What singleton name would you give such a relationship? There are only so many words in English that I can think of that consider a relationship as a separate thing: friendship, brotherhood, sisterhood, fraternity, rivalry, marriage, family, partnership, "enemyship", "frenemyship"... (Notice how I had to start making them up?)
"Mentorship"? Maybe, but that sounds too close to me like "internship," which is not a relationship, but a role. It's why I'm really glad I know some of the Japanese suffixes, such as: -sama, -san, -kun, -chan, -sensei, -senpai, and a few others. The relationship becomes inherent in the speech. Moreover, there are the plain and polite forms of speech, among others. And, which one is allowable changes based on the relationship between speaker and listener. If the relationship changes, then the speech is likely to change. (Now, that's overly simplified, but hopefully illustrates the point.)
Mentor/Mentee, Teacher/Student, and similar are about the only ways certain relationships can be said in English. If you can find a way to use a singular noun to describe such a relationship, then I suspect that would likely give more insight into the relationship.
I guess I just repeated what Jim said without seeing it first...
Though, I appreciate the expounding on the analogy with gravity.