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These are the celestial equivalent of longitude and latitude, respectively, and trigonometry is used to convert them to other coordinate systems, such as azimuth and elevation, which are necessary for aiming telescopes. Conversions often use spherical trigonometry formulas.

To calculate the synodic period (the time between successive conjunctions with the sun, as seen from Earth) of a planet, trigonometry can be employed to solve the geometric relations between Earth, the Sun, and the planet, given their respective sidereal periods.

Trigonometry is used to measure the parallax angle, which is the apparent shift in position of a close star against the background of distant objects caused by Earth's orbit around the Sun. By measuring the parallax angle, astronomers can calculate the distance to nearby stars using the parallax formula:

Trigonometry helps in analyzing the spatial distribution of stars within a cluster. This involves measuring angles and applying trigonometric functions to understand the three-dimensional structure and distances between stars in the cluster.

Trigonometric parallax is the first rung of the cosmic distance ladder, which is used for measuring the distances of celestial objects. Each rung of the ladder uses different trigonometric methods and principles to measure distances that are progressively farther out into the universe.

Trigonometric relationships are essential for predicting eclipses. By analyzing the angles and distances between the Earth, Sun, and Moon, astronomers can predict when the celestial bodies will align perfectly to create a solar or lunar eclipse.

Trigonometry is applied to calculate the actual size of an astronomical object when its angular diameter and distance are known. The formula is: