Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem P. 4664. (October 2014)

P. 4664. Mr. Tompkins (The chief character of the book titled Mr. Tompkins in Wonderland written by George Gamow) in his dreams enters to Wonderland where the laws of physics are nearly the same as in our Universe, ,,only'' gravity differs from the usual Newton's laws. When he woke up in the morning he remembered that there are several planets revolving around the single Sun of Wonderland, and there are three ,,Kepler's laws'' which hold true:

1. The planets revolve along elliptical paths, and the Sun is at the centre of these paths.

2. During the motion of the planet the ray drawn to the planet ...(unfortunately Mr. Tompkins forgot the end of this law.)

3. The period of each planet is the same (independently of the lengths of the major and the minor axes of the ellipses).

What can the law of gravity be in the physics book of Wonderland, and what may the end of Kepler's second law be?

(5 pont)

Deadline expired on November 10, 2014.

### Statistics:

 39 students sent a solution. 5 points: Asztalos Bogdán, Balogh Menyhért, Berta Dénes, Blum Balázs, Csathó Botond, Fekete Panna, Forrai Botond, Gula Miklós, Holczer András, Kasza Bence, Öreg Botond, Radnai Bálint, Sal Kristóf, Szabó 789 Barnabás, Szentivánszki Soma , Tompa Tamás Lajos, Trócsányi Péter, Wiandt Péter. 4 points: Bege Áron, Fehér 169 Szilveszter, Fülöp Erik. 3 points: 12 students. 2 points: 2 students. 1 point: 1 student. 0 point: 3 students.

Problems in Physics of KöMaL, October 2014