Nadir — Definition, Formula & Examples
Nadir is the point on the celestial sphere directly below an observer, exactly opposite the zenith (the point directly overhead). In everyday use, it refers to the lowest possible point.
The nadir is the intersection of the downward vertical direction at a given location with the celestial sphere. It lies at an altitude of from the observer's horizon, diametrically opposite the zenith along the line passing through the observer and the center of the Earth.
How It Works
Imagine you are standing on the Earth's surface. A line drawn straight down from your feet, through the center of the Earth, and continuing out the other side hits the celestial sphere at the nadir. The angle of depression from the horizon to the nadir is always . In coordinate systems used in astronomy and navigation, the nadir serves as a fixed reference point for measuring positions below the horizon.
Example
Problem: An observer stands at a point on Earth's surface. The zenith is at an altitude of 90° above the horizon. What is the angular distance from the zenith to the nadir?
Step 1: The zenith is at +90° altitude (directly overhead) and the nadir is at −90° altitude (directly below).
Step 2: The angular distance between two diametrically opposite points on a sphere is 180°.
Answer: The angular distance from the zenith to the nadir is .
Why It Matters
Understanding the nadir matters in navigation, astronomy, and satellite imaging, where positions are measured relative to the zenith-nadir axis. Satellite cameras, for instance, capture "nadir images" by pointing straight down at the Earth's surface. In geometry courses, the concept reinforces how reference points on a sphere define coordinate systems.
Common Mistakes
Mistake: Confusing nadir with zenith
Correction: The zenith is the point directly above the observer; the nadir is directly below. They are exact opposites, separated by 180°.