Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem P. 4829. (March 2016)

P. 4829. Two stars of different masses $\displaystyle m_1$ and $\displaystyle m_2$ are moving in the gravitational field of each other, while there are no other forces exerted on them. At a certain moment the distance between them is $\displaystyle d_0$, and their velocities (magnitude and direction) are such, as if they revolve about their common centre of mass at an angular speed of $\displaystyle \omega_0$.

$\displaystyle a)$ What is the maximum value of $\displaystyle \omega_0$ if $\displaystyle d_0$ is the greatest distance between the two stars, and what is the minimum value of $\displaystyle \omega_0$ if $\displaystyle d_0$ is the least distance between the two stars?

$\displaystyle b)$ What is the value of $\displaystyle \omega$ if the gravitational field cannot keep the system together?

$\displaystyle c)$ What is the period when gravitation keeps the system together?

(6 pont)

Deadline expired on April 11, 2016.

### Statistics:

 15 students sent a solution. 6 points: Asztalos Bogdán, Balogh Menyhért, Blum Balázs, Fehér 169 Szilveszter, Forrai Botond, Iván Balázs, Kasza Bence, Németh 777 Róbert, Sal Kristóf, Tomcsányi Gergely. 5 points: Kovács Péter Tamás. 4 points: 2 students. 3 points: 2 students.

Problems in Physics of KöMaL, March 2016