Vertical direction

In astronomy, geography, and related sciences and contexts, a direction or plane passing by a given point is said to be vertical if it contains the local gravity direction at that point.Conversely, a direction or plane is said to be horizontal if it is perpendicular to the vertical direction.In general, something that is vertical can be drawn from up to down (or down to up), such as the y-axis in the Cartesian coordinate system. In astronomy, geography, and related sciences and contexts, a direction or plane passing by a given point is said to be vertical if it contains the local gravity direction at that point.Conversely, a direction or plane is said to be horizontal if it is perpendicular to the vertical direction.In general, something that is vertical can be drawn from up to down (or down to up), such as the y-axis in the Cartesian coordinate system. Girard Desargues defined the vertical to be perpendicular to the horizon in his 1636 book Perspective. The word horizontal is derived from horizon, whereas vertical originates in the late Latin verticalis, which is from the same root as vertex, meaning 'highest point'. In physics, in engineering, and in construction, the direction designated as vertical is usually that along which a plumb-bob hangs. Alternatively, a spirit level that exploits the buoyancy of an air bubble and its tendency to go vertically upwards may be used to test for horizontality. Modern rotary laser levels that can level themselves automatically are robust sophisticated instruments and work on the same fundamental principle. In the flat earth scenario, where the earth is notionally a large (infinite) flat surface with gravitational field at a right angle to the surface, the earth surface is horizontal and any plane parallel to the earth surface is also horizontal. Vertical planes, e.g., walls, may be parallel to each other or they may intersect at a vertical line. Horizontal surfaces do not intersect. Furthermore, a plane cannot both be a horizontal plane at one place and a vertical plane somewhere else. When the curvature of the earth is taken into account, the concepts of vertical and horizontal take on yet another meaning. On the surface of a smoothly spherical, homogenous, non-rotating planet, the plumb bob picks out as vertical the radial direction. Strictly speaking, it is now no longer possible for vertical walls to be parallel: all verticals intersect. This fact has real practical applications in construction and civil engineering, e.g., the tops of the towers of a suspension bridge are further apart than at the bottom. Also, horizontal planes can intersect when they are tangent planes to separated points on the surface of the earth. In particular, a plane tangent to a point on the equator intersects the plane tangent to the North Pole at a right angle. (See diagram).Furthermore, the equatorial plane is parallel to the tangent plane at the North Pole and as such has claim to be a horizontal plane. But it is. at the same time, a vertical plane for points on the equator. In this sense, a plane can, arguably, be both horizontal and vertical, horizontal at one place, and vertical at another. For a spinning earth, the plumb line deviates from the radial direction as a function of latitude. Only at the North and South Poles does the plumb line align with the local radius. The situation is actually even more complicated because earth is not a homogeneous smooth sphere. It is a non homogeneous, non spherical, knobby planet in motion, and the vertical not only need not lie along a radial, it may even be curved and be varying with time. On a smaller scale, a mountain to one side may deflect the plumb bob away from the true zenith. On a larger scale the gravitational field of the earth, which is at least approximately radial near the earth, is not radial when it is affected by the moon at higher altitudes.