Astronomy
Astronomers define zenith as the point in the sky directly overhead; to be precise, it is the point where an invisible straight line, drawn upward at 90 degrees from the observer, would intersect the arc of the sky. The direction of the Earth's gravitational field affects the position of the zenith in the sky.
Calculations
Altazimuth is an astronomical coordinate system that describes the position of a celestial object by relating it to the horizon and zenith of the observer. The altitude of the zenith is 90 degrees above the celestial horizon. The celestial horizon is the spot where the earth and sky appear to meet. The zenith distance is the measure of the angle between the zenith and the celestial body (sun, moon, star, planet). Astronomers measure the altitude of the object from the celestial horizon. They also measure the azimuth, the distance along the horizon from the point directly south of the observer to the point where the object's vertical line would intercept the horizon. Because the Earth rotates on its axis, the altazimuth of a celestial body is constantly changing.
Geocentric Zenith
The geocentric zenith is a position shown by drawing a line from the geometric center of the Earth through the observer. Because the Earth rotates and is not a perfect sphere, the geocentric zenith is slightly different from the geographic zenith, except at the Equator and the poles. All forms of zenith differ slightly because of the non-spherical shape of the Earth. When the word is used without any modifier, "zenith" means the astronomical zenith.
Opposite
The nadir is the point 180 degrees opposite the zenith, directly under the observer. The term "nadir" also refers to the lowest point reached by a celestial body during its orbit, as seen from a fixed observation point.
Astronomical Horizon
Unlike the celestial horizon, which we can see, the astronomical horizon is a mathematical construct and exists exactly midway between the zenith (+90 degrees) and the nadir (-90 degrees).