co najmniej 12 miesiecy ksiezycowych w roku !

06.12.05, 07:08
To zadanie wymyslono dla studentow kursu astrofizyki gwiazdowej i planetarnej
2 roku w toronto, rozumiem ze ne kazdy wie co to sfera Roche'a, wiec dla
wiekszosci z was interesujace moze byc nie rozwiazanie zadania, ale sam wynik,
ktory faktycznie stosuje sie do wszystkich planet i ich ksiezycow we
wszechswiecie. Dla nieustraszonych: promien sfery roche'a planety to po prostu
((m/3M)^(1/3))a, gdzie m=masa planety, M=masa gwiazdy, a "a" to odleglosc
gwiazda-planeta. dla dowodu nic wiecej nie trzeba wiedziec, oprocz prawa
keplera oczywiscie.
przyjemnego dowodu.


"UTSC students disprove a hoax, claim
at least 12 moon months per year anywhere in the universe"

"An alleged message from an extraterrestrial civilization deciphered by a UTSC
dormitory resident Non E. Sutsch using his laptop hooked up to a satellite
dish via his stereo equipment, appeared yesterday on UTSC intranet and quickly
gathered attention inside and outside the campus. The message, in addition to
effusive greetings and a useful recipe for non-alcoholic cocktail from earth
worms, claimed that the E.T's are about to embark on a holiday similar to
Xmas, falling on the last, ninth moon month on their planet. However, just
one day after it started circulating, the message was shown to be a hoax by
the students in stellar/planetary astrophysics class. They demonstrated that
anywhere in the universe, there are at least 12 moon months in a year (orbital
period of a planet). This astonishing fact has so far escaped the scrutiny of
scientists and understandably raised a few eyebrows in academia.
The proof is reportedly based on the notion of Hill stability of the moon
orbit, requiring it to be within 3/11 of the so-called Hill sphere or Roche
lobe radius of the planet, as well as on the centuries-old Kepler's 3rd law.
The students illustrated their thesis by the fact that our Moon is nearly
Hill-unstable orbiting at the distance of 0.256 (somewhat less than 3/11) of
the Earth's Roche lobe radius, and completing about 13 revolutions in a year.
We eagerly await the promised publication of a full, foolproof proof."

Can you provide the proof?
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