Easterly 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.

Conditions:

1. The vector of free fall acceleration is constant.

Links:

1. Sivukhin D.V. (1979), Obshchiy kurs fiziki [General course of Physics], vol. 1, p. 355, (67.10).

easterly_deviation_from_plumbline

Easterly deviation of falling body from plumbline due to Earth’s rotation. See euclidean_distance

Symbol:

s_east

Latex:

\(s_\text{east}\)

Dimension:

length

fall_time

time of the body’s fall.

Symbol:

t

Latex:

\(t\)

Dimension:

time

rotation_period

period of the Earth’s rotation.

Symbol:

T

Latex:

\(T\)

Dimension:

time

initial_elevation

Initial elevation (height) of the body from the Earth’s surface.

Symbol:

h

Latex:

\(h\)

Dimension:

length

latitude

latitude of the location of the body.

Symbol:

phi

Latex:

\(\phi\)

Dimension:

angle

law

s_east = 4 * pi / 3 * t / T * h * cos(phi)

Latex:

\[s_\text{east} = \frac{4 \pi}{3} \frac{t}{T} h \cos{\left(\phi \right)}\]