Physics in Funnels

Grzegorz Karwasz, T. Wroblewski, Anna Niedzicka,
W. Niedzicki, Mauro Brunato

Proceedings of the Third International GIREP Seminar
"Informal Learning and Public Understanding of Physics",
Ljubljana, Slovenia, 5-9 september 2005.

GIREP's emblem is a funnel - this seems to be a parabolic funnel.
"Gravitational" funnels are well known for illustrating motion of
planets or collecting spare coins at London Stansted airport.
Orbits in these funnels are, to the first approximation,closed.
This reflects particular form of the gravitational potential,
1/r and is important, say, for the constancy of the climate on
Earth. In real gravitational funnels the orbits are not exactly
closed, due to finite dimensions of coins,their spin motions and
not exact 1/r potential. If you take any funnel, orbits are open
immediately, not into the "first" approximation. The only other
potential assuring closed orbits is the harmonic one, r^2 , i.e.
a ball kept by springs. This is due to a particular property of
the Hamiltonian for these two interactions, which is transformable
into a linear function of the action [3].
A different field than 1/r explains, as shown by Einstein, the
precession of the Mercury orbit. Precisely, one should speak not of
the different mathematical form, but a different measure of the
gravitationally deformed "r". For computer fans we show a programme,
in which one can experience difficulties in constructing a Solar
system. So funnels can be used to explain Physics, not only to
transfer it into pupils brains.