First of all, as long as we're in our comfortable familiar environment, "vertical" means
toward or away from the center of the earth. When you start talking about things in
space, the word "vertical" has no meaning.
You might expect the earth's axis of rotation to be perpendicular to the plane of the
earth's orbit around the sun. If that's what you expect, then you'll be disappointed.
The axis of rotation makes an angle of about 66.5 degrees with the orbital plane.
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Vertical. Vertical. Vertical. Vertical.
The X-Axis
yes
the y-axis is the horizontal axis
The first or X-co-ordinate is zero all along the vertical axis aka the Y-axis.