Graphic courtesy of John Cook

The Equinox in Geometric Terms

I was studying celestial mechanics one day. I pictured the International space Station ([ISS] – that I helped build) orbiting the earth every 90 minutes. It orbits in a plane inclined 51.6° to the equator. It orbits there instead of the originally planned 28.5° latitude of Kennedy Space Center so we could include the Russians in a joint space effort (similar to Apollo/Soyuz) but on a much larger scale. My initial work on ISS began by leading a team called Digital PreAssembly (DPA). The task was to take precise measurements of the Space Station module to module (known as element) interface surfaces. The goal was to ensure fit of the elements since very few real-world ground fit checks occurred. We verified this using 3D CAD models. My role morphed into leading a team called Assembly Analysis, which was an evolution of the digital CAD static fit checks of DPA and performed a kinematic simulation of the berthing process (assembly using either the Space Shuttle robotic arm, or the Space Station robotic arm) to ensure all surfaces in the berthing corridor were designed for contact or could withstand contact. If not, we had to have an operational workaround, redesign, or modify the hardware. In one instance, we had to do a spacewalk and remove a piece of hardware to clear the way for berthing.

The ISS + X axis typically points in the direction of travel; the + Y axis points starboard and the + Z axis points towards Earth. Beneath it, the Earth rotates once every 24 hours (approximately). So when the Space Station has returned 90 minutes later to cross the equator, the earth has rotated beneath it and the ISS passes over a different point on earth.

The Earth is orbiting the Sun (which is also spinning) approximately every 365 days (Hence Leap Years). The plane the Earth orbits the Sun in is called the ecliptic.

The Moon orbits the Earth every 28 days (approximately). The plane it orbits the Earth in is inclined ~5° to the ecliptic (which is why we don’t have a Solar and Lunar eclipse each Month). The Moon’s X axis points towards Earth. The Z axis points normal to the 5° inclination to the ecliptic.

Once I was able to visualize these spinning coordinate systems, my head began to spin.

The Earth’s XZ plane passes through Greenwich, England (GMT). The Earth’s North Pole is rotated 23.5° relative to the ecliptic. The equator projects out in a plane called the Celestial Plane.

Gentle reader, please visualize the solar system as an analog clock dial, with the 12 o’clock position being Summer. The Earth North Pole would be tilted towards the 6 o’clock position 23.5 degrees. The center of the clock dial would be the Sun. This would be Summer in the Northern Hemisphere.

The Autumn Equinox would be the 9 o’clock position Please see the figure that appears with this article.

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