Nadir

the lowest point -- the pole which is vertically below the observer in the CELESTIAL SPHERE. It is opposite to the ZENITH.

Taken from Dictionary of Science

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The nadir (from Arabic نظير nathir, "opposite") is the direction pointing directly below a particular location; that is, it is one of two vertical directions at the location, orthogonal to a horizontal flat surface there. Since the concept of being below is itself somewhat vague, scientists define the nadir in more rigorous terms. Specifically, in astronomy, geophysics and related sciences (e.g., meteorology), the nadir at a given point is the local vertical direction pointing in the direction of the force of gravity at that location. The direction opposite of the nadir is the zenith.

Nadir also refers to the downward-facing viewing geometry of an orbiting satellite, such as is employed during remote sensing of the atmosphere, as well as when an astronaut faces the Earth while performing an EVA.

The word is also used figuratively to mean the lowest point of a person's spirits.

The term nadir can also be used to represent the lowest point reached by a celestial body during its apparent orbit around a given point of observation. This can be used to describe the location of the Sun, but it is only technically accurate for one latitude at a time and only possible at the low latitudes. The sun is said to be at the nadir at a location when it is at the zenith at the location's antipode.

Taken from Wikipedia

Zenith

the highest point over head -- the pole which is vertically above the observer with the latter in the centre of the horizon circle. Zenith is opposite to the NADIR in the CELESTIAL SPHERE.

Taken from Dictionary of Science

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In general terms, the zenith is the direction pointing directly "above" a particular location; that is, it is one of two vertical directions at the location, orthogonal to a horizontal flat surface there. The concept of "above" is more specifically defined in astronomy, geophysics and related sciences (e.g., meteorology) as the vertical direction opposite to the net gravitational force at a given location. The opposite direction, i.e. the direction of the gravitational force is called the nadir. The term zenith also refers to the highest point reached by a celestial body during its apparent orbit around a given point of observation. This sense of the word is often used to describe the location of the Sun, but it is only technically accurate for one latitude at a time and only possible at the low latitudes.

Strictly speaking, the zenith is only approximately contained in the local meridian plane because the latter is defined in terms of the rotational characteristics of the celestial body, not in terms of its gravitational field. The two coincide only for a perfectly rotationally symmetric body. On Earth, the axis of rotation is not fixed with respect to the planet (for example due to constant displacements of its fluid components) so that the local vertical direction, as defined by the gravity field, is itself changing direction in time (for instance due to lunar and solar tides).

Taken from Wikipedia

Tangent

a function of an angle in a right-angled triangle, defined as the ratio of the side opposite the angle to the length of the side adjacent to it. Also, in geometry, a straight line that just touches the circumference of a circle.

Taken from Dictionary of Science

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In geometry, the tangent line (or simply the tangent) to a curve at a given point is the straight line that "just touches" the curve at that point (in the sense explained more precisely below). As it passes through the point of tangency, the tangent line is "going in the same direction" as the curve, and in this sense it is the best straight-line approximation to the curve at that point. The same definition applies to space curves and curves in n-dimensional Euclidean space.

Similarly, the tangent plane to a surface at a given point is the plane that "just touches" the surface at that point. The concept of a tangent is one of the most fundamental notions in differential geometry and has been extensively generalized; see Tangent space.

The word "tangent" comes from the Latin tangere, meaning "to touch".

Taken from Wikipedia