[time-nuts] FW: Pendulums & Atomic Clocks & Gravity
Bill Hawkins
bill at iaxs.net
Tue May 29 13:23:23 EDT 2007
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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