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For shame, not only putting a homework question up for the Internet to solve, but doing so in such a lazy inarticulate way that most people would not be able to understand what the frak the question actually asks. Also, there may be some shame for the instructor here, though it is hard to tell with such an ineptly phrased question if the instructor is clueless or not. The crucial factor is whether or not the Earth's added mass has any particular momentum.

Actually this horribly worded question relates to the position of the earth in the solar system as portrayed in the video game Mass Effect. Congrats on a wordy answer though.

If the Earth became more massive without any change to velocity, then the only orbital change would be that the Sun's annual Earth-inspired wobble would become more pronounced. Add so much mass that the Earth weighs as much as the Sun, and both objects would take on new paths with an orbit around some point precisely between them. Yet this all assumes the added mass has the same velocity as the pre-existing Earth.

If this is a high school or junior high student posing the question, it is possible that student's instructor expects an answer like, "more mass would increase gravitational attraction, pulling the two objects together and shrinking the Earth's orbit." Velocity is a relative thing. If the velocity of mass added to the Earth is zero relative to the Sun's motion, then from a terrestrial reference it would be quite fast in the opposite direction of the Earth's ongoing orbit. The net reduction in orbital velocity would lead to a smaller orbit or perhaps even a spiral path toward an Earth-Sun collision.

On the other hand, if the instructor is clever, he or she likely implied (or stated outright) that the added mass would be consistent with the Earth's velocity at the moment of addition. This brings us back to where we started -- a scenario where anything up through x100 Earth masses would likely change Earth's orbit only a little and give the Sun a slightly different wobble, while something like x300,000 Earth masses would transform local space into a binary system with the Earth and Sun both orbiting a point representing their collective center of gravity.

Certainly there are better places to go than a game wiki to ask questions about celestial mechanics. Also, hopefully, this homework assignment was due long before this response was posted. Also, hopefully, the individual asking this question will in future recognize the opportunity to read words before pressing "submit" thereby avoiding future incidents involving very nearly incomprehensible grunts presented in the guise of questions. For that matter, hopefully the individual asking this question will also realize that every bit of school work dodged as a tender young kid translates into one additional bit of stupid baggage that interferes with the prospect of any future achievements outside the virtually inaccessible realms of Hollywood and professional sports.

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