I'm wondering about some assumptions I have to make in deriving the gravitational potential energy. This arises from the following exercise:
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Since the net force acting on the satellite is conservative, $$W=\oint_\mathcal{C}\vec F\cdot\mathrm{d}\vec r=0$$
Although I don't think that bit of information is necessary.
$$W = -GMm \ \int_{r_0}^{r_1} 1/r^2 dr$$
$$W = -GMm \left[-\frac{1}{r}\right]_{r_0}^{r_1}$$
Now, to arrive at the equation I'm looking to express, $r_0$ must equal $\infty$. However, I don't why this must be the case, to derive the potential energy. I know it's conventional to take the reference point of potential energy from an infinitely far away point, which is why $GPE$ is always negative, but it doesn't logically follow in the integral for me to do this, as it seems to imply the object was brought from $\infty$ to $r_1$ which doesn't make sense to me. So why is it that we set $r_0 = \infty$?