### Question

Is weight determined strictly by the distance between and mass of two objects, or are other factors figured in; i.e. can a person be considered weightless underwater?

If weight is defined as the gravitational force on a body, then your statement that it depends only on the masses of the two objects and the distance between them (actually, the distance between their respective centers of gravity), is correct. But that definition implies that conditions we ordinarily call 'weightless' are not. Everything from orbiting astronauts to people in falling elevators have a gravitational force acting upon them. This definition implies they all have weight in spite of the fact we ordinarily consider them 'weightless'.

If you use a more specific definition of weight as 'the amount of external force required to keep a body at rest in its inertial frame of reference', you come closer to the more common understanding of 'weightlessness'. In this case an astronaut needs no further 'upward' force to remain stationary in his spacecraft and can be considered 'weightless'. Similarly, an object submerged under water would only weigh the difference between its gravitational force and the upward buoyant force.

Using this second definition, a person underwater wearing just enough weights to establish neutral buoyancy CAN be considered weightless since no additional external force is required to keep him at rest relative to the bottom. Of course, his internal organs still experience a net downward force and require support from within, so the feeling does not exactly duplicate the weightlessness of an orbiting astronaut.
Answered by: Paul Walorski, B.A. Physics, Part-time Physics Instructor

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