CHAPTER 3Five‐Dimensional Systems

“How did it get so late so soon? It's night before it's afternoon. December is here before it's June. My goodness, how the time has flewn. How did it get so late so soon?”

Dr. Seuss


Things change. Every day, the Earth is a little farther along in its orbit. Every hour, it wheels around 15 degrees about its axis. The Sun and the entire Solar System move relative to the center of the Milky Way Galaxy, which is also moving. Despite these many complexities, celestial mechanics often offer predictable methods for tracking heavenly bodies.

Occasionally, astronomers discover a previously unseen mass zipping across the sky as a point of light. Knowing the size, speed, and orbit of such things is helpful. Here in the United States, we have people who study such things for a living.

The National Aeronautics and Space Administration (NASA) searches for and identifies Near Earth Objects (NEOs), having discovered over 30,000 they have cataloged, transforming our understanding of our neck of the universe.1 They identified a unique body in space in 2002, as shown in Figure 3.1.

What is it? Where is it going? When does it get close to us? Astronomers initially could not resolve any of these questions about the Near Earth Object J002E3, pictured in the circle over time. Market analysts must analyze like questions about position, direction, speed, and proximity.

When it was first discovered, astronomers initially thought it was ...

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