Why Is the Larger Component in Coriolis Calculations Often Neglected?

[PeroK]

I've been trying to understand the Coriolis effect on the Earth's surface. The general equations produce two terms:

The first is R'' and the second is 2ΩxV, where R is the position of the point on the Earth's surface, V is the velocity (relative to Earth) and Ω = ωk. Where ω is the Earth's angular velocity.

In the book I'm using, the R'' term is neglected as it is too small, being of the order ω^2R and the focus is on the second (Coriolis) term. However, this is of the order of ω.

By my calculations w^2R is about 0.03 (ω = 7 X 10^-5 and R = 6.4 X 10^7m).

Even after resolving R'' into a component parallel to gravity, the residual component is still bigger than the Coriolis component.

I'm a bit stuck as why the apparently larger component is the one neglected. Does anyone have any ideas?

 

[PeroK]

I might see the answer to my own question here. This effect, far from negligible, produces a variation in gravity, resulting in gravity not being directed towards the centre of the Earth. But, since this is constant at a given latitute and varies only slowly across the surface it has no practical impact on motion in a given location. It's simply that gravity appears to act not quite towards the centre of the earth. But, since it's the same for everyone (it depends only on the angle of latitute, Earth's radius and angular momentum), it can be ignored.

Unlike the Coriolis effect, which will affect a pendulum over a long period of time or a falling object when it speeds up, the effect on the direction of gravity is essentially constant. So, Coriolis affects motion to a varying extent, so is significant in that respect.

Does that sound right?