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*From*: "Bob Sciamanda" <treborsci@verizon.net>*Date*: Wed, 02 Jan 2013 18:57:44 -0500

How about "free fall gravity" for 1, and "Newtonian gravitation" for 2 ?

-----Original Message-----

From: John Denker

Sent: Wednesday, January 02, 2013 5:05 PM

To: Phys-L@Phys-L.org

Subject: [Phys-L] two very different "gravity" concepts

Hi --

Sometimes multiple different concepts are hiding behind

one name. This is a recipe for endless confusion.

This does not necessarily mean that we should keep one

concept and get rid of the others. Oftentimes all the

concepts are valid and useful, and all we need to do is

give them new names.

The example for today is gravity, also known as gravitation.

A) One type of gravity is characterized by the equation

F1 = m g [1]

where g is the acceleration of "gravity" in some chosen

reference frame. This is almost certainly the first

type of gravity that students encounter.

In accordance with Einstein's principle of equivalence,

this type of gravity can be zeroed out by choosing a

different reference frame.

B) The other type of gravity is characterized by the equation

|F2| = G M m / r^2 [2]

This type of gravity cannot be zeroed out, not by

choosing a different reference frame or by any other

means.

In more detail: The g vector in Spain is very nearly

equal-and-opposite to the g vector in New Zealand.

By choosing a suitable reference frame you can zero

out one or the other, but not both at the same time.

At some risk, we can write

|g2| = G M / r^2 [3]

However, it must be emphasized that the g2 that appears

in equation [3] is rarely if ever equal to the g

that appears in equation [1]. In typical terrestrial

situations g2 is the largest contribution to g, but

the other contributions are definitely not negligible.

=============

As for naming these things, equation [2] is widely known

as the law of /universal/ gravitation.

For quite some time I have been struggling to find a

good name for equation [1]. The opposite of "universal"

is "local" but that doesn't capture the correct idea.

The crucial idea behind equation [1] is not that it is

local, but that it is frame-dependent.

You can't just say that [1] is relative and [2] is not,

because the g vector is always relative; the only

question is relative to /what/. Equation [1] tells us

to measure the g vector relative to some chosen reference

frame. Equation [2] tells to measure the g vector in

Spain relative to the g vector in New Zealand.

Unless/until somebody comes up with a better word, I'm

going to call equation [1] the _framative_ gravity.

That's a contraction for "frame-relative".

As for equation [2], I'm mostly content to call it the

universal gravity. However ... one could argue that

by combining equation [2] with Einstein's principle of

equivalence, we discover that universal gravity doesn't

directly tell us about the g vector at all, but rather

about place-to-place differences in g. In other words,

the only universal thing about equation [2] is the

/tidal stress/.

Therefore on alternate Tuesdays I'm tempted to call

equation [2] the equation of universal tidal stress.

I'm not saying this is perfect, but it does have some

advantages.

I am quite aware that talking about tidal stress runs

the risk of confusing students ... but OTOH taking about

universal gravitation in a way that is inconsistent with

the equivalence principle runs a far greater risk of

far more serious confusion.

==============

I leave it as a question: Does anybody out there have a

better way of thinking about and talking about the two

different "gravity" concepts?

_______________________________________________

Forum for Physics Educators

Phys-l@phys-l.org

http://www.phys-l.org/mailman/listinfo/phys-l

Bob Sciamanda

Physics, Edinboro Univ of PA (Em)

treborsci@verizon.net

http://mysite.verizon.net/res12merh/

**Follow-Ups**:**Re: [Phys-L] two very different "gravity" concepts***From:*John Denker <jsd@av8n.com>

**References**:**[Phys-L] two very different "gravity" concepts***From:*John Denker <jsd@av8n.com>

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