From: njzy@vax5.cit.cornell.edu (T. Joseph Lazio, Cornell University)
Newsgroups: sci.astro
Subject: Re: Standard model of QSOsex
Date: 17 Aug 92 08:57:41 EDT
Distribution: sci
Organization: Cornell University

In article <Bt44Hu.6Hx@well.sf.ca.us>,
metares@well.sf.ca.us (Tom Van Flandern) writes: 
> 
> njzy@vax5.cit.cornell.edu (T. Joseph Lazio, Cornell University) writes:
> 
>> I infer that [Tom] disagrees with the notion that gravitational and
>> inertial masses are equal [in his Meta Model].  I would also infer that the
>> inertial mass is larger.  Hence, in the Meta model, stellar masses which
>> are derived from binary star orbits are underestimates of the inertial
>> mass.
>>
>> However, galactic rotation curves, derived from stellar velocity dispersion
>> measurements, are estimates of the inertial mass.  These rotation curves
>> measure the velocity of the stars as they respond to an external force,
>> namely the gravitational potential produced by the other stars.
> 
>      You have a confusion here in the distinction between types of masses. In
> dynamics, *all* effective masses are active gravitational masses only.
> Inertial masses of stars do not affect their velocities in the gravitational
> potential.  To see this, recall that the acceleration of a body in response
> to a gravitational force is independent of its own mass.  [Lead and aluminum
> balls drop at the same rate.]

 Somebody else has made a similar comment.  Fearing that I was messing up 
 the distinction between grav. and inertial masses, I went back to 
 Halliday & Resnick.  After reading H & R, I disagree with the above.
 
 The acceleration of a star in a grav. potential is 
 
              A = (1/m_i)*(do/dr)

 where A is the acceleration, m_i is the inertial mass, and o is the 
 grav. potential.  I would argue that the inertial mass quite clearly 
 enters into the acceleration, and hence the velocity of a star.  The 
 equation below only applies to a spherical system.

>      In more technical language, let m(i) be inertial mass [response to
> collisions], m(p) be passive gravitational mass [weight], and m(a) be active
> gravitational mass [pull on other bodies].  Then consider the acceleration,
> A, of a small mass, m, in the field of a larger mass, M, at a distance r:
> 
>      m(i) A = G m(p) M(a) / r^2,
> 
> where G = gravitational constant.  Experiments place only mild constraints on
> the relationship between active gravitational masses and either of the other
> two types.  However Eotvos-type experiments have shown the equality of
> passive gravitational masses and inertial masses to more than 10 significant
> figures.  So m(i) and m(p) in the above equation cancel, leaving the
> acceleration A dependent upon the active gravitational mass in the system
> only.

 I'm afraid I don't know what the active gravitational mass is.  Moreover, 
 you clearly (or so I thought) indicated in an earlier post that 
 m(i) > m(g) resulting in A being less than if m(i) = m(g).  Of course, 
 it was later pointed out to me that the difference was very small 
 except for extremely massive stars, so the effect probably could not be 
 seen.

>> It is still not clear how extra interior matter increases stability.  The
>> stability of a star depends upon its surface gravitational field.
> 
>      Since the extra matter lowers the gravity, temperature, and pressure at
> the surface, it increases stability and lifetime.

 How does the extra matter affect the temperature?  The stability of a 
 massive star is a balance between radiation pressure and gravity.  If
 the gravity drops, the luminosity must drop by the same factor or the 
 star will become less stable; luminosity decreasing by a factor x is 
 equivalent to the surface temperature dropping by a factor x^{1/4} 
 (of course if the surface temperature drops by an even greater factor 
 the star will then be more stable).  Is this the behavior predicted by 
 the Meta model?

-- 
 T. Joseph Lazio                | Why relativity? and Why  
 514 Space Sciences             | turbulence?  I really believe   
 Ithaca, NY  14853              | [God] will have an answer for the
 (607) 255-6420                 | first [question].
 lazio@astrosun.tn.cornell.edu  |   -- W. Heisenberg, on his death bed
ICBM:                           |
 42 deg. 20' 08" N              |              STOP RAPE
 76 deg. 28' 48" W              |