The following is in response to a long letter sent to Amnon Goldberg
from Harald Heinze, a copy of which was sent to your editor, among
others. Heinze's letter was dated of April 13, 1994 and was in response
to a Panorama article entitled The LMC Moves Across the Sky,
Biblical Astronomer 4(67):13, 1994.
Harald spends most of the letter critiquing redshift (Doppler shift)
which nowhere enters either into the determination of the distance to
the Large Magellanic Cloud (LMC) or into the Panorama article.
The article reports on the detection of movement across the sky, not
away from us (redshift) or toward us (blue shift). What was measured
was the angular velocity across the line of sight. Radial velocity is
measured along the line of sight.
The note mentioned the first observation of tangential motion
(technically, proper motion) of a galaxy. If the LMC is 170,000 light
years away, then the measured angular velocity corresponds to an orbital
speed of 220 km/sec. As far as the 170,000 l.y. distance to the
LMC is concerned, that number is based on the characteristics of
Cepheid variables and other types of stars which, in turn, are based on
parallax. So in no case do radial velocity, redshift, or the Doppler
shift enter the picture.
Now the orbital speed of an object must be such that it balances
the centripetal and centrifugal forces. The formula for the orbital
speed, v, is v=Ö(GM/R) where G is the gravitational constant, M is the
mass (of the Milky Way) and R is the distance from the center of the
Milky Way to the object. According to gravity, the orbital speed of
the LMC about the Milky Way should be roughly 220 km/sec which
agrees with the observed angular velocity's value.
Now Harald would have somewhat to say if v were proportional to
1/R. In that case the angular velocity would be the same, regardless
of distance (and all the planets would have the same orbital period).
But according to gravity, v varies as ÖR, so, if for example, the LMC
were actually 42,000 l.y. from the Milky Way, (a quarter of its
170,000 l.y.,) then the observed orbital speed is 55 km/sec which, according
to Harald's analysis, is what the gravitational speed should
be. Not so, the predicted gravitational speed at that distance is 110
km/sec, twice the value of Harald's argument.
So my argument is not circular, as Harald claims, because the
170,000 l.y. distance to the LMC was not based on orbital dynamics
but on intrinsic properties of variable stars. The new observation
does allow us to now consider orbital dynamics and we find agreement
between the two. I cannot stress this enough: the distance to the
Large Magellanic Cloud has now been estimated by two independent
techniques, and the two are in reasonable agreement.
On occasion Harald refers to the missing mass as if it proves his
small universe model. True, the missing mass problem would be
solved by a smaller universe, but the universe's radius would only
have to decrease from 20 billion to 4 billion light years: a far, far cry
from Harald's couple of light months size.
Some retorts to other misconceptions promulgated by Heinze's
letter: 1) Contrary to Harald's assertion, never in my life have I
claimed that light is not effected by gravitational or electromagnetic
fields. 2) Never have I claimed that the sun causes all the stars to
move with the sun. Since my early geocentric days I have consistently
maintained that it is a vibration of the universe which carries
the sun and stars with it in a yearly cycle: the complement of what
Harald claims I say. 3) Harald claims that there is no mathematical
evidence for a large universe and that I should provide it. Why
should I when the math may be found by anyone who would do a
cursory search of the literature. (Try Stars and Stellar Systems
volumes 2 and 3, for example. 4) Although he does not use the word
evolution, Harald argues that star formation by natural processes
(stellar evolution) is possible in his model while it is impossible in the
large-universe model. To me, that's all the more reason to believe in
the large universe model. Of course stellar formation doesn't work in
the large universe model: the stars were created, they did not evolve.
On the other hand, Harald does not substantiate his claim with any
references or math, either. 5) Harald writes as if Hannes Alfven
has solved all stellar problems with his plasma model of stars. All
Alfven has done insofar as stars-as-plasma is concerned is that he's
suggesting that we describe a star as a hot ball of plasma instead of
a hot ball of ionized gas. There's no difference between the two
descriptions. Alfven's main contribution lies in his description of the
gas between the stars, not in its description of the stars themselves.
A little knowledge can be a dangerous thing.