As mentioned previously, our sun’s original nebula was approximately 1.1 solar masses with only 0.2% made up of solid matter according to current theory. The Bok globules also mentioned earlier have been observed to occur with sizes ranging from 0.06 parsecs in diameter up to about 0.5 parsecs (ref. 2 p526). We will assume a value of 0.06 parsecs. This will give preference to the nebular collapse proponents since the cloud would be denser for the assumed mass. (Lagoon Nebula, M8, Bok globules shown below)
The analysis of the dust portion of the cloud will be ignored since its limited mass would contribute little to the collapse except at the very end during the planetary accretion phase. Also, even though the dust portion of the cloud might collapse, unless the gaseous portion follows in the collapse, there would be no central host star for the newly formed planetary system. We will further assume the cloud’s gaseous constituents are 70% hydrogen and 28% helium (ref. 1 p388). The virial theorem (ref. 2 pp502-503) gives the relationship between cloud particle velocity, the cloud mass, and size or radius of the cloud for stability to occur. The solar nebula would have a mass of 2.2×10+33 gm distributed homogeneously throughout a sphere of 0.03 parsecs radius. The virial theorem states that the mean particle velocity must be no more than the square root of the universal gravitational constant times the mass divided by twice the radius.
V = sqrt(GM/2R) V = particle vel., G = grav. const., M = cloud mass, R = cloud radius
For our solar system test case that comes out to be 280 meters/sec. In order to determine the actual gas velocity (which will determine if collapse can occur) we must know the mean absolute temperature of the cloud and use the kinetic temperature relationship (ref. 2 pp272-273). In this relationship the velocity is the square root of three times the Boltzman coefficient times the temperature divided by the cloud particle’s mass. The earliest attempts to determine that temperature was made by Ewen and Purcell in 1951 when they used radio telescopes to measure both the strength and width of the 21 cm emission line of neutral hydrogen (ref. 2 p533). The strength of the spectral line gave the relative density of the hydrogen and the width indicated the particle velocity due to the doppler effect. From those observations the velocity was found to be about 1000 meters/sec corresponding to 100 degrees Kelvin in temperature. Because this data is older than that obtained more recently from satellites and cannot be absolutely confirmed to be representative of the colder and denser molecular clouds, we will use the more current data. Satellite telescopes such as Spitzer, WISE, and Herschel (ref. 8 p12) have been probing interstellar gas and dust clouds for several years in the far infrared (3-600 microns wave length). They have indicated temperatures of 10 to 40 degrees Kelvin corresponding to the characteristic blackbody radiation from dust particles within the clouds. We will assume the colder 10 degrees based on only the dust grain temperatures. With the earlier mentioned percentage distribution of hydrogen and helium, we will also assume the hydrogen is equally divided between atomic and molecular particles (ref. 1 p388). If we use this information, we can arrive at a mean molecular weight of 1.9 times the mass of a proton (= 1.67×10-24 gm). Putting this information into the kinetic temperature relationship, we arrive at a mean molecular velocity of 361 meters/sec. This is in spite of the gas particle velocities likely being much higher than indicated by the cloud temperature. Indeed, if the number of molecules to dust grains in the cloud (ratio approx. 10+38) is taken into account along with the particle mass ratio (approx. 10+12), and elastic particle collision mechanics included, the required molecular velocities would have to be on the order of 10 km/sec to impart sufficient thermal energy to the dust grains to register at a temperature of 10 degrees Kelvin. As we remember from the earlier calculation for our solar nebula, the maximum velocity allowed for cloud contraction to occur was 280 meters/sec. We can also look at the upper end of the Bok globule size range for confirmation of the cloud collapse problem based on existing observations. The object known as Thackery’s Globule (I.C. 2944) is made up of two globules each about 1.4 light years (approx. 0.43 parsecs) in size and consisting of about 15 solar masses each (ref. 10 p82).
If this size and mass is used in the virial theorem, the maximum collapse velocity is 214 meters/sec, still lower than those corresponding to the coldest observed temperatures. So, in spite of giving the nebular theorist every benefit of data assumptions in this analysis, the resulting molecular velocities are still too high for collapse to occur. Some theorists have suggested that a shock wave from a nearby supernova could cause a cloud collapse (ref. 1 p157). The resulting planar wave would more likely pass through the cloud carying some material with it as well as erode the cloud away forming objects called proplyds which are small teardrop shaped clouds found in some large diffuse nebulae (ref. 7 p38). In any case the effect of the shock would probably be more diffusive than compressive. Next we will summarize the information given so far in the light of God’s Word. (Proplyd examples shown below)