A Day of Fascination

November 19th, 2016

Yesterday was hack day at the office - where everybody on the team gets some time to learn the new things they’ve been eyeing and experiment. After learning about ReactiveX/RXJava, I sat down to lunch and continued reading Red Mars by Kim Stanley Robinson. The particular chapter I was on mentioned a gian hole in the ground. This got me thinking about the age old question of “What if I made a tunnel from one end of the earth to the other?” I continued: “What if an object was dropped from one end of the hole?” Ignoring the fact that the earth is made of magma, solid metal, molten metal, etc., an object dropped from one end of the hole would oscillate between the ends indefinitely (assuming no wind resistance).

What if the earth were rotating? Would the object collide with the sides of the tunnel? Well, when the object is dropped it has velocity in the direction and magnitude of the rotation of the earth, then it accellerates towards the center (via gravity). At the exact moment, without gravity, the object would be hurled off the planet in a direction tangent to the planet’s surface.

Firstly, to make things simpler, imagine the object has that velocity tangent to the earth and the acceleration of gravity without the earth actually rotating. What path does the object take as it travels towards the center of the stationary earth? A coworker and I determined the object would make a sine wave kind of path. Assuming the earth is rotating clockwise and if in your diagram the object is dropped from the ‘top’ of the earth, it would be somewhere down and to the right of where it started.

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