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*From*: John Denker <jsd@av8n.com>*Date*: Fri, 19 Jan 2018 09:31:53 -0700

Hi --

To make a long story short, I find it helpful to write

the law of universal gravitation in terms of δg, namely:

G M

δg = - rhat ------- [1]

r^2

where rhat is a unit vector in the r direction. The

equation can be used to tell you how much g /changes/

on account of the mass M as you go from the center of

the earth to someplace else, separated by the displacement

vector r.

If you apply the equation twice, it tells you how

much g /changes/ on account of M as you go from

Spain to New Zealand, which may be more convenient

than trying to make direct measurements at the center

of the earth.

The emphasis here is on the idea of /change/ in g, as

expressed by the δ operator on the LHS of equation [1].

To say the same thing the other way, it would be a

blunder to leave off the δ operator. Equation [1]

does not and can not tell you the value of g. The

equivalence principle guarantees that g depends on

the choice of reference frame, whereas the RHS of

equation [1] is manifestly frame-independent

Let's be clear:

g = acceleration of a free particle, [2]

relative to the chosen reference frame

Beware that the RHS of equation [1] is called "gravity"

and the RHS of equation [2] is also called "gravity". No

wonder students are confused.

Every introductory physics book I've ever seen screws

this up royally ... even the Feynman lectures (which are

in general vastly more reliable than most other books).

This is an example of what I call a bisconception: two

ideas masquerading under the same name.

This sort of thing is exceedingly common. For example,

on a race track, one lap brings you back to the starting

point ... whereas in the pool, you have to swim two laps

to get back to the starting point.

Each definition is correct /in context/. It would be a

mistake to imagine that one is right and the other is

wrong. Instead, *three* ideas are needed: the first

definition, the second definition, and a higher-level

/traffic cop/ idea that indicates which context to use

in any given situation.

An essential first step is to repair the names, perhaps

by adding adjectives.

-- I call equation [2] the /framative/ gravity. That's

short for "frame-relative". This is denoted g.

-- I call equation [1] the /massogenic/ gravity. It is

the contribution to g on account of the mass M.

Obviously, the massogenic contribution is not the only

contribution to g.

Less obviously, the massogenic contribution may not even

be the only contribution to δg ... because there are also

centrifugal contributions, if you choose a rotating frame.

The rule is:

Centrifugal fields exist in the rotating frame

and not otherwise. [3]

In the introductory course, teach everybody rule [3]. It

takes only a moment. Then, if you decide that rotating

frames are outside the scope of the course, that's OK.

To say the same thing the other way, it's not OK to

pretend that such things don't exist. Avoiding them

is a choice, not a law of nature.

You can "mostly" avoid them, but not entirely. The

bisconception exists, and you have to deal with it

at least briefly. Students have seen space-station

videos, and have first-hand experience with cars and

playground equipment where it is perfectly natural

to analyze things in some frame other than the usual

terrestrial lab frame. If you tell them such things

don't exist they simply won't believe you. Even if

you don't want to deal with rotating frames, you still

need the /traffic cop/ to distinguish the two contexts.

And for that matter, the terrestrial lab frame is a

rotating frame. The massogenic contribution is the

main contribution to g, but there are also centrifugal

terms that affect the magnitude and direction of g to

a readily-measurable extent. If you try to calculate

g using equation [1] alone, you will get the wrong

answer.

Everything aboard the space station is really-and-truly

weightless (to an excellent approximation) ... relative

to the frame comoving with the station. The equivalence

principle guarantees this frame is as valid as any other.

To say the same thing the other way, it is a bad idea

to introduce notions of "apparent" weight or "apparent"

weightlessness. The weight is frame-dependent, but it's

not illusory or imaginary or merely apparent.

**Follow-Ups**:**Re: [Phys-L] gravity, weightlessness, etc.***From:*"LaMontagne, Bob" <RLAMONT@providence.edu>

**References**:**[Phys-L] Circular Motion in 20 GIFs***From:*"Derek McKenzie" <derek@physicsfootnotes.com>

**Re: [Phys-L] Circular Motion in 20 GIFs***From:*John Denker <jsd@av8n.com>

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