i need an answer that you would write for an exam -gm1m2/r

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the concept of potential energy arises due to force which may be attractive or repulsive. when the force is attractive, the concerned potential will always be negative. since gravitational force can only be attractive( it is never negative ) the gravitational potenitla energy will always be negative.
( the electrostatic potential energy and magnetic potential energy can be both positive and negative, becuase both electric and magnetic force can be attractive as well as repulsive)

In general, negative energy just means energy below the energy of the datum state at which we define energy to equal zero. For many types of energy (GPE, EPE, Thermal energy, Chemical energy) It is usually difficult to predict absolute energy, and therefore, in such a case we must define zero energy at a particular state or location.
In the case of the GPE formula which was derived from Newton’s law of gravity, the datum is placed at infinity, where the bodies are fully separated. Because objects will come in to proximity, falling under the force of gravity alone, no non-gravity force needs to do work on the objects to bring them together. In fact, an outside stopping force is needed instead, which will do negative work on the objects. GPE is equal to amount of work required to be done by an outside force to bring objects from the datum position to their position. Since negative work is done countering gravity, the GPE is negative.
The datum is placed at r = infinity, because it makes the calculus of deriving the formula more straightforward.
In the formula for uniform gravity, you are free to select any datum you like. Often the ground or the floor is convenient.
Notation note:
GPE = -G*m1*m2/r
F = G*m1*m2/r^2
It is crucial to use an uppercase G to represent the universal constant of gravitation. Lowercase g refers to local gravitational field, and on earth, lowercase g is the famous value 9.8 N/kg.
Also, be certain to use asterisks for all multiplication, and carats for all exponents (unless using “exp()” for natural exponential). This confuses us less, and enables us to tell the difference between multi-letter variables and multiplication.

Potential energy is measured relative to an arbitrary zero reference point. “Infinity”, meaning as far as possible from all masses, is often chosen as zero potential, and there is no higher potential than infinity. So relative to infinity, all gravitational potentials are negative. However, you can just as properly choose sea level on planet Earth or the center of planet Earth to represent zero potential; you may choose the table top in your lab as zero potential, or any other convenient reference point. It’s only when you choose infinity that all gravitational potentials are negative.

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the concept of potential energy arises due to force which may be attractive or repulsive. when the force is attractive, the concerned potential will always be negative. since gravitational force can only be attractive( it is never negative ) the gravitational potenitla energy will always be negative.

( the electrostatic potential energy and magnetic potential energy can be both positive and negative, becuase both electric and magnetic force can be attractive as well as repulsive)

In general, negative energy just means energy below the energy of the datum state at which we define energy to equal zero. For many types of energy (GPE, EPE, Thermal energy, Chemical energy) It is usually difficult to predict absolute energy, and therefore, in such a case we must define zero energy at a particular state or location.

In the case of the GPE formula which was derived from Newton’s law of gravity, the datum is placed at infinity, where the bodies are fully separated. Because objects will come in to proximity, falling under the force of gravity alone, no non-gravity force needs to do work on the objects to bring them together. In fact, an outside stopping force is needed instead, which will do negative work on the objects. GPE is equal to amount of work required to be done by an outside force to bring objects from the datum position to their position. Since negative work is done countering gravity, the GPE is negative.

The datum is placed at r = infinity, because it makes the calculus of deriving the formula more straightforward.

In the formula for uniform gravity, you are free to select any datum you like. Often the ground or the floor is convenient.

Notation note:

GPE = -G*m1*m2/r

F = G*m1*m2/r^2

It is crucial to use an uppercase G to represent the universal constant of gravitation. Lowercase g refers to local gravitational field, and on earth, lowercase g is the famous value 9.8 N/kg.

Also, be certain to use asterisks for all multiplication, and carats for all exponents (unless using “exp()” for natural exponential). This confuses us less, and enables us to tell the difference between multi-letter variables and multiplication.

Potential energy is measured relative to an arbitrary zero reference point. “Infinity”, meaning as far as possible from all masses, is often chosen as zero potential, and there is no higher potential than infinity. So relative to infinity, all gravitational potentials are negative. However, you can just as properly choose sea level on planet Earth or the center of planet Earth to represent zero potential; you may choose the table top in your lab as zero potential, or any other convenient reference point. It’s only when you choose infinity that all gravitational potentials are negative.