#25: What goes up must come down (in the same place)

The Question

Kurt and Glenn Say:

March 7th, 2005 at 3:12 pm

We were at lunch discussing Airplanes and flight times and such. He is flying to San diego and we thought of this. We were wondering if the Roatation of the Earth has any measurable bearing on the flight time. Along those lines Glenn, my esteemed colleague had the thought, that if you were to go straight up into the air in a helicopter and hover for several hours would you land in a different place when you came directly down, or would you travel along with the rotation of the Earth. Thanks all-knowing and ever wondrous Shaun.

The Answer

Well, Kurt and Glenn, it turns out (after consultation with many a secret source) that the rotation of the Earth has no measurable impact on flight time. Also, if you went straight up in a helicopter, hovered, then came down, you would land in the same place. Here’s why:

When you leave the Earth’s surface, you don’t leave its momentum as well. There are still two forces (that we care about) pulling on the helicopter – gravity (pulling down), and the momentum of the Earth’s rotation, pulling you along with it. You are still within the Earth’s power to force you to rotate with it (since the atmosphere is going along with it). Now, if you managed to get yourself into space AND fire some rockets to counteract the momentum you took with you from the Earth, then you could watch it spin under you. But you’ll never be able to escape the Earth’s rotation in a helicopter. Well, you could, but it would be hard. So hard that I won’t even tell you how to do it. Harder than painting a stairwell.

Here’s a little picture in MSPaint that may or may not be related to the answer. I stole most of it.

Thievery is never pretty