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Actually, the Sun and Earth orbit one another. In the simple version of the scenario, both bodies orbit the center of mass of the Sun-Earth system. Since the mass of the Sun is far greater than that of the Earth, the Sun appears to remain stationary while the Earth orbits. This relationship can be described with a relatively simple differential equation describing circular orbits, and allowing for perturbation in the initial conditions which would cause elliptical orbits. While the solution can be computed by hand, adding bodies to the problem (3-body, 4-body,...n-body) makes the calculation arbitrarily more difficult. While solutions can be found, in reality they are considered chaotic systems because any perturbation in the initial conditions cause the error to increase rapidly over time until the solution is useless as a model for reality.
Back the the problem at hand, if the force of gravity between the Earth and the Sun were to suddenly shut off, and we can safely assume that other bodies would play an insignificant role in the subsequent motions of each, it would still be impossible for the two to collide. At any given time in the two body system, the unit vectors describing the motion of both bodies point in opposite directions. In other words, were gravity to shut off, the Sun and the earth would fly off in opposite directions, and not get closer to one another at any point.
tl;dr i'm a nerd faggot
Actually... the sun orbits the center of the galaxy, spiraling closer and closer to the black hole that we can assume is at the center... and while the earth and other planets may affect its orbit slightly (in minuscule amounts) the sun never does orbit the earth. Galaxies are the only thing we can assume have no set orbit because we havent found a center of the universe yet. So im not disagreeing with you. just adding another part to the story
If you knew anything about Newton's Law of Gravitation F=Gm1m2/r^2 you would know that everything orbits everything else. We as human beings can assume a reference frame only pertaining to our solar system since it takes the sun roughly 226 million years to orbit the galaxy. In our solar system, each of the 8 planets impacts the path of the Sun separately, and the planets also impact each other's motion by a small amount. Since the planets almost never lie along the same direction vector, the pull from each body will affect the Sun in different directions. Therefore, the Sun will not appear to move in an elliptical or circular orbit, but rather more of a slight gyration depending on the positions of the planets.
However, my point with the above comment was to illustrate the fact that, if one were to look at the motion of the Sun with 7 planets neglecting earth, and then look again at its motion with Earth included, the difference would be of the same order as the two body problem describing just the Sun and the Earth together. This relationship is analogous to an oscillation problem with at least two linearly independent solutions and a forcing term that is not in phase with these solutions. The maximum possible amplitude of the resulting wave is exactly equal to what the amplitude would be if the forcing term and the solutions were in phase with one another. However, in reality, the amplitudes of the waves in the actual predicted model are all between 0 and this maximum amplitude. This problem is similar to a child being pushed on a swing. If the pusher pushes at a constant frequency, but the swinger swings at a different frequency, some pushes will increase the swingers speed, and some will dampen it.
What I mean by all this is that the Earth provides a component of motion to the Sun as if it were forcing it to orbit. The Sun may not do so perfectly, but the relationship between the two is one of "attempted" orbit.
Then where do the other planets come into play D":
Of course, given the infinite size of the Universe, it is possible that the new Earth hurtling through the infinite reaches of space, could eventually collide with a star. Chances are slim to none, but hey, what's probability when you're dealing with the infinite?
*Earth now hurtling, sorry
well actually at some point in the future we will finish our slow-motion collide with the andromeda galaxy and any time between then and now our chances of hitting another astral body of equal or greater mass are ridiculously high.
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