1 colonizing a black hole 10 points image credit freepik the year is 2
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
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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