[time-nuts] FW: Pendulums & Atomic Clocks & Gravity

Ulrich Bangert df6jb at ulrich-bangert.de
Tue May 29 14:38:53 EDT 2007


Bill,

in general I would underwrite every single sentence of your explanation
with the exception of

> The idea that the centripetal force that balances the 
> gravitational force is fictitious was not popular when I was 
> educated, before 1960.

because gravitation IS the centripetal force for the satellite's motion.
In this case the right word would have beeen indeed "centrifugal".
Centripetal forces are REAL forces and are the source of the permanent
"falling". While "forces" are one of the very first things that pupils
are confronted with in learning physics they are by no means trivial and
can be tricky to an high extend. 

If you would like to dive even deeper into this subject consider the
following question:

If I stand on the floor of my flat, clearly no acceleration is to be
noticed on my body although it is clear that earth attracs me with my
weight force (being much too high since years). If no acceleration is to
be noticed at my body then a second force must be there that balances
the gravitational force, and in this case it is really a BALANCE. Since
I stand on the floor the floor must be the source of that force. Big
question: HOW does it manage to exhibit this force to my body?

Regards
Ulrich Bangert

Regards
Ulrich Bangert

> -----Ursprüngliche Nachricht-----
> Von: time-nuts-bounces at febo.com 
> [mailto:time-nuts-bounces at febo.com] Im Auftrag von Bill Hawkins
> Gesendet: Dienstag, 29. Mai 2007 19:23
> An: 'Discussion of precise time and frequency measurement'
> Betreff: Re: [time-nuts] FW: Pendulums & Atomic Clocks & Gravity
> 
> 
> Aargh!
> 
> Please change "Centripetal force also goes away if radial 
> motion goes away." to "Centripetal force also goes away if 
> angular motion goes away."
> 
> 
> -----Original Message-----
> From: Bill Hawkins [mailto:bill at iaxs.net] 
> Sent: Tuesday, May 29, 2007 12:17 PM
> To: 'Discussion of precise time and frequency measurement'
> Subject: RE: [time-nuts] FW: Pendulums & Atomic Clocks & Gravity
> 
> Finally, something that makes sense! Thanks, James Maynard.
> 
> The idea that the centripetal force that balances the 
> gravitational force is fictitious was not popular when I was 
> educated, before 1960.
> 
> But centripetal force goes away if gravity goes away. The 
> orbiting object continues in a straight line because no 
> forces are causing acceleration. When there is gravity, and 
> an object falls around the Earth, the velocity vector is not 
> constant - it rotates 360 degrees for each orbit of the 
> Earth. An additional acceleration is required to make that 
> happen, hence centripetal force.
> 
> Gravity and centripetal force must balance if the object is 
> to keep falling in an orbit, which does not have to be  
> circular. If the orbit is not circular then the object's 
> velocity magnitude changes to match its altitude.
> 
> Centripetal force also goes away if radial motion goes away. 
> The space shuttle has rocket engines that can reduce the 
> radial motion so that the altitude falls low enough to start 
> atmospheric braking. Note that great forces are required to 
> change the angle of the velocity vector. A shuttle can not 
> drive around the sky like an aircraft (when it is in
> space) but it does have some control of altitude.
> 
> Bill Hawkins
> 
> 
> -----Original Message-----
> From: James Maynard
> Sent: Tuesday, May 29, 2007 11:26 AM
> To: Discussion of precise time and frequency measurement
> Subject: Re: [time-nuts] FW: Pendulums & Atomic Clocks & Gravity
> 
> Didier Juges wrote:
> > Bruce,
> >
> > A lot of the statements that have been made lately on this subject
> kind of make sense to me in a way taken in isolation, but 
> they do not all agree with each other, and that makes me 
> uncomfortable.
> >
> > Example:
> >
> > I do not understand why the frame of reference would matter when you
> talk about gravity field. There is a gravity field or not, 
> and the frame of reference should not matter. I understand 
> that the frame of reference matters when you talk about 
> displacement, velocity or acceleration. But the magnitude of 
> a field, or a force, does not depend on the observer as it is 
> static, or maybe a better term would be absolute or self-referenced?
> >   
> The reason that the frame of reference matters is that 
> gravity is indistinguishable from acceleration. (This is an 
> assumption that Einstein made when deriving his general 
> theory of relativity. It seems to work.)
> 
> An "inertial" frame of reference is a non-accelerating frame 
> of reference. In an inertial frame of reference, Newton's 
> laws of motion work -- if you use Newton's gravitational 
> relationship, that the gravitational force (weight) that each 
> of two bodies exerts on the other is proportional to both 
> their masses, and inversely proportional to the square of the 
> distance between them.
> 
> In an accelerating frame of reference (either linear 
> acceleration, or rotational acceleration, or both) additional 
> forces, technically called "fictitious" forces, must be 
> introduced in order to explain the motions of bodies with 
> Newtonian mechanics. The "fictitious" forces on a body are 
> also proportional to the body's mass. (A body's mass is just 
> a measure of its inertia: to accelerate at an acceleration 
> "a", a force "F" must be applied, and the mass "m" is just F/a.)
> 
> If the frame of reference has linear acceleration (relative 
> to an inertial frame of reference), bodies within that frame 
> of reference will experience a fictitious force that is 
> proportional to their masses and to the acceleration of the 
> frame of reference. Viewed from the frame of reference of a 
> car that is accelerating away from a stop light, the 
> passengers are pressed back in their seats by a force 
> proportional to the acceleration of the car and to their 
> masses. This fictitious force disappears when you view the 
> situation from the an inertial frame of reference. Viewed 
> from that point of view, the seats are pressing forward on 
> the passengers to cause them to accelerate with the car.
> 
> Viewed from a rotating frame of reference, we have other fictitious
> forces: centrifugal force and Coriolis force. Both of these 
> are proportional to the mass of the body on which they act -- 
> when viewed from the rotating frame of reference. Both vanish 
> if you view the situation from a non-rotating frame of reference.
> 
> Sometimes - usually, even - it's simpler to view the problem 
> from an inertial frame of reference. Sometimes, though, it's 
> easier to look at the problem in an accelerating frame of 
> reference. If you do that, you account for the frame of 
> reference's acceleration by introducing fictitious forces.
> > Now, it makes sense that an object immersed in gravity fields from
> several larger objects may not be able to tell the difference 
> between multiple fields, and a unique, "net" field (in the 
> sense of Newton's net force), at least as long as the 
> gradient is small enough that it cannot be observed within 
> the dimensions of the object. So if the "net" field is zero 
> and the gradient small enough to be ignored, the object will 
> behave the same as if there were no field.
> >   
> When you say "within the dimensions of the object" I assume 
> that you are looking at the problem from the frame of 
> reference of the object. That's natural if you are, for 
> example, in an orbiting satellite, such as the International 
> Space Station. Viewed from an inertial frame of reference, 
> the ISS is following an orbit determined by the vector sum of 
> the gravitational forces (from earth, moon, sun, etc.) that 
> act upon it. 
> Viewed from the frame of reference of the space station, 
> however, these forces add to zero.
> > However, for an observer on earth, a satellite is in the 
> gravity field
> 
> > of earth (let's assume all other gravity fields from the 
> sun and other
> 
> > planets are negligible), which is not zero at the altitude of the
> > satellite,
> Even an observer on earth is on an accelerating frame of 
> reference. (The earth rotates on its axis.)
> > ... yet for an observer on the satellite, the net field 
> appears to be
> zero. Where is the counter-field coming from? And why can't 
> we observe it from earth? How can the field be different when 
> observed from different points?
> >   
> For an observer on the satellite (in the satellite's frame of 
> reference), the counter-field is created by the fictitious 
> forces due to the satellite's acceleration. For example, 
> "centrifugal" force due to the satellite's gravitational 
> acceleration towards the center of mass of the earth.
> > Could it be that the effect of the gravity field (with is a
> centripetal force applied to the object in orbit) is 
> compensated by a centrifugal force, (which I was close to 
> admit is not a real force and does not exist) so that the 
> effect of the gravity field, which would be a force of 
> attraction towards the planet, is compensated by another 
> force in the opposite direction so that the net force is 
> zero, as it would be if there were no gravity field? So that 
> the object does not know the difference between two forces 
> that compensate each other and no force at all.
> >   
> Yes! The "fictitious" forces, however, do exist -- when 
> viewed from the frame of reference of the accelerating 
> satellite. I wouldn't say that fictitious forces are not real 
> - just that they only exist when viewed in an accelerating 
> (non-inertial) frame of reference.
> 
> 
> 
> 
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