Earth revolves around Sun in an elliptical orbit that lies in a plane called the ecliptic plane. At the same time, Earth rotates on its own axis which is tilted by about 23.4° relative to the ecliptic plane. The direction of Earth’s axis is fixed, pointing toward two imaginary points in the sky known as the north and south celestial poles. (Polaris, also known as the North Star, is within 1 degree of the north celestial pole.) When viewed from above the northern hemisphere, Earth’s rotation on its axis and its orbit around Sun both proceed in counter-clockwise direction.

Earth’s axial tilt is responsible for seasonal variation in weather. When the North Pole tilts toward the sun, it is summer in the northern hemisphere and winter in the southern hemisphere; when it tilts away from the sun some six months later, it is winter in the northern hemisphere and summer in the southern hemisphere.

Sun takes about six months to go from its southernmost position over the southern tropic (23.4° S) to its northernmost position over the northern tropic (23.4° N), and six months to return. As Sun appears to circle Earth, it is continually moving either northward or southward while tracing a helical path over Earth, completing a full circuit every year. Our goal in the next few pages is to explore this slow spiral curve described by Sun’s passage.

We won’t try to model Earth’s motion exactly, but rather model just the basic factors responsible for the seasons and Sun’s helical path over Earth. Our simulated earth’s orbit will be circular whereas Earth’s actual orbit is elliptical (though nearly circular). Our earth’s inclination can be fixed to any angle unlike Earth’s which is fixed at around 23.4°.¹ When our simulated earth’s inclination is t degrees, it traces a helical curve between latitudes t degrees S and t degrees N. At the extremes, this curve is just the equatorial circle when t=0, and a globe-spanning helix reaching the north and south poles when t=90.