The option that can be used as a one-word substitute for the given group of words "The date when both day and night are of approximately equal length" is "Equinox."

Explanation of the options:

☀ Equilibrium: This word refers to a state of balance or equal distribution.

☀ Equine: This word pertains to horses or related to horses.

☀ Equator: This word refers to the imaginary line that divides the Earth into the Northern and Southern Hemispheres.

☀ Equinox: This word specifically refers to the two times in a year (around March 20th and September 22nd) when the sun crosses the celestial equator, resulting in approximately equal lengths of day and night worldwide.