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Going ballistic: the many varieties of free fall

Natural History, Nov, 2002 by Neil deGrasse Tyson

In nearly all sports that use balls, the balls go ballistic at one time or another. Whether you're playing baseball, cricket, football, golf, jai alai, soccer, tennis, or water polo, a ball gets thrown, smacked, or kicked and then briefly becomes airborne before returning to Earth.

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Air resistance affects the trajectory of all these balls, but regardless of what set them in motion or where they might land, their basic paths are described by a simple equation found in Newton's Principia, his seminal 1687 book on motion and gravity. Several years later, Newton interpreted his discoveries for the Latin-literate lay reader in The System of the World, which includes a description of what would happen if you hurled stones horizontally at higher and higher speeds. Newton first notes the obvious: the stones would hit the ground farther and farther away from the release point, eventually landing beyond the horizon. He then reasons that if the speed were high enough, a stone would travel the Earth's entire circumference, never hit the ground, and return to whack you in the back of the head. If you ducked at that instant, the object would continue forever in what is commonly called an orbit. You can't get more ballistic than that.

The speed needed to achieve Low' Earth Orbit (affectionately called LEO) is a little less than 18,000 miles per hour--sideways--making the round trip about an hour and a half. Had Sputnik 1, the first artificial satellite, or Yury Gagarin, the first human to travel beyond Earth's atmosphere, not reached that speed, they would never have made it into orbit.

Newton also showed that the gravity exerted by any spherical object acts as though all the object's mass were concentrated at its center. As a consequence, anything tossed between two people on the Earth's surface is also in orbit--except that the trajectory happens to intersect the ground. This was as true for Alan B. Shepard's fifteen-minute ride aboard the Mercury spacecraft Freedom 7 in 1961 as it is for a golf drive by Tiger Woods, a home run by Sammy Sosa, or a ball tossed by a child: they have executed what are sensibly called suborbital trajectories. Were the Earth's surface not in the way, all these objects would execute perfect, albeit elongated, orbits around Earth's center. And though the law of gravity doesn't distinguish among these trajectories, NASA does. Shepard's journey was mostly free of air resistance, because it reached all altitude where there's hardly any atmosphere. For that reason alone, the media promptly crowned him America's first space traveler.

Suborbital paths are the trajectories of choice for ballistic missiles. Like a hand grenade that arcs ballistically toward its target after being hurled, a ballistic missile "flies" only under the action of gravity after being launched. These weapons of mass destruction travel hypersonically, fast enough to traverse half the Earth's circumference in forty-five minutes before plunging back to the surface at thousands of miles an hour. If a ballistic missile is heavy enough, the thing can do more damage just by falling out of the sky than can the explosion of the conventional bomb it carries on board.

The world's first ballistic missile was the V-2 rocket, designed by a team of German scientists under the leadership of Wernher von Braun and used by the Nazis during the Second World War. As the first object to be launched above Earth's atmosphere, the bullet-shaped, large-finned V-2 inspired an entire generation of spaceship illustrations. After surrendering to the Allied forces, von Braun was brought to the United States, where in 1958 he directed the launch of Explorer 1, the first U.S. satellite. Shortly thereafter, he was transferred to the newly created National Aeronautics and Space Administration. There he developed the Saturn V, the most powerful rocket ever created, making it possible to fulfill the American dream of landing on the Moon.

While hundreds of artificial satellites orbit Earth, the Earth itself orbits the Sun. In his 1543 magnum opus, De Revolutionibus, Nicolaus Copernicus placed the Sun in the center of the universe and asserted that Earth plus the five known planets--Mercury, Venus, Mars, Jupiter, and Saturn--executed perfect circular orbits around it. Unknown to Copernicus, a circle is an extremely rare shape for an orbit and does not describe the path of any planet in our solar system. The actual shape was deduced by the German mathematician and astronomer Johannes Kepler, who published his calculations in 1609. The first of his laws of planetary motion asserts that planets orbit the Sun in ellipses.

An ellipse is a flattened circle, and the degree of flatness is indicated by a numerical quantity called eccentricity, abbreviated e. If e is zero, you get a perfect circle. As e increases from zero to one, your ellipse gets more and more elongated. Of course, the greater your eccentricity, the more likely you are to cross somebody else's orbit. Comets that plunge in from the outer solar system have highly eccentric orbits, whereas the orbits of Earth and Venus closely resemble circles, with very low eccentricities. The most eccentric "planet" is Pluto, and sure enough, every time it goes around the Sun, it crosses the orbit of Neptune, acting suspiciously like a comet (see my column "Pluto's Honor," February 1999).

Going ballistic: the many varieties of free fall

Natural History, Nov, 2002 by Neil deGrasse Tyson

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