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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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