Caption: The heating effect of the Sun at an equinox is equal for the Northern Hemisphere and Southern Hemisphere as is clear from the symmetry seen in the diagram.

Note the Earth's axis is at a direction perpendicular the Earth-Sun line and tilts out of the plane of the diagram by 23.4°.

As one can see from the diagram, the Sun is directly overhead on the equator at solar noon. Also, at the North and South Poles on an equinox, the Sun travels just on the horizon throughout the whole 24-hour day. Also again, at an equinox, daytime and nighttime are both nearly exactly 12 hours everywhere on Earth.

Actually, on the equator, daytime and nighttime are always both nearly about 12 hours NOT just at equinoxes (see Wikipedia: Equator: Geodesy of the Equator). There are 2 ways of explaining this feature:

1. Easy way: The horizon plane on the equator is aligned with the celestial axis, and so cuts all declination circles in half.

   Thus, all astronomical objects are above and below the horizon plane for almost equal times.

   Ergo, the Sun is above and below the horizon plane for almost equal times, and so the daytime and nighttime are both always nearly about 12 hours.

2. Hard way: This is takes a tricky explanation in words---diagrammatically the feature is sort of obvious---but why use one picture when a 1000 words will do?

   Consider a 1st great circle on a sphere.

   Now draw a 2nd great circle on the sphere.

   If great circle 2 never intersected great circle 1, it would all be on one hemisphere---and then it could NOT be a great circle.

   So the 2 great circles must intersect once at least.

   A diameter from the intersection point must hit both great circles on the other side of the sphere.

   So the 2 great circles must intersect twice.

   It's geometrically intuitvely clear that there are only 2 intersections and they cut the 2 great circles both in half.

   Now the equator and the Earth's terminator (the line dividing the dayside and the nightside Earth) are both great circles.

   They intersect on the terminator, of course.

   It takes half a rotational period (i.e., half a day or 12 hours) for the Earth's rotation to move an equatorial location (e.g., the Galapogos Islands) half way around the spherical shape of the Earth.

   So from terminator to terminator also takes 12 hours.

   Including the complications makes the 2 periods only nearly 12 hours.

   Whew.