What are the two intersection points between the celestial equator and the ecliptic called?

Answer

The equinoxes.

When the celestial equator and the ecliptic—the two primary reference great circles in the sky—are mapped onto the celestial sphere, they cross each other at two specific points. These two intersection points are designated as the equinoxes. The angular separation, or tilt, between the plane of the celestial equator (defined by spin) and the plane of the ecliptic (defined by orbit) is known as the obliquity of the ecliptic, and this angle is what determines the severity of the planet's seasons. The moments the Sun crosses these equinox points mark the beginning of spring and autumn.

What are the two intersection points between the celestial equator and the ecliptic called?

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