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Do planets sometimes wobble and get off their paths? What if an asteroid were to hit it?

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In the solar system, the planets follow orbits determined mainly by the Sun's gravity --- since the Sun is the most massive object in the system (it is about 1000 times as massive as Jupiter, which is about 300 times more massive than Earth). If the Sun and Earth were the only things in the solar system, our planet's orbit would be an ellipse of virtually constant shape and orientation in space. However, because the other planets pull on Earth, our orbit does change slightly over time, in orientation and in shape. Same for the other planets' orbits. The biggest effect is that the orbit of a planet (which is nearly exaclty an ellipse) gradually shifts its orientation over time: the shifting is like how a circular hula-hoop (representing the orbit) shifts in location around the hula-hooper as the person shakes their hips (ask your teacher what a hula-hoop is). But the shifting of a planet's orbit is much slower than for the hula hoop. It takes many, many centuries for the Earth's orbit to shift entirely around once. These changes would be slow and small. It is an active area of research whether or not the orbiting objects in the solar system can indefinitely orbit the Sun without ever undergoing drastic changes in their orbits --- they may actually change dramatically at some point: such changes would be called "chaotic" and the area of research is called "chaos theory". No new forces would be necessary to make this possibility happen; it would simply be the application of gravity once again. There are known examples of chaotic behavior in the solar system, but only involving a few small objects orbiting the outer planets, or in the asteroid belt. Chaotic behavior is defined as happening when very small differences in the initial or current conditions of an experiment, or of the solar system's motions (perhaps so small as to not be easily measured), would lead to drastically different results later in time.

Besides the planets in the solar system, it is even possible (over a much longer time scale) for a passing neighbor star to cause small changes in the planets' orbits. That's actually how comets, which otherwise have large orbits that never take them near the Sun, are caused to change orbit and pass near the Sun, allowing us to see them. If the incoming comet passes near Jupiter, it may be permanently moved into a small orbit that will keep it repeatedly passing near the Sun (once every 75 years, or so, for Halley's comet, for example). An example of chaos: in this case, if Jupiter is in just a slightly different position when the comet passes during its first fall toward the Sun, the comet may not end up in a small orbit due to Jupiter's gravitational pull, but may instead end up hitting the Sun! Or it might be "ejected" from the solar system entirely.

From here

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The orbits of the planets and other bodies are changing all the time, because of the influence of other bodies.

Yes, planets can change orbit significantly because of the influence of other planets. There is a theory that has Neptune and Uranus swapping orbital positions a long time ago.

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