Check the Math

I took Sociology 304 Research Methods in the spring of 2007. The professor was Young S. Kim. We were assigned to review two research papers each week. In the first class meeting, Dr. Kim said that these were not to be summaries but must be criticisms. After class, I approached his desk and asked if undergraduates could competently criticize a peer-reviewed publication. He replied, “Check the math.”

 

I do not know that I found any mathematical errors because I only archived three of my assignments from that class and none of those identified any such problems. However, a few months ago, researching an article for the American Astronomical Society, I found this from 1948: 

• “Evolution of the Universe” by Ralph A. Alpher and Robert Herman, Nature, No. 4124 ,Vol. 162, November 13, 1948 identified errors in 
• “The Evolution of the Universe” by George Gamow, Nature, No. 4122, Vol. 162, October 30, 1948. 

 “The condensation-mass obtained from this corrected density comes out not much different from Gamow's original estimate. However, the intersectionpoint r_mat. = r_rad. occurs at t=8·6 x 1017 sec. ≅ 3 x 1010 years (that is, about ten times the present age of the universe). This indicates that, in findingthe intersection, one should not neglect the curvature term in the general equation of the expanding universe. In other words, the formation ofcondensations must have taken place when the expansion was becoming linear with time.”  

 

Interesting as that was to read, I was more impressed with the discovery that cosmologists in 1948 accepted an estimated age of the Universe at 3 billion (3*10⁹) years. The simple truth is that estimates of the size and age of the universe have been expanding. 

It is also interesting that their work required the radius of the known universe to be proportional to  [the square root of (minus one)] light years. Imagine that!

 

For more on Young S. Kim see:

Kim, Y. S., Barak, G., & Shelton, D. E. (2009). Examining the “CSI-effect” in the cases of circumstantial evidence and eyewitness testimony: Multivariate and path analyses. Journal of Criminal Justice, 37(5), 452–460. https://doi.org/10.1016/j.jcrimjus.2009.07.005

https://psycnet.apa.org/record/2009-15801-001

  

Previously on NecessaryFacts

 

Imaginary Numbers are Real; Pegasus is Not 

Two Books on Fermat’s Last Theorem 

Pi in the Sky over Austin

Elisha Loomis and the Pythagorean Proposition

 

Sigma Orionis

We think of Orion as a winter constellation because with shorter days it appears in the early evening sky. It is on the median at 9:00 PM on February 5, but even on April 21, it is just above the western horizon. In September, Orion rises above my eastern tree line by 5:00 AM, and before the Sun erases the night sky at 6:00 AM, it is high in the east. The group associated with Sigma Orionis just below the Belt of Orion consists of stars that are gravitationally bound as well as others that just happen to be there from our point of view.

SIGMA ORI (Sigma Orionis). Double stars are among the amateur's favorite targets, Albireo, Mizar always on the list. Multiples are better yet, and there are few more attractive than Sigma Orionis (which has no proper name), where you see a quartet of stars, the brightest of which is also a close double. Indeed, Sigma Ori, whose five stars together shine in Orion at bright fourth magnitude (3.66) just south of Alnitak in Orion's belt, is really at the pinnacle of a small star cluster that lies a somewhat-uncertain 1150 light years away. In turn, the stars and the cluster are a part of the Orion OB1 association, which includes many of the other stars in the constellation. Sigma's main component, "AB," dominates, the two a mere 0.25 seconds of arc apart shining at magnitudes 4.2 and 5.1. Both very young hydrogen-fusing dwarfs only a few million years old, the brighter is a magnificent blue class O (09.5) star, while the lesser is class B (B0.5). The pair orbit every 170 years at a distance of about 90 Astronomical Units. After correction for ultraviolet light from very hot (32,000 and 29,600 Kelvin) surfaces, they respectively radiate at a rate of 35,000 and 30,000 Suns. Temperature and luminosity give masses of 18 and 13.5 times that of the Sun, the sum of nearly 32 solar masses making the close AB pair among the most massive of visual binaries. Together they illuminate their surroundings, causing interstellar gas to glow. The next brightest stars in the system are Sigma Ori "D" and "E," bright seventh magnitude class B (B2) dwarf stars that at magnitudes 6.62 and 6.65 are nearly identical in brightness and have masses around 7 times that of the Sun. The similarity stops there. "E" is the prototype of the weird "helium-rich" stars that have strangely elevate abundances of helium. Even odder, the helium in "E" seems to be concentrated toward particular patches that involve a combination of the rotational and magnetic field axes. They may be related to cooler magnetic stars such as Cor Caroli, but no one really understands them. The last of Sigma's stars, "C," appears to be a normal ninth magnitude class A dwarf. In projection on the sky, "C" is the closest to the AB pair, and is at least 3900 AU away, while "D" and "E" lie at least 4600 and 15,000 AU distant. While the orbit of the AB pair is stable, the orbits of the other three are not, and long before they die they will probably be gravitationally sped up and forced out. "A" will explode first and may even kick "B" (which will explode next) out of the system. The other stars, wherever they wind up, will die as white dwarfs. The cluster seems also to contain numerous low-mass stars, brown dwarfs, that have masses only a few times that of Jupiter. -- http://stars.astro.illinois.edu/sow/sigmaori.html

 

For early references to the open cluster, see, “On the supposed Variability of the closest Companion of σ Orionis” by W. R. Dawes, in the Monthly Notices of the Royal Astronomical Society for April 1860 (247 1860MNRAS..20..253W 1860/04 and “Correspondence - The Trapezium and σ in Orion” by D. A. Freeman, in the Monthly Notices of the Royal Astronomical Societyfor May 1860 (248  1860MNRAS..20..285D 1860/05). 

 

Drawn with PointPoint from a recorded observation

In 1776, Christian Mayer described σ Ori as a triple star, having seen components AB and E, and suspected another between the two. Component D was confirmed by FGW Struve who also added a fourth (C), published in 1876. In 1892 Sherburne Wesley Burnham reported that σ Ori A was itself a very close double, although a number of later observers failed to confirm it. In the second half of the twentieth century, the orbit o  σ Ori A/B was solved and at the time was one of the most massive binaries known.[22] -- https://en.wikipedia.org/wiki/Sigma_Orionis

 

PREVIOUSLY ON NECESSARY FACTS

Burnham’s Celestial Handbook 

The Andromeda Galaxy 

Asterisms 

What Color is the Orion Nebula?