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.