# Gravitational Potential Definition

## Main Question or Discussion Point

In my text book, the definition of the Gravitational Potential, V is defined as :" the gravitational potential of a point in a gravitational field is the work done per unit mass by the pull of gravity to bring a body from infinity to that point. "
Who make this definition ? As i know, infinity is a quite abstract concept, most of the time it causes confusion, hence, why physicist still choose to use "infinity" ? Is there any benefit they will get by using inifinity in the definition ?

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Yes. The potential is zero at infinity so you lose a constant term from the equation. If infinity gives you problems just think of it as very very very very very far away.

Firstly, i don't understand what you mean by "lose a constant term from the equation" ?
Secondly, i believe you claim that the potential at infinity is zero because you base on that equation. Of course, if just base on the equation, even me also will claim that the potential at infinity is zero, this is the highest potential value, other potential will be negative value.
Now let's make some imagination, imagine that you are the first physicist who trying to give a definition to potential. A correct definition should able to imply something which consistent with the observed fact. One example is the potential will increases if the distant from the source is increased. Hence the lowest potential is when you are inside that point (nearest to the source). Normally, people will give the lowest value as zero and highest as infinity when deal with something just scalar. So, why don't you or the ancient physicist define potential as "the work done per unit mass to bring a mass from the source to that point." ?
I believe this definition is much easier! Don't forget that the potential concept was exist at the ancient time, you really think that the people at that time will have a complete understand of the word Infinity ?
Anyway, i believe there is some reasons why ancient physicist choose to use inifinity, but what is it ?

I meant that when you calculate the said work done by gravitation the term $$U(\infty)$$ is zero. Did you mean gravitational potential energy btw?

I see. No i don't mean gravitational potential energy, i mean gravitational potential. (but this is not a big problem, gravitational potential energy is really an energy value while the gravitational potential is energy per mass, that is all.)
Could you give some comment on my second part of the previous message!