1 Colonizing a Black Hole (10 points) Image credit: freepik The year is 2237. Having developed interstellar travel and begun vast mining operations, humanity has decided to begin a scientific operation to build a base around the small black hole M231 X-3. The goal is to build a hollow sphere of metal around the black hole, to act as an artificial planet from which research into the black hole's nature can be performed. But in order to do so, scientists and engineers need to perform some crucial calculations in order to determine the scale of the project. We have sent a space probe to measure and photograph M231 X-3. The probe was, ultimately, destroyed, but not before sending us valuable data on the black hole's characteristics. We have created a standardized rectangular coordinate grid with which to map out M231 X-3 and surrounding structures, with the black hole itself centered at the origin. (a) (2 points) According to the probe's measurements, the following equation dictates the gravitational field created by M231 X-3 at a given position in space: 300000 9 = 2² + y² + 2² (Here the gravitational field is given in m/s², and the positional coordinates are given in km.) List the independent and dependent variable(s) in this equation.

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