Gravitational potential energy

Two masses held apart store energy in their separation, and AP gives you two expressions for it depending on the scale.

Near a planet's surface the field is nearly constant, so only the change matters and the sheet prints $\Delta U_g = mg\Delta y$. Note the $\Delta$ on both sides. This form gives a change, never an absolute value, so you choose the height that counts as zero and then stay with that choice.

For any separation the sheet prints $U_G = -G m_1 m_2 / r$. Here the zero is not up to you: the CED fixes it by defining the gravitational potential energy of a satellite and massive central object system to be zero when the satellite is an infinite distance from the central object.

That is where the minus sign comes from. Zero means infinitely far apart, so any bound pair has less energy than that and sits below zero. Move the masses closer and $r$ shrinks, $U_G$ becomes more negative, and kinetic energy grows to match. Negative here means bound, not impossible.

Two traps. Writing $-Gm_1m_2/r^2$ puts a force expression where an energy expression belongs; energy carries one power of $r$ and force carries two. And $mg\Delta y$ is an approximation that breaks down once the height change becomes comparable to the planet's radius, which is precisely when orbit questions turn up.