Subject: Re: [LPNY DISCUSS](OT) Mr. Science bad
Date: Mon, 29 Sep 2003 19:00:01 -0400
To:        <lpny_discuss@yahoogroups.com>
From:     Bob Armstrong <bob@cosy.com>
 Blay ,

 Given your more accurate than the average here insights
 about this off topic , I'm surprized you were unfamiliar
 with the notion of angular velocity , generally measured
 in radians per second which makes the linear speed
 ( directionless velocity ) equal to the angular velocity
 for a unit circle ; the circumference of the unit circle ,
  2 pi , defining the number of radians .

 By Kepler's law which I stated in Message 19426 , if the
 radius of an orbit is increased by 1.1 times , the period
 increases by  1.1 ^ 3%2  or about 1.1537 .  So the speed
 decrease to  1.1 % 1.1537  or about  0.9535  of the
 original .

 I have not had the product of time and interest to grok
 orbital energetics , but it's clearly not as simple as
 just saying the speed goes down as r ^ 2 . Obviously 
 Kepler found it to be  r % r ^ 3%2 as I had in my table
 in message 19428 .

--
On Mon, 29 Sep 2003 08:42:40 -0400, Blay Tarnoff wrote:
>=A0Blay Tarnoff wrote:
>=A0>
>=A0>=A0[W]hen the moon's angular velocity slows, say, 10% due to
>=A0>=A0a higher orbit, its linear velocity slows 10% as well.
>
>=A0Hmmm.... actually, scratch this statement. =A0As the moon moves=
 into a
>=A0higher orbit, if its linear velocity were to stay the same, its=
 angular
>=A0velocity would be slower. =A0Likewise, if its angular velocity=
 were to
>=A0stay the same at the higher orbit, its linear velocity would=
 have to
>=A0increase to keep the same rate of movement per arc.
>
>=A0So, as the moon moves X% further from the Earth, its linear=
 velocity
>=A0slows by X*2 (X squared) due to the lower gravity and its=
 angular
>=A0velocity slows by X in addition to that due to the increased=
 distance or
>=A0X*3 in total. =A0So, for example, if the moon were to move 10%=
 farther
>=A0from the Earth, its linear velocity would slow by 1.21 times=
 (=3D17.36%)
>=A0and its angular velocity would slow by 1.331 times (=3D24.87%).=
 =A0Is that
>=A0right?
>
>=A0Of course, all of this still boils down to the fact that, as=
 the moon
>=A0moves farther away, both its linear and angular velocities=
 decrease.
>=A0One does not increase while the other decreases.
>
>=A0Blay
>
>=A0-------------------------------------------------
>
>=A0Blay Tarnoff wrote:
>=A0>
>=A0>=A0Interesting. =A0I never heard of angular velocity before. =A0I=
 would think
>=A0>=A0that in a circle, though, angular velocity and velocity would=
 be the
>=A0>=A0same measurement, since each degree traces a fixed unit of=
 length.
>=A0>=A0(IOW, since every degree is X miles long, saying that one is=
 traveling
>=A0>=A0at one degree/minute, e.g. is really just saying that one is=
 traveling
>=A0>=A0at X miles per minute.) =A0So, when the moon's angular velocity=
 slows,
>=A0>=A0say, 10% due to a higher orbit, its linear velocity slows 10%=
 as well.
>=A0>
>=A0>=A0Blay
>=A0>

--=A0
=A0Bob Armstrong -- http://CoSy.com -- 212-285-1864
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=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A0=A02003/09/29 5:28:38 PM