A site once used as an observatory by the Anasazi, ancient pueblo dwellers of New Mexico, has been recently discovered where patterns of light and shadow were employed to establish the precise limits of the positions of the Sun and Moon over a nineteen-year cycle.
(A) A site once used as an observatory by the Anasazi, ancient pueblo dwellers of New Mexico, has been recently discovered where patterns of light and shadow were employed to establish the precise limits of the positions of the Sun and Moon over a nineteen-year cycle.
(B) A recently discovered site was once used as an observatory by the Anasazi, ancient pueblo dwellers of New Mexico, where patterns of light and shadow were employed to establish the precise limits of the positions of the Sun and Moon over a nineteen-year cycle.
(C) At a recently discovered site once used as an observatory by the Anasazi, ancient pueblo dwellers of New Mexico, patterns of light and shadow were employed to establish the precise limits of the positions of the Sun and Moon over a nineteen-year cycle.
(D) Patterns of light and shadow were employed to establish the precise limits of the positions of the Sun and Moon over a nineteen-year cycle at a site that was recently discovered and was once used by the Anasazi, ancient pueblo dwellers of New Mexico.
(E) Patterns of light and shadow were employed to establish the precise limits of the positions of the Sun and Moon over a nineteen-year cycle at a recently discovered place that the Anasazi, ancient pueblo dwellers of New Mexico, once used the site as an observatory.

(C) At a recently discovered site once used as an observatory by the Anasazi, ancient pueblo dwellers of New Mexico, patterns of light and shadow were employed to establish the precise limits of the positions of the Sun and Moon over a nineteen-year cycle.

Explanation:

Option D does not convey the information that the site was once used as an observatory

Option E alters the meaning of the sentence. The two phrases, "....at a recently discovered place" and "....once used the site as an observatory", used together in this sentence bring about an unnecessary redundancy that change the meaning of the sentence.

The adjective "Where" is used to refer to the Anasazi, a population of humans. This is wrong.

Only option C clearly and correctly conveys the true meaning of the sentence.