Problems for the 2014 University

Problems for the 2014 University Physics Competition

Problem A:  Circumbinary

Planets

Consider two stars, one with 50% of the mass of our Sun and one equal in mass to our Sun. 

This binary star system has an orbital period of 30 Earth days. 

Where could a planet have a stable orbit in this system? 

Describe the possible stable planetary orbits.

Problem B:  A Water

Fountain

A water fountain located at the middle of a circular pondejects water straight up, and the water spreads out into a cone shape with theaxis of the cone being vertical. As the water moves, its molecules collide witheach other. Determine the probability that any molecule of the ejected waterhits the pond at the point (x, y). Assume that the fountain’s ejectionpoint is at (0, 0). From your model, determine the most probable place wherethe water lands and also the median circle, that is, that circle around thefountain inside which exactly half of the water lands.

2014年大学物理竞赛的问题

问题A：圆周行星

考虑两颗恒星，一颗太阳质量的50%，一颗太阳质量相等。这种二元星系的轨道周期为30个地球日。一个行星在这个系统中有一个稳定的轨道在哪里？描述可能的稳定行星轨道。

问题B：喷水机

位于圆形池塘中间的喷泉器将水直接向上喷射，水散布成锥形，锥体的轴线垂直。随着水的移动，它的分子相互碰撞。确定喷射水的任何分子在（x，y）点撞击池塘的概率。假设喷泉的射血点在（0,0）。从你的模型中，确定最有可能的水域以及中间圆圈，即喷泉周围的圆圈，其中正好一半的水域位于其中。