Pole Escape

The pole-flight force is at the earth's rotation, the component of the centrifugal force , the tangentially acting to the surface. ${\displaystyle F_{\mathrm {Pf} }}$

The daily rotation of the earth (more precisely: within a sidereal day of 23.93447 hours) around its axis of rotation causes every body on earth to experience a centrifugal force that points perpendicularly away from the earth's axis, i.e. obliquely to the earth's surface depending on the latitude . Centrifugal force contains a component that is tangential to the surface of the earth from the pole ; this component is called the pole evacuation.

calculation

The amount of centrifugal force is:

${\displaystyle F_{\mathrm {Zf} }=m\cdot \omega ^{2}\cdot r}$

in which

• ${\displaystyle m}$ the mass of the body (not the earth!)
• r is its distance from the polar axis
• ${\displaystyle \omega =0{,}00007292116/\mathrm {s} }$is the angular velocity of the earth's rotation in radians .

The distance depends on the geographic latitude over a mean earth radius : ${\displaystyle R=6371\,\mathrm {km} }$ ${\displaystyle \varphi }$

${\displaystyle r=R\cdot \cos \varphi }$

so that it results:

${\displaystyle \Rightarrow F_{\mathrm {Zf} }=m\cdot \omega ^{2}\cdot R\cdot \cos \varphi }$

Only at the equator does the centrifugal force exactly counteract the force of gravity . At all other latitudes it acts at an angle to the horizontal . ${\displaystyle \alpha =90^{\circ }-\varphi }$

For the pole evacuation the following applies:

${\displaystyle {\begin{aligned}F_{\mathrm {Pf} }&=F_{\mathrm {Zf} }\cdot \sin \varphi \\&=m\cdot \omega ^{2}\cdot R\cdot \cos \varphi \cdot \sin \varphi \end{aligned}}}$

impact

If one only considers that component of the force that acts parallel to the earth's surface, it is directed south in the northern hemisphere and north in the southern hemisphere . The constant action of this force is the reason why the earth is not a perfect sphere , but is flattened at the poles . The inner somewhat elastic body of the earth adjusts to the prevailing earth rotation, in that its mass distribution yields in the long term to the polar displacement force and the equatorial radius increases at the expense of the polar radius. Today's earth flattening is 0.3353 percent or 21 km.

Isaac Newton was the first to formulate this deformation mathematically. Around 1920 postulated Alfred Wegener the polflucht the continents and suspected the centrifugal force as the cause of which he discovered continental drift . This was refuted a few years later, but the term pole escape force found its way into specialist literature.