Vertical direction

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Vertical direction

In astronomy

Astronomy

Astronomy is the science of Astronomical object and Phenomenon that originate outside the Earth's atmosphere . It is concerned with the evolution, physics, chemistry, meteorology, and motion of celestial objects, as well as the physical cosmology....
, geography

Geography

Geography is the study of the Earth and its lands, features, inhabitants, and phenomena. A literal translation would be "to describe or write about the Earth"....
, geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
and related sciences and contexts, a direction
Direction (geometry, geography)

Direction is the information contained in the relative position of one point with respect to another point without the distance information. Directions may be either Relative direction to some indicated reference , or absolute according to some previously agreed upon frame of reference ....
passing by a given point is said to be vertical if it is locally aligned with the gradient

Gradient

In vector calculus, the gradient of a scalar field is a vector field which points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....
of the gravity

Gravitation

Gravitation is a natural phenomenon that gives weight to objects. In everyday life, attraction due to gravity is the result of the presence of relatively large bodies, such as the Earth and the Moon....
field

Field (physics)

In physics, a field is a physical quantity associated to each point of spacetime. A field can be classified as a scalar field, a vector field, or a tensor field, according to whether the value of the field at each point is a scalar , a vector , or, more generally, a tensor, respectively....
, i.e., with the direction of the gravitational force (per unit mass) at that point.

Discussion
Although the word vertical is very commonly used in daily life and language (see below), it is subject to many misconceptions.

Discussion

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Encyclopedia

In astronomy

Astronomy

Geography

Geography is the study of the Earth and its lands, features, inhabitants, and phenomena. A literal translation would be "to describe or write about the Earth"....
, geometry

Geometry

Gradient

Gravitation

Field (physics)

Discussion

Although the word vertical is very commonly used in daily life and language (see below), it is subject to many misconceptions. The precise definition above and the following discussion points will hopefully clarify these issues.

The concept of verticality only makes sense in the context of a clearly measurable gravity field, i.e., in the 'neighborhood' of a planet, star, etc. When the gravity field becomes very weak (the masses are too small or too distant from the point of interest), the notion of being vertical loses its meaning.

In the presence of a simple, time-invariant, rotationally symmetric gravity field, the vertical directions passing by different points in space (and not belonging to the same vertical direction) intersect at the center of mass
Center of mass

The center of mass of a system of wiktionary:Particles is a specific point at which, for many purposes, the system's mass behaves as if it were concentrated....
of that gravity field. This implies that no two different vertical directions are ever parallel to each other.

In general, a vertical direction will only be perpendicular to a horizontal plane
Horizontal plane

In astronomy, geography, geometry and related sciences and contexts, a Plane is said to be horizontal at a given point if it is locally perpendicular to the gradient of the Gravitation Field , i.e., with the direction of the gravitational force at that point....
if both are specifically defined with respect to the same point: a plane is only horizontal at the point of reference. Thus both verticality and horizontality are strictly speaking local concepts, and it is always necessary to state to which location the direction or the plane refers to.

In reality, the gravity field of a heterogeneous planet such as Earth
Earth

Earth is the third planet from the Sun. Earth is the largest of the terrestrial planets in the Solar System in diameter, mass and density. It is also referred to as the World and Wiktionary:Terra.Note that by International Astronomical Union convention, the term "Terra" is used for naming extensive land masses, rather...
is deformed due to the inhomogeneous spatial distribution of materials with different densities
Density

The density of a material is defined as its mass per unit volume. The symbol of density is ....
. Actual vertical directions are thus neither straight lines nor even convergent.

At any given location, the total gravitational force is a function of time
Time

Time is a component of the measurement used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects....
, because the objects that generate the reference gravity field move relative to each other. For instance, on Earth, the local vertical direction at a given point (as materialized by a plumb line
Plumb-bob

A plumb-bob or a plummet is a weight, usually with a pointed tip on the bottom, that is suspended from a string and used as a vertical reference line....
) changes with the relative position of the Moon (air, sea and land tide
Tide

Tides are the rising of Earth's ocean surface caused by the tidal forces of the Moon and the Sun acting on the oceans. Tides cause changes in the depth of the marine and estuary water bodies and produce oscillating currents known as tidal streams, making prediction of tides important for coastal navigation ....
s).

Furthermore, on a rotating planet such as Earth, there is a difference between the strictly gravitational pull of the planet (and possibly other celestial objects such as the Moon, the Sun
Sun

The Sun , a G V star, is the star at the center of the Solar System. The Earth and other matter orbit the Sun, which by itself accounts for about 98.6% of the Solar System's mass....
, etc), and the apparent net force applied (e.g., on a free-falling object) that can be measured in the laboratory or in the field. This difference is due to the centrifugal force
Centrifugal force

In classical mechanics, centrifugal force is an outward force associated with rotation. Centrifugal force is one of several so-called pseudo-forces , so named because, unlike Fundamental interaction, they do not originate in interactions with other bodies situated in the environment of the particle upon which they act....
associated with the planet's rotation. This is a fictitious force
Centrifugal force

In classical mechanics, centrifugal force is an outward force associated with rotation. Centrifugal force is one of several so-called pseudo-forces , so named because, unlike Fundamental interaction, they do not originate in interactions with other bodies situated in the environment of the particle upon which they act....
: it only arises when calculations or experiments are conducted in non-inertial frames of reference
Inertial frame of reference

In physics, an inertial frame of reference is a frame of reference, tied to the state of motion of an Observer , with the property that each physical law portrays itself in the same form in every inertial frame....
.

Practical use in daily life

The concept of a vertical line is thus anything but simple, although, in practice, most of these effects and variations are rather small: they are measurable and can be predicted with great accuracy, but they may not greatly affect our daily life.

This dichotomy between the apparent simplicity of a usual concept and an actual complexity of defining (and measuring) it in scientific terms is because the typical linear scales and dimensions of relevance in daily life are 3 orders of magnitude (or more) smaller than the size of the Earth. Hence, the latter appears to be flat locally, and vertical directions in nearby locations appear to be parallel. Such statements are nevertheless approximations; whether they are acceptable in any particular context or application depends on the applicable requirements, in particular in terms of accuracy.

In graphical contexts, such as drawing and drafting on rectangular paper, it is very common to associate one of the dimensions of the paper with a vertical, even though the entire sheet of paper is standing on a flat horizontal (or slanted) table. In this case, the vertical direction is typically from the side of the paper closest to the user to the opposite side (farthest away). This is purely conventional (although it is somehow 'natural' when drawing a natural scene as it is seen in reality), and may lead to misunderstandings or misconceptions, especially in an educational context.

Vertical direction

Discussion

Practical use in daily life

See also