Proxemics
The term proxemics was introduced by researcher Edward T. Hall in 1963 when he investigated people's use of personal space. He used four categories for informal space: the intimate distance for embracing or whispering (6-18 inches), the personal distance for conversations among good friends (1.5-4 feet), social distance for conversations among acquaintances (4-12 feet), and public distance used for public speaking (12 feet or more).
Physical closeness and touching are forms of physical intimacy. What distance is appropriate for a particular social situation depends on culture. It is also a matter of personal preference. People may feel uncomfortable if the distance is too large (cold) or too small (intrusive).
Similar observations apply to figurative senses of distance, such as emotional distance.
A related term is propinquity. Propinquity is one of the factors, set out by Jeremy Bentham, used to measure the amount of pleasure in a method known as felicific calculus.
See also T-V distinction, Skinship.