stieß die
Zinken in den Boden; drapierte die
verschränkten Arme dicker auf den Stiel, und
erkundigte sich tiefsinnig: „Wo
käm' man da eigentlich hin ? Wenn man
immerfort 'Der Sonn' entgegen' ginge ?"<<
Quelle: Arno Schmidt, Der Sonn' entgegen
....., in: Werke. Bargfelder Ausgabe. I/3, S.
293-311. A mathematical
astronomy problem From
a
point on the Earth, a walker starts at sunrise,
walking at a constant speed always in the
direction of the Sun, and ending at sunset. What
is the path ? Bargfeld
(Germany,
52.7039°N,
10.3459°
E)
was
the
residence
of Arno Schmidt (*1914, +1979).
Niederschrift des Textes: 1960, erstmals
erschienen in dem Band "Kühe in Halbtrauer"
(1964).
Opening this page the applet is showing
the complete path from sunrise to sunset. To walk stepwise, press the button
"Clear", and then press the key "+": The time
will increase by 10 minutes. The speed is preset to v=5 km/h, and can
be changed. Select from the menu to change the speed
v, or the time step dT. Select "Positions on/off" from the menu
to draw the position at every hour after sunrise. The calculation is performed step by
step, using the time interval selected. For
sunrise and sunset the refraction of light is
taken into account, as well as the (small) change
of the declination during the walk. Latitude 50° N, summer solstice
(δ=23.44°), v=5 km/h, path 81.7 km (dT=5 min)
Latitude 50° N, equinox (δ=0°), v=5 km/h, path 60.9 km (dT=5 min)
Latitude 50° N, winter solstice
(δ=-23.4°), v=5 km/h, path 40.4 km (dT=5 min)
Latitude 0° N (equator), summer
solstice (δ=23.4°), v=5 km/h, path 60.8 km (dT=5 min)
Latitude 0° N (equator), equinox
(δ=0°), v=5 km/h, path 60.8 km (dT=5 min)
Pressing the key "h", the time will
increase by 1 hour.
Use the keys d, or m to increase the date, or month.
daylight 16h 22m,
daylight 12h 09m,
daylight 8h 04m,
daylight 12h 07m,
daylight 12h 06m,
There is a
small difference between the curves for the step
size dT=1 min and dT=10 min.
the accuracy increases using a small stepsize dT:
| dT / min |
East / km |
North / km |
South / km |
| 60 |
35.23 |
7.68 |
-16.78 |
| 30 |
34.35 |
6.81 |
-17.63 |
| 20 |
34.02 |
6.53 |
-17.90 |
| 10 |
33.69 |
6.26 |
-18.17 |
| 5 |
33.53 |
6.12 |
-18.30 |
| 1 |
33.41 |
6.02 |
-18.41 |
At Bargfeld, on August 1, the total path length is 77.83 km, walking v=5 km/h.
A sophisticated analysis of the curve:
The evolute of a given curve is the envelope of the normals to it.
This can also be thought of as the locus of the centres of curvature.
The evolute of a circle woul be it's center.
The evolute (red curve) at Bargfeld on August 1.
Choose "Evolute from the "Select" menu.
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Der
Sonne entgegen (Wikipedia) Jean Meeus: Pursuing the
Sun. Arno Schmidt
Stiftung, Bargfeld U. Finkenzeller: Sterne und
Wortraum Arno Schmidts Berthold Schuppar: Der Sonn' entgegen
- Ein mathematisch- Wolfgang Müller: Der Lösung
entgegen - Arno Schmidts "Wanderkurve" in erster
Annäherung. Bargfelder Bote, Materialien zum
Werk Arno Schmidts, Lfg. 89-90/April 1985, S.
12-23. Susanne
Neuhäusler: Verfolgungsprobleme mit Java Pursuit
Curve (Wolfram MathWorld) Andrew
J.
Simoson:
Pursuit
Curves
for
the
Man
in
the Moone Pursuit
Curves (K. Steiner, J. Franchi, PDF) National
Curve Bank, A Simulation of Pursuit Curves Ulrich Goerdten: Arno Schmidts
'Ländliche Erzählungen'. Sechs
Interpretationen, Bangert & Metzler 2011, ISBN
978-3-924147-63-1. |
(c) 2006-2012, J. Giesen
Updated: 2012, Feb 2