Southerly deviation from plumbline of falling bodies

Suppose a body is falling freely in Earth’s gravity field with its initial velocity being zero. Then the effect of the Coriolis force on the falling body can be found in the fact that it deflects from plumbline in the easterly and southerly (equatorial) directions.

Notes:

  1. The southerly deviation is extremely small and almost unobservable due to the \(t / T\) factor.

  2. Also see Easterly deviation from plumbline of falling bodies.

Conditions:

  1. The vector of free fall acceleration is considered constant.

Links:

  1. Sivukhin D.V. (1979), Obshchiy kurs fiziki [General course of Physics], vol. 1, p. 355, (67.11).

southerly_deviation_from_plumbline

Southerly (equatorial) deviation of falling body from plumbline due to Earth’s rotation. See euclidean_distance.

Symbol:

s_south

Latex:

\(s_\text{south}\)

Dimension:

length

fall_time

time elapsed during the body’s fall.

Symbol:

t

Latex:

\(t\)

Dimension:

time

rotation_period

period of Earth’s rotation.

Symbol:

T

Latex:

\(T\)

Dimension:

time

easterly_deviation_from_plumbline

Easterly deviation of falling body from plumbline. See euclidean_distance.

Symbol:

s_east

Latex:

\(s_\text{east}\)

Dimension:

length

latitude

latitude of the place the body is located in.

Symbol:

phi

Latex:

\(\phi\)

Dimension:

angle

law

s_south = pi * t / T * s_east * sin(phi)

Latex:
\[s_\text{south} = \pi \frac{t}{T} s_\text{east} \sin{\left(\phi \right)}\]