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

James Maynard james.h.maynard at usa.net
Tue May 29 21:37:09 UTC 2007


Bill Hawkins wrote:
> Finally, something that makes sense! Thanks, James Maynard.
>   
Thank you. However, in the following paragraphs you should use the term 
"centrifugal" rather than "centripetal".  A centripetal force is 
directed towards the axis of rotation. A centrifugal force is directed 
outward, away from the axis of rotation. I have edited your reply, with 
my changes indicated in [bracketed] text.
> The idea that the [centrifugal] force that balances the gravitational
> force is fictitious was not popular when I was educated, before 1960.
>
> But centripetal force [that is, the satellite's weight, mg] goes away if gravity [g] 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.
[Right. Here, the centripetal force is the gravitational force, the 
satellite's weight. The fictitious "centrifugal" force that balances the 
satellite's weight is only present when you view the problem from the 
frame of reference of the orbiting satellite.]
> Gravity and [centrifugal] 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.
I would say, rather, that the centripetal force, mg in this case, causes 
the satellite's velocity to change its direction. When viewed in the 
non-inertial frame of reference of the satellite, the corresponding 
fictitious centrifugal force also goes away, because the satellite is 
not accelerating in a direction perpendicular to its velocity.
>  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
>   
[I should also edit part of my previous post, as indicated in the 
bracketed text below.]

> -----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 youtalk 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 fromseveral 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* [together with fictitious forces such as centrifugal force]* 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.

---
James Maynard
Salem, Oregon, USA





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