Re: weightless in orbit

[John Denker <jsd@MONMOUTH.COM>]

At 11:59 PM 1/25/01 -0800, Leigh Palmer wrote:

> g is what is measured by a gravimeter, or it is the initial acceleration
> of an object released from rest in any frame whatever.

This is a fine definition of g.  This is simultaneously the simplest
definition, and also the most sophisticated definition (since it is
consistent with Einstein's principle of equivalence).

> I do not separate out "the gravitational interaction of the earth and the
> object". All those parenthetical items I mentioned are *included*
> in g,

Right.

> and there is no practical way to separate them;

Right.

> they are not of any concern whatever to the student.

Right, not during the introductory phases, which is what we are discussing.

Similarly at 10:17 AM 1/25/01 -0800, Leigh Palmer wrote:
> In the orbiting Space Shuttle the gravitational field is nearly zero, so
> we say the astronauts inside are weightless, or very nearly so.

Right.

> All of these statements conform to both scientific and common cultural
> understanding.

Right.

However at 10:29 AM 1/26/01 +0200, Savinainen Antti wrote:

> I disagree with Leigh that the gravitational field would be zero (or very
> nearly zero) in the orbiting space shuttle. The very reason for the
> orbiting is the gravitational force exerted by the Earth and hence the
> gravitational field cannot be zero. Of course astronauts inside the
> shuttle feel apparent weightlessness because the satellite is in a free fall.

This position is inconsistent with modern physics.

We are accustomed to measuring quantities that are very sensitive to what
frame of reference is used;  this includes velocity, kinetic energy, and
many other frame-dependent quantities.   So it is with something that Antti
would call "apparent gravity" and modern physics calls "gravity":  inside
the orbiting shuttle this quantity is essentially zero.  An observer on a
tall (!) tower, in the earth's reference frame, would measure a value of
9.8m/s^2 for this same quantity at the same location as the shuttle flies past.

Leigh's statement is 100% correct in the specified orbiting frame of
reference.  Antti's counterargument that "the gravitational field cannot be
zero" is not true in the orbiting frame of reference, although it would be
true in a nearby tower-based frame of reference.