# vertical direction

In astronomy, geography, geometry and related sciences and contexts, a direction passing by a given point is said to be vertical if it is locally aligned with the gradient of the gravity field, 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. 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 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 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 is deformed due to the inhomogeneous spatial distribution of materials with different densities. Actual vertical directions are thus neither straight lines nor even convergent.
• At any given location, the total gravitational force is a function of time, 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) changes with the relative position of the Moon (air, sea and land tides).
• 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, 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 associated with the planet's rotation. This is a fictitious force: it only arises when calculations or experiments are conducted in non-inertial frames of reference.

## 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 due to the fact that 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.

Astronomy is the scientific study of celestial objects (such as stars, planets, comets, and galaxies) and phenomena that originate outside the Earth's atmosphere (such as the cosmic background radiation).
Geography - (from the Greek words Geo (γη) or Gaea (γαία), both meaning "Earth", and graphein (γράφειν) meaning "to describe" or "to write"
Geometry (Greek γεωμετρία; geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. Geometry is one of the oldest sciences.
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 to some indicated reference (the violins in a full orchestra are typically seated to the left of 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.
Gravitation is a natural phenomenon by which all objects with mass attract each other. In everyday life, gravitation is most familiar as the agency that endows objects with weight.
field is an assignment of a physical quantity to every point in space (or, more generally, spacetime). A field is thus viewed as extending throughout a large region of space so that its influence is all-pervading. The strength of a field usually varies over a region.
center of mass of a system of particles is a specific point at which, for many purposes, the system's mass behaves as if it were concentrated. The center of mass is a function only of the positions and masses of the particles that comprise the system.
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 gravity field, i.e., with the direction of the gravitational force (per unit mass) at that point.
EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001. Their greatest hit, their debut single "time after time", peaked at #13 in the Oricon singles chart.
In physics, density is mass m per unit volume V—how heavy something is compared to its size. A small, heavy object, such as a rock or a lump of lead, is denser than a lighter object of the same size or a larger object of the same weight, such as pieces of
time.

One view is that time is part of the fundamental structure of the universe, a dimension in which events occur in sequence, and time itself is something that can be measured.
plumb-bob or a plummet is a weight with a pointed tip on the bottom that is suspended from a string and used as a vertical reference line.

This instrument has been used since the time of the ancient Egyptians by bricklayers, masons, and carpenters to ensure that their
Tides are the cyclic rising and falling of Earth's ocean surface caused by the tidal forces of the Moon and the Sun acting on the oceans. More generally, tidal phenomena can occur in any object that is subjected to a gravitational field that varies in time and space, such as the
The Sun

Observation data
Mean distance
from Earth 1.4961011 m
(8.31 min at light speed)
Visual brightness (V) −26.74m [1]
Absolute magnitude 4.
Centrifugal force (from Latin centrum "centre" and fugere "to flee") is a term which may refer to two different forces which are related to rotation.
An inertial frame of reference, or inertial reference frame, is one in which Newton's first and second laws of motion are valid. Newton's laws are valid in any reference frame that is neither rotating nor accelerating relative to the sun and other stars.