Earth's rotation axis perpendicular to Sun-Earth line during equinox

Wikipedia says that the following happens during the equinox:

More precisely, an equinox is traditionally defined as the time when the plane of Earth's equator passes through the geometric center of the Sun's disk.[7][8] Equivalently, this is the moment when Earth's rotation axis is directly perpendicular to the Sun-Earth line, tilting neither toward nor away from the Sun.

I am confused why it is stated that the rotation axis of the Earth is directly perpendicular to the Sun-Earth line. As a matter of fact I am not even sure what the Sun-Earth line is, I assume it is just a straight line connecting Sun and Earth. The rotation axis is tilted all the time so how can it at any point be perpendicular to this line?

The Sun-Earth line is indeed the line connecting the centers of the sun and the earth, which exists on the ecliptic plane. At the earth's location, there is exactly one line perpendicular to the ecliptic plane (the one that points "straight up" at 90 degrees), but there are an infinite number of lines that are perpendicular to the Sun-Earth line - you can rotate any perpendicular line around the Sun-Earth line, and it will still be perpendicular. The rotational axis of the earth and the Sun-Earth line do indeed form a perpendicular angle at the equinox, the key is to note that this perpendicular angle does not point straight up from the ecliptic - it's still tipped over at 23.5 degrees relative to the ecliptic, but still perpendicular to the Sun-Earth line (not the ecliptic plane).

During the summer months, one pole is tipped toward the Sun-Earth line. During the winter months, it's tipped away. In between summer and winter, the rotational axis moves through all the intervening angles. At the equinox, the axis is tipped neither toward nor away - it's at exactly a right angle perpendicular to the Sun-Earth line. The rotational axis is still tipped, but the direction of the tip is entirely perpendicular to the Sun-Earth line - at the equinox, no component of the axis tip is in the direction of the Sun-Earth line. It's also worth noting that this would still occur no matter what the angle of the earth's rotational axis was, at the equinox the tilt of the axis is always perpendicular to the Sun-Earth line.

• This answer gets the point across, but to be pedantic the rotational axis extends both north and south simultaneously, so you cannot say it is tipped "towards" the sun without clarifying that you are using northern hemisphere seasons and the northward axis. More generally, an equinox occurs when the plane extending from the center of the earth perpendicular to the axis of rotation passes through the center of the Sun. Commented Jan 31 at 3:56
• @Yos233 I agree that it's worth being clearer about the fact that the axis points both toward and away from the Sun simultaneously, but there is no need for specifying the northern or southern seasons. The part of Earth where it is summer is the part of Earth where the axis is tilted toward the Sun. The part of Earth where it is winter is where it is tilted away. This is true regardless of hemisphere. Commented Jan 31 at 4:45

During one solstice, the angle between the earth's axis and the line connecting the center of the Earth to the center of the Sun is as acute as it can get.

Six months later, the angle is as oblique as it can possibly be.

Halfway between the two, the angle has to be 90 degrees, perpendicular.

The axis is still tilted, but the tilt is entirely in the direction of earth's travel (or exactly opposite that). If you rotate a right angle slightly on the Z-axis, it's still a right angle from the X-Y perspective.

At the equinoxes, the Sun crosses the celestial equator, so it's at 90° to the celestial poles. At the June solstice, the Sun is ~23.5° north of the equator, and at the December solstice it's ~23.5° south of the equator.

It's hard to draw an effective diagram in 2D, but it's a lot easier to see in 3D. Here's a Sage script that creates an interactive 3D diagram of the celestial globe and the ecliptic plane (the orbital plane), with red lines indicating the Sun's direction at the equinoxes and solstices.

""" Globe with RA-declination grid
Written by PM 2Ring 2021.06.24
"""

var('u, v')
pp = parametric_plot3d
deg = pi / 180
dth = 15 * deg

# Obliquity of the ecliptic, J2000
oe = 23.439278 * deg

def xyz(lat, lon):
r = cos(lat)
return r*cos(lon), r*sin(lon), sin(lat)

# Globe grid
udom, vdom = (u, -pi/2, pi/2), (v, -pi, pi)
G = sum(pp(xyz(u, lon), udom, color='#00c' if lon else '#0ac') for lon in srange(0, pi*2, dth))
G += sum(pp(xyz(lat, v), vdom, color='#00c' if lat else '#0ac') for lat in srange(dth-pi/2, pi/2, dth))
# Extended polar axis
G += line3d([(0, 0, -1.5), (0, 0, 1.5)], color="#0ac")

# Ecliptic circle, in 2D
R = 2.5
fcircle = R * cos(v), R * sin(v)

P = parametric_plot(fcircle, vdom, thickness=2, fill=True,
color="#800", fillcolor="#fcc", alpha=0.9, fillalpha=0.3)
color = "red"
# Equinox & solstice lines
P += line2d([(-R, 0), (R, 0)], color=color)
P += line2d([(0, -R), (0, R)], color=color)
# Convert to 3D, and rotate
G += P.plot3d().rotateX(-oe)

# Equinox & solstice labels
G += text3d("M", R*vector(xyz(0, 0)))
G += text3d("J", R*vector(xyz(oe, 90*deg)))
G += text3d("S", R*vector(xyz(0, 180*deg)))
G += text3d("D", R*vector(xyz(-oe, 270*deg)))

@interact
Q = G if plane == 'Equator' else G.rotateX(oe)
Q.show(frame=frame, theme='dark', projection='orthographic', online=True)


Here's a live version running on the SageMathCell server. It should run in any browser.

You can select whether you want the equatorial plane or the ecliptic plane to be horizontal. The letters around the ecliptic circle mark the Sun's direction at the equinoxes and solstices. M is the March equinox, J is the June solstice, S is the September equinox, and D is the December solstice.

Here are the 3D interface controls.

• Orbit - right mouse, or left mouse + ctrl/meta/shiftKey
• touch: one-finger rotate
• Zoom - middle mouse, or mousewheel
• touch: two-finger spread or squish
• Pan - left mouse, or arrow keys
• touch: two-finger move