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One of my daydreams is a non rotating sky hook anchored on Phobos.

Phobos Tether

I was wondering how to calculate the Coriolis Force induced by ascending or descending elevator cars.

Wikipedia tells me:
Coriolis Force = -2m(ω X v')

It seems to me traveling straight up (or down) that v' would be perpendicular to ω, correct? So to get magnitude of this cross product I could use straight multiplication?

So let's say I have a 5 tonne elevator car doing straight up the tether at 200 meters/second. Phobos has a period of about 7.66 hours.

ω = .00023 rads/sec.
v' = 200 meters/sec straight up.
mass elevator car = 5000 kg

5000 kg * 200 m/s * .00023/sec = 460 newtons

So in this scenario I get a 460 newton push sideways.

Did I do that correctly?

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    $\begingroup$ Keep in mind that fictitious forces are coordinate system artifacts. You can't measure them with an accelerometer on the body that the force is acting on. You measure them with a range-finder and a clock from an accelerated reference frame (like the surface of Mars or the surface of Phobos); they are the force that would account for the coordinate acceleration measured by the accelerated frame if the accelerated frame were an inertial frame. $\endgroup$ Commented Oct 11 at 4:27
  • $\begingroup$ In this case we want the force that would account for the body appearing to accelerate as it rises or falls at a constant rate. In the Phobos frame, we measure no coordinate acceleration. In the Mars frame, we measure it accelerate in the direction of the orbit as it rises (since its path length increases while its period stays the same). $\endgroup$ Commented Oct 11 at 4:32
  • $\begingroup$ To check your own work, prove that after the boost provided by applying the Coriolis force (as measured on Mars) across the time of a given displacement, the body is still adjacent to and comoving with the tether at the corresponding height. $\endgroup$ Commented Oct 11 at 4:35
  • $\begingroup$ @gs the rotating frame is Phobos' frame. The tether is rotating around the same center and at the same angular velocity as Phobos. There are tidal forces keeping the tether vertically aligned. I am concerned that Coriolis forces of ascending or descending cars with push the tether out of alignment to the local Mars vertical. $\endgroup$ Commented Oct 11 at 14:47

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