论文标题
通过旋转身体的直式隧道上的笔记
A note on a straight gravity tunnel through a rotating body
论文作者
论文摘要
众所周知，在非旋转地球上任意两个不同位置之间的直式隧道，其密度均匀，即最初在静止状态的物体将通过两个方向的重力隧道到达其目的地。而且，跌倒所花费的时间始终是恒定的。如果允许旋转，这些事实将不再正确。该注释的目的是得出带有球形对称重力场的旋转身体的直线隧道的必要条件。秋季时间以线性和恒定重力场的封闭形式表示。总之，将这些模型与使用地球的内部结构进行数值获得的数据进行了比较。
It is well-known that the straight gravity tunnel between any two different positions on a non-rotating Earth, which has uniform density, is traversable, i.e., an object initially at rest will reach its destination through the gravity tunnel in both directions. Moreover, the time taken to fall is always constant. These facts are no longer true if rotation is allowed. The aim of this note is to derive the necessary and sufficient condition for traversability of straight gravity tunnels through a rotating physical body with spherically symmetric gravitational field. Fall-through times are expressed in a closed form for linear and constant gravitational fields. In conclusion, these models are compared to numerically obtained data using the internal structure of the Earth.
