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Why can't the zero value of gravitational potential energy be set at a different point instead of infinite distance within Newtonian gravity?

I am not asking why is gravitational potential energy considered negative. I am asking why does it necessarily need to be negative in Newtonian gravity.

I quoted it from: https://ned.ipac.caltech.edu/level5/Guth/Guth3.html

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    $\begingroup$ Possible duplicate of Why the gravitational potential energy at infinity is zero? $\endgroup$
    – joseph h
    Commented Mar 24 at 3:08
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/17082/2451 and links therein. $\endgroup$
    – Qmechanic
    Commented Mar 24 at 3:56
  • $\begingroup$ As the linked answers say, it's just numerically convenient to set the integration constant to zero at infinite radius. But we don't always do that. Sometimes, other choices make the arithmetic simpler. Eg, for a system on Earth we might set the zero at ground level, or sea level. When analysing a pendulum, it can be convenient to assign zero PE to the bottom of the arc of the pendulum's motion. $\endgroup$
    – PM 2Ring
    Commented May 26 at 16:48

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