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A major scientific breakthrough occurred in 1609 when the German mathematician Johannes Kepler published his theory that the planets orbit the Sun in elliptical, rather than circular, paths. Kepler also showed that as orbiting bodies make their closest approach to the Sun, they speed up, and then slow down as they move away. This effect explains why a planet travels from point A to point B in the same time that it takes  to cover the much shorter span between C and D (right). Because the areas shaded blue are equal, the concept is described as "sweeping out equal areas in equal times." Building on Kepler's work, Newton showed that other types of trajectories are possible (below), as borne out by the orbits of the moons of Jupiter  (opposite) and the eccentric, or extremely elliptical, paths of comets.
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Jupiter 's Assorted Clan
The moons that orbit Jupiter offer a sample of orbital variety. Eight regular moons, probably born of the disk-shaped nebula that circled the protoplanet, travel in rounded orbits in the planet's equatorial plane (beige and blue). Two groups of irregular moons (red and orange) orbit at huge distances from the planet in eccentric orbits highly inclined to Jupiter 's equator, a sign that they are captured asteroids . The outermost irregulars have retrograde orbits, traveling in the direction opposite to Jupiter 's own rotation.
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Conics
Newton's laws of motion and gravitation showed that under the influence of gravity all planets, moons, comets, and any kind of projectile will follow paths that can be described as conic sections--cuts made by the intersection of a flat plane and a cone.
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Ellipse
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Parabola
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Hyperbola
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shapes you can produce by slicing a cone with a sharp plane at various angles. There are as many different shapes of orbits in our solar system as there are objects. Some comets swoop in from the depths of space on near-hyperbolic paths, never to be seen again. Millions of icy particles orbit within Saturn's rings  , each tracking its own near-circular course while bumping gently into its neighbors on occasion. The orbits of Mercury and Pluto are noticeably elliptical, whereas that of Venus is almost circular.
These orbits are displays of general relativity in action. The Sun creates a huge bowl in the fabric of space-time. Earth and the other planets travel along the banks of this bowl , much as marbles revolve around the sloped outer rim of a roulette wheel. The planets have just the right amount of sideways motion to keep them from spiraling into the center of the bowl or slipping out of it entirely. Earth, for instance, travels at an average speed of about 66,000 miles per hour. Its distance from the Sun varies in a stable manner between 91 million and 95 million miles. But it's not hard to imagine that smaller bodies, such as distant comets or the thousands of asteroids between Mars and Jupiter , can travel more erratically. Indeed, we have learned that wayward travelers zip through our bowl in space-time with alarming frequency.
Gravitational interactions among the many bodies in the solar system, large and small, lead to long-term unpredictability in the orbits of objects. The physical principle behind these changes is called chaos . When a system is chaotic, we can only predict its motion a short time into the future. After that, even the tiniest initial changes in an object's velocity or position result in drastically different outcomes. Weather patterns in Earth's atmosphere are chaotic, which explains why forecasts aren't useful beyond a week or so. In the solar system, the combined tugs of the planets and other objects are extremely difficult to calculate. Given enough time, they will perturb an asteroid or a moon into an entirely new orbit.
It comes as no surprise that Jupiter is our solar system's gravitational bully. Close encounters with this giant planet can eject objects from the Sun's grasp or send them into our neighborhood. We know of dozens of asteroids ' orbits that cross Earth's or (continued)
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