> > > Since you talked about closing speeds, can you explain what you mean by such an expression?

> ... in this post he says..."Closing speed is the rate of change of the distance between two objects as they both move.

Yes, that's basically it. The closing speed between two entities is the rate of change of the distance (separation) between them, as measured by a given frame (system of coordinates). Its "v1 ± v2" depending of sign conventions.

On 9/30/22 10:17 PM, rotchm wrote:
>>>> Since you talked about closing speeds, can you explain what
>>>> you mean by such an expression?
>> ... in this post he says..."Closing speed is the rate of change of
>> the distance between two objects as they both move.
>
> Yes, that's basically it. The closing speed between two entities is
> the rate of change of the distance (separation) between them, as
> measured by a given frame (system of coordinates).

Yes, but only for inertial coordinates. The closing speed for a given
pair of objects varies, depending on which inertial frame is used to
calculate/measure it.

> Its "v1 ± v2" depending of sign conventions.

Only when the two objects are moving along a single axis in the inertial
frame used. If that isn't so, the calculation is MUCH more complicated.

Tom Roberts

On Saturday, October 1, 2022 at 10:02:56 AM UTC-7, tjrob137 wrote:
> On 9/30/22 10:17 PM, rotchm wrote:
> >>>> Since you talked about closing speeds, can you explain what
> >>>> you mean by such an expression?
> >> ... in this post he says..."Closing speed is the rate of change of
> >> the distance between two objects as they both move.
> >
> > Yes, that's basically it. The closing speed between two entities is
> > the rate of change of the distance (separation) between them, as
> > measured by a given frame (system of coordinates).
> Yes, but only for inertial coordinates. The closing speed for a given
> pair of objects varies, depending on which inertial frame is used to
> calculate/measure it.
> > Its "v1 ± v2" depending of sign conventions.
> Only when the two objects are moving along a single axis in the inertial
> frame used. If that isn't so, the calculation is MUCH more complicated.
>
> Tom Roberts
Now, Tom Roberts, provide this forum with the proper and coordinate closing speeds, as calulated by observers on each closing object. I will state up front that you won't/can't do it.

On Saturday, October 1, 2022 at 10:02:56 AM UTC-7, tjrob137 wrote:
> On 9/30/22 10:17 PM, rotchm wrote:
> > Its "v1 ± v2" depending of sign conventions.
>
> Only when the two objects are moving along a single axis in the inertial
> frame used.

The same kinematics apply to motion along any curve, i.e., within any one-dimensional manifold, taking "distance" to refer to distance along the curve (i.e., distance within that 1D manifold), e.g., to cars moving along a curved road. The rate of change of the distance in this manifold satisfies the same kinematics. Since this is pure kinematics, the key is not inertialness, it is 1-dimensionalness.

> If that isn't so, the calculation is MUCH more complicated.

In a flat three dimensional manifold with inertial coordinates x,y,z,t we typically we are given x(t), y(t), z(t) for each object, and the rate of change of distance is just dL/dt where L = sqrt[(x2-x1)^2 +(y2-y1)^2 +(z2-z1)^2], so it isn't particularly difficult. For any other coordinate system x',y',z',t' we can also determine x'(t'), y'(t'), and z'(t') by direct application of the Lorentz transformation, and compute dL'/dt'. We can also easily transform to an inertial system in terms of which one object is at rest.

On Saturday, October 1, 2022 at 1:02:56 PM UTC-4, tjrob137 wrote:
> On 9/30/22 10:17 PM, rotchm wrote:

> Yes, but only for inertial coordinates. The closing speed for a given
> pair of objects varies, depending on which inertial frame is used to
> calculate/measure it.

Yes that is what we have been repeating all along this thread.

> > Its "v1 ± v2" depending of sign conventions.
> Only when the two objects are moving along a single axis in the inertial
> frame used.

Yes as we have been repeating all along this thread.

On Saturday, October 1, 2022 at 1:59:40 PM UTC-4, Stan Fultoni wrote:

> The same kinematics apply to motion along any curve, i.e., within any one-dimensional manifold, taking "distance" to
> refer to distance along the curve (i.e., distance within that 1D manifold), e.g., to cars moving along a curved road.
> The rate of change of the distance in this manifold satisfies the same kinematics. Since this is pure
> kinematics, the key is not inertialness, it is 1-dimensionalness.

Yes, that's more accurate!

On Saturday, October 1, 2022 at 10:58:33 AM UTC-7, patdolan wrote:
> On Saturday, October 1, 2022 at 10:02:56 AM UTC-7, tjrob137 wrote:
> > On 9/30/22 10:17 PM, rotchm wrote:
> > >>>> Since you talked about closing speeds, can you explain what
> > >>>> you mean by such an expression?
> > >> ... in this post he says..."Closing speed is the rate of change of
> > >> the distance between two objects as they both move.
> > >
> > > Yes, that's basically it. The closing speed between two entities is
> > > the rate of change of the distance (separation) between them, as
> > > measured by a given frame (system of coordinates).
> > Yes, but only for inertial coordinates. The closing speed for a given
> > pair of objects varies, depending on which inertial frame is used to
> > calculate/measure it.
> > > Its "v1 ± v2" depending of sign conventions.
> > Only when the two objects are moving along a single axis in the inertial
> > frame used. If that isn't so, the calculation is MUCH more complicated.
> >
> > Tom Roberts

> Now, Tom Roberts, provide this forum with the proper and coordinate closing speeds, as calulated by observers on each closing object. I will state up front that you won't/can't do it.

No one can do it, as I already told you. Closing speed *cannot* be observed by any observer on a closing object, by definition. You apparently are clueless about this really simple concept.

rotchm wrote:

> On Saturday, October 1, 2022 at 1:02:56 PM UTC-4, tjrob137 wrote:
>> On 9/30/22 10:17 PM, rotchm wrote:
>
>> Yes, but only for inertial coordinates. The closing speed for a given
>> pair of objects varies, depending on which inertial frame is used to
>> calculate/measure it.
>
> Yes that is what we have been repeating all along this thread.
>
>> > Its "v1 ± v2" depending of sign conventions.
>> Only when the two objects are moving along a single axis in the
>> inertial frame used.
>
> Yes as we have been repeating all along this thread.

nonsense, you are both wrong. The motion is always in one dimension, the
point is where you embed this dimension, 2D, 3D, 3D+t, 4D etc. You guys
are talking not knowing what you are talking about.

watch out, not to cross my borderline.

On Saturday, October 1, 2022 at 11:34:20 AM UTC-7, Paul Alsing wrote:
> On Saturday, October 1, 2022 at 10:58:33 AM UTC-7, patdolan wrote:
> > On Saturday, October 1, 2022 at 10:02:56 AM UTC-7, tjrob137 wrote:
> > > On 9/30/22 10:17 PM, rotchm wrote:
> > > >>>> Since you talked about closing speeds, can you explain what
> > > >>>> you mean by such an expression?
> > > >> ... in this post he says..."Closing speed is the rate of change of
> > > >> the distance between two objects as they both move.
> > > >
> > > > Yes, that's basically it. The closing speed between two entities is
> > > > the rate of change of the distance (separation) between them, as
> > > > measured by a given frame (system of coordinates).
> > > Yes, but only for inertial coordinates. The closing speed for a given
> > > pair of objects varies, depending on which inertial frame is used to
> > > calculate/measure it.
> > > > Its "v1 ± v2" depending of sign conventions.
> > > Only when the two objects are moving along a single axis in the inertial
> > > frame used. If that isn't so, the calculation is MUCH more complicated.
> > >
> > > Tom Roberts
>
> > Now, Tom Roberts, provide this forum with the proper and coordinate closing speeds, as calulated by observers on each closing object. I will state up front that you won't/can't do it.
> No one can do it, as I already told you. Closing speed *cannot* be observed by any observer on a closing object, by definition. You apparently are clueless about this really simple concept.

How can an atom leave light behind if it does not have its own absolute speed in expanding space?
That is a motion BH that is only temporary.

On Saturday, October 1, 2022 at 11:34:20 AM UTC-7, Paul Alsing wrote:
> On Saturday, October 1, 2022 at 10:58:33 AM UTC-7, patdolan wrote:
> > On Saturday, October 1, 2022 at 10:02:56 AM UTC-7, tjrob137 wrote:
> > > On 9/30/22 10:17 PM, rotchm wrote:
> > > >>>> Since you talked about closing speeds, can you explain what
> > > >>>> you mean by such an expression?
> > > >> ... in this post he says..."Closing speed is the rate of change of
> > > >> the distance between two objects as they both move.
> > > >
> > > > Yes, that's basically it. The closing speed between two entities is
> > > > the rate of change of the distance (separation) between them, as
> > > > measured by a given frame (system of coordinates).
> > > Yes, but only for inertial coordinates. The closing speed for a given
> > > pair of objects varies, depending on which inertial frame is used to
> > > calculate/measure it.
> > > > Its "v1 ± v2" depending of sign conventions.
> > > Only when the two objects are moving along a single axis in the inertial
> > > frame used. If that isn't so, the calculation is MUCH more complicated.
> > >
> > > Tom Roberts
>
> > Now, Tom Roberts, provide this forum with the proper and coordinate closing speeds, as calulated by observers on each closing object. I will state up front that you won't/can't do it.
> No one can do it, as I already told you. Closing speed *cannot* be observed by any observer on a closing object, by definition. You apparently are clueless about this really simple concept.
Increase in angle subtended by object, divided by proper time. This method will even give you acceleration.

On Saturday, October 1, 2022 at 12:14:19 PM UTC-7, mitchr...@gmail.com wrote:
> On Saturday, October 1, 2022 at 11:34:20 AM UTC-7, Paul Alsing wrote:
> > On Saturday, October 1, 2022 at 10:58:33 AM UTC-7, patdolan wrote:
> > > On Saturday, October 1, 2022 at 10:02:56 AM UTC-7, tjrob137 wrote:
> > > > On 9/30/22 10:17 PM, rotchm wrote:
> > > > >>>> Since you talked about closing speeds, can you explain what
> > > > >>>> you mean by such an expression?
> > > > >> ... in this post he says..."Closing speed is the rate of change of
> > > > >> the distance between two objects as they both move.
> > > > >
> > > > > Yes, that's basically it. The closing speed between two entities is
> > > > > the rate of change of the distance (separation) between them, as
> > > > > measured by a given frame (system of coordinates).
> > > > Yes, but only for inertial coordinates. The closing speed for a given
> > > > pair of objects varies, depending on which inertial frame is used to
> > > > calculate/measure it.
> > > > > Its "v1 ± v2" depending of sign conventions.
> > > > Only when the two objects are moving along a single axis in the inertial
> > > > frame used. If that isn't so, the calculation is MUCH more complicated.
> > > >
> > > > Tom Roberts
> >
> > > Now, Tom Roberts, provide this forum with the proper and coordinate closing speeds, as calulated by observers on each closing object. I will state up front that you won't/can't do it.
> > No one can do it, as I already told you. Closing speed *cannot* be observed by any observer on a closing object, by definition. You apparently are clueless about this really simple concept.
> How can an atom leave light behind if it does not have its own absolute speed in expanding space?
> That is a motion BH that is only temporary.

How can an atom
leave light behind
if it does not, will not
Have its own absolute speed

Expanding space?

That is a motion of Blackness
that is only temporary

On Saturday, October 1, 2022 at 12:29:34 PM UTC-7, patdolan wrote:
> On Saturday, October 1, 2022 at 11:34:20 AM UTC-7, Paul Alsing wrote:
> > On Saturday, October 1, 2022 at 10:58:33 AM UTC-7, patdolan wrote:
> > > On Saturday, October 1, 2022 at 10:02:56 AM UTC-7, tjrob137 wrote:
> > > > On 9/30/22 10:17 PM, rotchm wrote:
> > > > >>>> Since you talked about closing speeds, can you explain what
> > > > >>>> you mean by such an expression?
> > > > >> ... in this post he says..."Closing speed is the rate of change of
> > > > >> the distance between two objects as they both move.
> > > > >
> > > > > Yes, that's basically it. The closing speed between two entities is
> > > > > the rate of change of the distance (separation) between them, as
> > > > > measured by a given frame (system of coordinates).
> > > > Yes, but only for inertial coordinates. The closing speed for a given
> > > > pair of objects varies, depending on which inertial frame is used to
> > > > calculate/measure it.
> > > > > Its "v1 ± v2" depending of sign conventions.
> > > > Only when the two objects are moving along a single axis in the inertial
> > > > frame used. If that isn't so, the calculation is MUCH more complicated.
> > > >
> > > > Tom Roberts
> >
> > > Now, Tom Roberts, provide this forum with the proper and coordinate closing speeds, as calulated by observers on each closing object. I will state up front that you won't/can't do it.
> > No one can do it, as I already told you. Closing speed *cannot* be observed by any observer on a closing object, by definition. You apparently are clueless about this really simple concept.
> Increase in angle subtended by object, divided by proper time. This method will even give you acceleration.

The distance d of an object of cross-section h subtended by an angle 𝜃 is

d = sqrt[ ( 1 - h^2 )/( 2 cos𝜃 ) - ( h^2/4 ) ]

The it's ∆d/∆t and ∆d/∆t^2

On Saturday, October 1, 2022 at 2:29:37 PM UTC-7, patdolan wrote:
> On Saturday, October 1, 2022 at 12:29:34 PM UTC-7, patdolan wrote:
> > On Saturday, October 1, 2022 at 11:34:20 AM UTC-7, Paul Alsing wrote:
> > > On Saturday, October 1, 2022 at 10:58:33 AM UTC-7, patdolan wrote:
> > > > On Saturday, October 1, 2022 at 10:02:56 AM UTC-7, tjrob137 wrote:
> > > > > On 9/30/22 10:17 PM, rotchm wrote:
> > > > > >>>> Since you talked about closing speeds, can you explain what
> > > > > >>>> you mean by such an expression?
> > > > > >> ... in this post he says..."Closing speed is the rate of change of
> > > > > >> the distance between two objects as they both move.
> > > > > >
> > > > > > Yes, that's basically it. The closing speed between two entities is
> > > > > > the rate of change of the distance (separation) between them, as
> > > > > > measured by a given frame (system of coordinates).
> > > > > Yes, but only for inertial coordinates. The closing speed for a given
> > > > > pair of objects varies, depending on which inertial frame is used to
> > > > > calculate/measure it.
> > > > > > Its "v1 ± v2" depending of sign conventions.
> > > > > Only when the two objects are moving along a single axis in the inertial
> > > > > frame used. If that isn't so, the calculation is MUCH more complicated.
> > > > >
> > > > > Tom Roberts
> > >
> > > > Now, Tom Roberts, provide this forum with the proper and coordinate closing speeds, as calulated by observers on each closing object. I will state up front that you won't/can't do it.
> > > No one can do it, as I already told you. Closing speed *cannot* be observed by any observer on a closing object, by definition. You apparently are clueless about this really simple concept.
> > Increase in angle subtended by object, divided by proper time. This method will even give you acceleration.
> The distance d of an object of cross-section h subtended by an angle 𝜃 is
>
> d = sqrt[ ( 1 - h^2 )/( 2 cos𝜃 ) - ( h^2/4 ) ]
>
> The it's ∆d/∆t and ∆d/∆t^2

Where did you go, Paul A#2 ? Surely you are not so mortified that you are at a loss for more words to type. Come now, my boy. Admit your lack of mathematical and physical circumspection then continue to struggle. Just like Uncle Bodkin used to do.

On Monday, October 3, 2022 at 10:32:43 AM UTC-7, patdolan wrote:
> On Saturday, October 1, 2022 at 2:29:37 PM UTC-7, patdolan wrote:
> > On Saturday, October 1, 2022 at 12:29:34 PM UTC-7, patdolan wrote:
> > > On Saturday, October 1, 2022 at 11:34:20 AM UTC-7, Paul Alsing wrote:
> > > > On Saturday, October 1, 2022 at 10:58:33 AM UTC-7, patdolan wrote:
> > > > > On Saturday, October 1, 2022 at 10:02:56 AM UTC-7, tjrob137 wrote:
> > > > > > On 9/30/22 10:17 PM, rotchm wrote:
> > > > > > >>>> Since you talked about closing speeds, can you explain what
> > > > > > >>>> you mean by such an expression?
> > > > > > >> ... in this post he says..."Closing speed is the rate of change of
> > > > > > >> the distance between two objects as they both move.
> > > > > > >
> > > > > > > Yes, that's basically it. The closing speed between two entities is
> > > > > > > the rate of change of the distance (separation) between them, as
> > > > > > > measured by a given frame (system of coordinates).
> > > > > > Yes, but only for inertial coordinates. The closing speed for a given
> > > > > > pair of objects varies, depending on which inertial frame is used to
> > > > > > calculate/measure it.
> > > > > > > Its "v1 ± v2" depending of sign conventions.
> > > > > > Only when the two objects are moving along a single axis in the inertial
> > > > > > frame used. If that isn't so, the calculation is MUCH more complicated.
> > > > > >
> > > > > > Tom Roberts
> > > >
> > > > > Now, Tom Roberts, provide this forum with the proper and coordinate closing speeds, as calulated by observers on each closing object. I will state up front that you won't/can't do it.
> > > > No one can do it, as I already told you. Closing speed *cannot* be observed by any observer on a closing object, by definition. You apparently are clueless about this really simple concept.

> > > Increase in angle subtended by object, divided by proper time. This method will even give you acceleration.
> > The distance d of an object of cross-section h subtended by an angle 𝜃 is
> >
> > d = sqrt[ ( 1 - h^2 )/( 2 cos𝜃 ) - ( h^2/4 ) ]
> >
> > The it's ∆d/∆t and ∆d/∆t^2

> Where did you go, Paul A#2 ? Surely you are not so mortified that you are at a loss for more words to type. Come now, my boy. Admit your lack of mathematical and physical circumspection then continue to struggle. Just like Uncle Bodkin used to do.

You are just bloviating evasive nonsense, Dolan. Closing speed is a really simple concept that has nothing whatsoever to do with subtended angles, acceleration, or the cross-section of an object. Desperate much? Again, you don't know what you don't know.

On Saturday, October 1, 2022 at 5:29:37 PM UTC-4, patdolan wrote:
> On Saturday, October 1, 2022 at 12:29:34 PM UTC-7, patdolan wrote:
> > On Saturday, October 1, 2022 at 11:34:20 AM UTC-7, Paul Alsing wrote:
> > > On Saturday, October 1, 2022 at 10:58:33 AM UTC-7, patdolan wrote:
> > > > On Saturday, October 1, 2022 at 10:02:56 AM UTC-7, tjrob137 wrote:
> > > > > On 9/30/22 10:17 PM, rotchm wrote:
> > > > > >>>> Since you talked about closing speeds, can you explain what
> > > > > >>>> you mean by such an expression?
> > > > > >> ... in this post he says..."Closing speed is the rate of change of
> > > > > >> the distance between two objects as they both move.
> > > > > >
> > > > > > Yes, that's basically it. The closing speed between two entities is
> > > > > > the rate of change of the distance (separation) between them, as
> > > > > > measured by a given frame (system of coordinates).
> > > > > Yes, but only for inertial coordinates. The closing speed for a given
> > > > > pair of objects varies, depending on which inertial frame is used to
> > > > > calculate/measure it.
> > > > > > Its "v1 ± v2" depending of sign conventions.
> > > > > Only when the two objects are moving along a single axis in the inertial
> > > > > frame used. If that isn't so, the calculation is MUCH more complicated.
> > > > >
> > > > > Tom Roberts
> > >
> > > > Now, Tom Roberts, provide this forum with the proper and coordinate closing speeds, as calulated by observers on each closing object. I will state up front that you won't/can't do it.
> > > No one can do it, as I already told you. Closing speed *cannot* be observed by any observer on a closing object, by definition. You apparently are clueless about this really simple concept.
> > Increase in angle subtended by object, divided by proper time. This method will even give you acceleration.
> The distance d of an object of cross-section h subtended by an angle 𝜃 is
>
> d = sqrt[ ( 1 - h^2 )/( 2 cos𝜃 ) - ( h^2/4 ) ]
>
> The it's ∆d/∆t and ∆d/∆t^2

English please

On Wednesday, October 5, 2022 at 5:25:34 AM UTC-7, lostgold wrote:
> On Saturday, October 1, 2022 at 5:29:37 PM UTC-4, patdolan wrote:
> > On Saturday, October 1, 2022 at 12:29:34 PM UTC-7, patdolan wrote:
> > > On Saturday, October 1, 2022 at 11:34:20 AM UTC-7, Paul Alsing wrote:
> > > > On Saturday, October 1, 2022 at 10:58:33 AM UTC-7, patdolan wrote:
> > > > > On Saturday, October 1, 2022 at 10:02:56 AM UTC-7, tjrob137 wrote:
> > > > > > On 9/30/22 10:17 PM, rotchm wrote:
> > > > > > >>>> Since you talked about closing speeds, can you explain what
> > > > > > >>>> you mean by such an expression?
> > > > > > >> ... in this post he says..."Closing speed is the rate of change of
> > > > > > >> the distance between two objects as they both move.
> > > > > > >
> > > > > > > Yes, that's basically it. The closing speed between two entities is
> > > > > > > the rate of change of the distance (separation) between them, as
> > > > > > > measured by a given frame (system of coordinates).
> > > > > > Yes, but only for inertial coordinates. The closing speed for a given
> > > > > > pair of objects varies, depending on which inertial frame is used to
> > > > > > calculate/measure it.
> > > > > > > Its "v1 ± v2" depending of sign conventions.
> > > > > > Only when the two objects are moving along a single axis in the inertial
> > > > > > frame used. If that isn't so, the calculation is MUCH more complicated.
> > > > > >
> > > > > > Tom Roberts
> > > >
> > > > > Now, Tom Roberts, provide this forum with the proper and coordinate closing speeds, as calulated by observers on each closing object. I will state up front that you won't/can't do it.
> > > > No one can do it, as I already told you. Closing speed *cannot* be observed by any observer on a closing object, by definition. You apparently are clueless about this really simple concept.
> > > Increase in angle subtended by object, divided by proper time. This method will even give you acceleration.
> > The distance d of an object of cross-section h subtended by an angle 𝜃 is
> >
> > d = sqrt[ ( 1 - h^2 )/( 2 cos𝜃 ) - ( h^2/4 ) ]
> >
> > The it's ∆d/∆t and ∆d/∆t^2
> English please
Gladly. By measuring the change in the size of the angle subtended by a distant object for a given time interval, that object's closing speed can be determined.

On Saturday, October 1, 2022 at 2:29:37 PM UTC-7, patdolan wrote:
> On Saturday, October 1, 2022 at 12:29:34 PM UTC-7, patdolan wrote:
> > On Saturday, October 1, 2022 at 11:34:20 AM UTC-7, Paul Alsing wrote:
> > > On Saturday, October 1, 2022 at 10:58:33 AM UTC-7, patdolan wrote:
> > > > On Saturday, October 1, 2022 at 10:02:56 AM UTC-7, tjrob137 wrote:
> > > > > On 9/30/22 10:17 PM, rotchm wrote:
> > > > > >>>> Since you talked about closing speeds, can you explain what
> > > > > >>>> you mean by such an expression?
> > > > > >> ... in this post he says..."Closing speed is the rate of change of
> > > > > >> the distance between two objects as they both move.
> > > > > >
> > > > > > Yes, that's basically it. The closing speed between two entities is
> > > > > > the rate of change of the distance (separation) between them, as
> > > > > > measured by a given frame (system of coordinates).
> > > > > Yes, but only for inertial coordinates. The closing speed for a given
> > > > > pair of objects varies, depending on which inertial frame is used to
> > > > > calculate/measure it.
> > > > > > Its "v1 ± v2" depending of sign conventions.
> > > > > Only when the two objects are moving along a single axis in the inertial
> > > > > frame used. If that isn't so, the calculation is MUCH more complicated.
> > > > >
> > > > > Tom Roberts
> > >
> > > > Now, Tom Roberts, provide this forum with the proper and coordinate closing speeds, as calulated by observers on each closing object. I will state up front that you won't/can't do it.
> > > No one can do it, as I already told you. Closing speed *cannot* be observed by any observer on a closing object, by definition. You apparently are clueless about this really simple concept.
> > Increase in angle subtended by object, divided by proper time. This method will even give you acceleration.
> The distance d of an object of cross-section h subtended by an angle 𝜃 is
>
> d = sqrt[ ( 1 - h^2 )/( 2 cos𝜃 ) - ( h^2/4 ) ]
>
> The it's ∆d/∆t and ∆d/∆t^2

You are assuming that you know the values of d and h... which would be unlikely in the real world. You are changing the initial conditions.

On Wednesday, October 5, 2022 at 11:02:33 AM UTC-4, patdolan wrote:
> On Wednesday, October 5, 2022 at 5:25:34 AM UTC-7, lostgold wrote:
> > On Saturday, October 1, 2022 at 5:29:37 PM UTC-4, patdolan wrote:
> > > On Saturday, October 1, 2022 at 12:29:34 PM UTC-7, patdolan wrote:
> > > > On Saturday, October 1, 2022 at 11:34:20 AM UTC-7, Paul Alsing wrote:
> > > > > On Saturday, October 1, 2022 at 10:58:33 AM UTC-7, patdolan wrote:
> > > > > > On Saturday, October 1, 2022 at 10:02:56 AM UTC-7, tjrob137 wrote:
> > > > > > > On 9/30/22 10:17 PM, rotchm wrote:
> > > > > > > >>>> Since you talked about closing speeds, can you explain what
> > > > > > > >>>> you mean by such an expression?
> > > > > > > >> ... in this post he says..."Closing speed is the rate of change of
> > > > > > > >> the distance between two objects as they both move.
> > > > > > > >
> > > > > > > > Yes, that's basically it. The closing speed between two entities is
> > > > > > > > the rate of change of the distance (separation) between them, as
> > > > > > > > measured by a given frame (system of coordinates).
> > > > > > > Yes, but only for inertial coordinates. The closing speed for a given
> > > > > > > pair of objects varies, depending on which inertial frame is used to
> > > > > > > calculate/measure it.
> > > > > > > > Its "v1 ± v2" depending of sign conventions.
> > > > > > > Only when the two objects are moving along a single axis in the inertial
> > > > > > > frame used. If that isn't so, the calculation is MUCH more complicated.
> > > > > > >
> > > > > > > Tom Roberts
> > > > >
> > > > > > Now, Tom Roberts, provide this forum with the proper and coordinate closing speeds, as calulated by observers on each closing object. I will state up front that you won't/can't do it.
> > > > > No one can do it, as I already told you. Closing speed *cannot* be observed by any observer on a closing object, by definition. You apparently are clueless about this really simple concept.
> > > > Increase in angle subtended by object, divided by proper time. This method will even give you acceleration.
> > > The distance d of an object of cross-section h subtended by an angle 𝜃 is
> > >
> > > d = sqrt[ ( 1 - h^2 )/( 2 cos𝜃 ) - ( h^2/4 ) ]
> > >
> > > The it's ∆d/∆t and ∆d/∆t^2
> > English please
> Gladly. By measuring the change in the size of the angle subtended by a distant object for a given time interval, that object's closing speed can be determined.
thanks

On Wednesday, October 5, 2022 at 8:30:10 AM UTC-7, Paul Alsing wrote:
> On Saturday, October 1, 2022 at 2:29:37 PM UTC-7, patdolan wrote:
> > On Saturday, October 1, 2022 at 12:29:34 PM UTC-7, patdolan wrote:
> > > On Saturday, October 1, 2022 at 11:34:20 AM UTC-7, Paul Alsing wrote:
> > > > On Saturday, October 1, 2022 at 10:58:33 AM UTC-7, patdolan wrote:
> > > > > On Saturday, October 1, 2022 at 10:02:56 AM UTC-7, tjrob137 wrote:
> > > > > > On 9/30/22 10:17 PM, rotchm wrote:
> > > > > > >>>> Since you talked about closing speeds, can you explain what
> > > > > > >>>> you mean by such an expression?
> > > > > > >> ... in this post he says..."Closing speed is the rate of change of
> > > > > > >> the distance between two objects as they both move.
> > > > > > >
> > > > > > > Yes, that's basically it. The closing speed between two entities is
> > > > > > > the rate of change of the distance (separation) between them, as
> > > > > > > measured by a given frame (system of coordinates).
> > > > > > Yes, but only for inertial coordinates. The closing speed for a given
> > > > > > pair of objects varies, depending on which inertial frame is used to
> > > > > > calculate/measure it.
> > > > > > > Its "v1 ± v2" depending of sign conventions.
> > > > > > Only when the two objects are moving along a single axis in the inertial
> > > > > > frame used. If that isn't so, the calculation is MUCH more complicated.
> > > > > >
> > > > > > Tom Roberts
> > > >
> > > > > Now, Tom Roberts, provide this forum with the proper and coordinate closing speeds, as calulated by observers on each closing object. I will state up front that you won't/can't do it.
> > > > No one can do it, as I already told you. Closing speed *cannot* be observed by any observer on a closing object, by definition. You apparently are clueless about this really simple concept.
> > > Increase in angle subtended by object, divided by proper time. This method will even give you acceleration.
> > The distance d of an object of cross-section h subtended by an angle 𝜃 is
> >
> > d = sqrt[ ( 1 - h^2 )/( 2 cos𝜃 ) - ( h^2/4 ) ]
> >
> > The it's ∆d/∆t and ∆d/∆t^2
> You are assuming that you know the values of d and h... which would be unlikely in the real world. You are changing the initial conditions.

Paul A#2, you foolish fool. Paul A#1 is an excellent algebracist. By that standard, you are actually Paul A#1,001.

You don't need to know the value of h or d in order to determine an accurate closing speed. Assume any value for h. Then ∆d = f(∆cos𝜃) divided by ∆t will give you the same value for closing speed as if you knew d and h.

On Wednesday, October 5, 2022 at 8:02:33 AM UTC-7, patdolan wrote:
> By measuring the change in the size of the angle subtended by a distant object for a given time interval, that object's closing speed can be determined.

You've overlooked the effect of the finite speed of light. The rays from the object arrive at your eye after a certain delay, and if the object is receding from you, the amount of delay is changing. As a result, the rate of change of the subtended angle q at your eye is not related to the rate of change of the distance L by the simplistic dL/dt = -h/[4sin(q)^2](dq/dt) as it would be if the speed of light was infinite.

To correct for the effect of the finite speed of light (even in Galilean relativity), you need to account for how fast the delay time is changing, and this depends on the relative speed of the receding object... which is what you are trying to determine, so you are chasing your tail. Fortunately, all is not lost, because if you know the "rest color" of the object, you can infer the relative speed using the Doppler effect. Of course, once you have done this, you're done, and there is no point in trying to measure the rate of change of the subtended angle (which would not be practical in most cases anyway).

Up to this point, we're just talking about basic Galilean relativity. To be exact, you would need to use the relativistic Doppler formula, and you would have another reason for not trying to infer the speed from the angles, because you would need to account for relativistic aberration.

Lastly, what you get when you correctly infer the speed of the object using the Doppler effect is the relative speed, meaning the speed of the object in terms of the system of coordinates in which the eye is at rest. This is generally not the closing speed, because the closing speed refers to the sum or difference of the speeds in terms of some arbitrary coordinate system.. In Galilean relativity the closing speed and the relative speed are the same, but in special relativity they are not.

On Wednesday, October 5, 2022 at 10:01:25 AM UTC-7, patdolan wrote:
> On Wednesday, October 5, 2022 at 8:30:10 AM UTC-7, Paul Alsing wrote:
> > On Saturday, October 1, 2022 at 2:29:37 PM UTC-7, patdolan wrote:
> > > On Saturday, October 1, 2022 at 12:29:34 PM UTC-7, patdolan wrote:
> > > > On Saturday, October 1, 2022 at 11:34:20 AM UTC-7, Paul Alsing wrote:
> > > > > On Saturday, October 1, 2022 at 10:58:33 AM UTC-7, patdolan wrote:
> > > > > > On Saturday, October 1, 2022 at 10:02:56 AM UTC-7, tjrob137 wrote:
> > > > > > > On 9/30/22 10:17 PM, rotchm wrote:
> > > > > > > >>>> Since you talked about closing speeds, can you explain what
> > > > > > > >>>> you mean by such an expression?
> > > > > > > >> ... in this post he says..."Closing speed is the rate of change of
> > > > > > > >> the distance between two objects as they both move.
> > > > > > > >
> > > > > > > > Yes, that's basically it. The closing speed between two entities is
> > > > > > > > the rate of change of the distance (separation) between them, as
> > > > > > > > measured by a given frame (system of coordinates).
> > > > > > > Yes, but only for inertial coordinates. The closing speed for a given
> > > > > > > pair of objects varies, depending on which inertial frame is used to
> > > > > > > calculate/measure it.
> > > > > > > > Its "v1 ± v2" depending of sign conventions.
> > > > > > > Only when the two objects are moving along a single axis in the inertial
> > > > > > > frame used. If that isn't so, the calculation is MUCH more complicated.
> > > > > > >
> > > > > > > Tom Roberts
> > > > >
> > > > > > Now, Tom Roberts, provide this forum with the proper and coordinate closing speeds, as calulated by observers on each closing object. I will state up front that you won't/can't do it.
> > > > > No one can do it, as I already told you. Closing speed *cannot* be observed by any observer on a closing object, by definition. You apparently are clueless about this really simple concept.
> > > > Increase in angle subtended by object, divided by proper time. This method will even give you acceleration.
> > > The distance d of an object of cross-section h subtended by an angle 𝜃 is
> > >
> > > d = sqrt[ ( 1 - h^2 )/( 2 cos𝜃 ) - ( h^2/4 ) ]
> > >
> > > The it's ∆d/∆t and ∆d/∆t^2
> > You are assuming that you know the values of d and h... which would be unlikely in the real world. You are changing the initial conditions.
> Paul A#2, you foolish fool. Paul A#1 is an excellent algebracist. By that standard, you are actually Paul A#1,001.
>
> You don't need to know the value of h or d in order to determine an accurate closing speed. Assume any value for h. Then ∆d = f(∆cos𝜃) divided by ∆t will give you the same value for closing speed as if you knew d and h.

No, your math is fatally flawed...

On Thursday, 6 October 2022 at 06:36:12 UTC+2, Paul Alsing wrote:

No, your math is fatally flawed...

Speaking of math, it's always good to remind that
your idiot guru had to announce its oldest, very
important and very successful part false - as
it didn't want to fit his idiotic postulates.

On Wednesday, October 5, 2022 at 7:21:51 PM UTC-7, Trevor Lange wrote:
> On Wednesday, October 5, 2022 at 8:02:33 AM UTC-7, patdolan wrote:
> > By measuring the change in the size of the angle subtended by a distant object for a given time interval, that object's closing speed can be determined.
> You've overlooked the effect of the finite speed of light. The rays from the object arrive at your eye after a certain delay, and if the object is receding from you, the amount of delay is changing. As a result, the rate of change of the subtended angle q at your eye is not related to the rate of change of the distance L by the simplistic dL/dt = -h/[4sin(q)^2](dq/dt) as it would be if the speed of light was infinite.
>
> To correct for the effect of the finite speed of light (even in Galilean relativity), you need to account for how fast the delay time is changing, and this depends on the relative speed of the receding object... which is what you are trying to determine, so you are chasing your tail. Fortunately, all is not lost, because if you know the "rest color" of the object, you can infer the relative speed using the Doppler effect. Of course, once you have done this, you're done, and there is no point in trying to measure the rate of change of the subtended angle (which would not be practical in most cases anyway).
>
> Up to this point, we're just talking about basic Galilean relativity. To be exact, you would need to use the relativistic Doppler formula, and you would have another reason for not trying to infer the speed from the angles, because you would need to account for relativistic aberration.
>
> Lastly, what you get when you correctly infer the speed of the object using the Doppler effect is the relative speed, meaning the speed of the object in terms of the system of coordinates in which the eye is at rest. This is generally not the closing speed, because the closing speed refers to the sum or difference of the speeds in terms of some arbitrary coordinate system. In Galilean relativity the closing speed and the relative speed are the same, but in special relativity they are not.

Your last point is a good one. As to the previous points, in this forum we always assume that relativistic doppler has been taken into account. But thanks for pointing it out.

My overall effort was more to instruct young Paul A#2 in the multifarious ways that velocity can be ascertained, as he was laboring under another one of his many misconceptions. Your final point did cross my mind. But I considered it way beyond the scope of what the callow Paul A#2 was capable of digesting in a single post. But thanks again.

On Wednesday, October 5, 2022 at 7:21:51 PM UTC-7, Trevor Lange wrote:
> On Wednesday, October 5, 2022 at 8:02:33 AM UTC-7, patdolan wrote:
> > By measuring the change in the size of the angle subtended by a distant object for a given time interval, that object's closing speed can be determined.
> You've overlooked the effect of the finite speed of light. The rays from the object arrive at your eye after a certain delay, and if the object is receding from you, the amount of delay is changing. As a result, the rate of change of the subtended angle q at your eye is not related to the rate of change of the distance L by the simplistic dL/dt = -h/[4sin(q)^2](dq/dt) as it would be if the speed of light was infinite.
>
> To correct for the effect of the finite speed of light (even in Galilean relativity), you need to account for how fast the delay time is changing, and this depends on the relative speed of the receding object... which is what you are trying to determine, so you are chasing your tail. Fortunately, all is not lost, because if you know the "rest color" of the object, you can infer the relative speed using the Doppler effect. Of course, once you have done this, you're done, and there is no point in trying to measure the rate of change of the subtended angle (which would not be practical in most cases anyway).
>
> Up to this point, we're just talking about basic Galilean relativity. To be exact, you would need to use the relativistic Doppler formula, and you would have another reason for not trying to infer the speed from the angles, because you would need to account for relativistic aberration.
>
> Lastly, what you get when you correctly infer the speed of the object using the Doppler effect is the relative speed, meaning the speed of the object in terms of the system of coordinates in which the eye is at rest. This is generally not the closing speed, because the closing speed refers to the sum or difference of the speeds in terms of some arbitrary coordinate system. In Galilean relativity the closing speed and the relative speed are the same, but in special relativity they are not.

You final point also appears to provide fertile ground for thought on yet another means of falsifying the concept of the absolute relativity of motion.. I hope to get back to you on it.

On 10/1/22 12:58 PM, patdolan wrote:
> On Saturday, October 1, 2022 at 10:02:56 AM UTC-7, tjrob137 wrote:
>> On 9/30/22 10:17 PM, rotchm wrote:
>>>>>> Since you talked about closing speeds, can you explain
>>>>>> what you mean by such an expression?
>>>> ... in this post he says..."Closing speed is the rate of
>>>> change of the distance between two objects as they both move.
>>>
>>> Yes, that's basically it. The closing speed between two entities
>>> is the rate of change of the distance (separation) between them,
>>> as measured by a given frame (system of coordinates).
>> Yes, but only for inertial coordinates. The closing speed for a
>> given pair of objects varies, depending on which inertial frame is
>> used to calculate/measure it.
>>> Its "v1 ± v2" depending of sign conventions.
>> Only when the two objects are moving along a single axis in the
>> inertial frame used. If that isn't so, the calculation is MUCH
>> more complicated.
>>
>> Tom Roberts
> Now, Tom Roberts, provide this forum with the proper and coordinate
> closing speeds, as calulated by observers on each closing object.

Consider inertial frame S with coordinates (x,t) -- ignore y and z as
they don't appear in this problem. Object A is located at x>0 and is
moving inertially along the x axis of S with velocity Va, Va<0. Object B
is located at x<0 and is moving inertially along the x axis of S with
velocity Vb, Vb>0. These two objects are clearly approaching each other.

In frame S, the closing speed of these two objects is |Va|+|Vb| = Vb-Va.

(Remember my V's are 3-velocities along the x axis, with
Va<0 and Vb>0.)

In the rest frame of A, object B has velocity Vba such that
Vb = (Va+Vba)/(1+Va*Vba/c^2)
so
Vba = (Vb-Va)/(1-Va*Vb/c^2)
In the rest frame of A, their closing speed is |Vba| = Vba.

In the rest frame of B, object A has velocity Vab such that
Vb = (Va+Vab)/(1+Va*Vab/c^2)
so
Vab = (Va-Vb)/(1-Va*Vb/c^2)
In the rest frame of B, their closing speed is |Vab| = -Vab.

While the expressions are different, |Vab| = |Vba|, and the closing
speeds in the two object's rest frames are the same.

Note that if Va<<c and Vb<<c, the closing speeds in all three frames are
approximately the same, |Va|+|Vb| = Vb-Va.

> I will state up front that you won't/can't do it.

As usual, you are wrong.

Tom Roberts