One of the books I purchased recently was “Cosmic Numbers: The Numbers That Define Our Universe” by James D. Stein. What attracted me to the book is that I am fascinated by mathematical constants (my favorite number is π) and how they came about. Stein talks about the following constants in the book:
1. The Gravitational Constant (G)
2. The Speed of Light (c)
3. The Ideal Gas Constant
4. Absolute Zero
5. Avogardo’s Number
6. Electricity and the Proportionality Constant
7. The Boltzmann Constant
8. The Plank Constant
9. The Schwarzschild Radius (which the value depends on the object’s mass)
10. The Efficiency of Hydrogen Fusion
11. The Chandrasekhar Limit
12. The Hubble Constant
While I have not yet finished the book (got three more chapters to go), I recommend this book. Stein writes in a straight-forward, entertaining matter. Here of some of my favorite highlights of the book:
* The concept of the gravitational constant comes from Issac Newton’s Principia (1687), and as we are aware, we have two constants: Big G for the universal constant and little g for the local constant.
* Little g (local gravity) was fairly easy to get, at least for Earth, using the relationship d = 1/2*g*t^2. It would take until the mid-1700s before Henry Cavendish would propose a way to calculate big G, and even later before the first values of G were found.
Speed of Light:
* The first calculation of the speed of light was inspired by Galileo Galilei’s discovery of moons in front of Jupiter in 1610, which inspired Ole Rømer to come up with the first estimation of the speed of light.
* Albert Michelson is most connected with the speed of light, which will lead to the famous Michelson-Morely experiment, in which a beam of light was split into two separate, divergent beams. Each of the diverged beams would reach two separate mirrors, and the difference between the wave’s speeds were calculated.
* An interesting paradox was presented in the chapter, involving lighthouse and a beach with the wall behind the lighthouse, and the speed of light is calculated using the distance between the lighthouse and the beam, in which the speed would reach a limit.
* I know how refrigerators keep its food cold: Liquid chlorine circulates in coils which evaporates into chlorine hydrate from the surrounding environment. An electric pump pressurizes the gas, allowing the chlorine to turn back into a liquid, and the absorbed heat is released into the refrigerator. Thank you Michael Faraday. (OT?)
* In practice, temperatures near absolute zero have been reached (0 K, -273.15°C), both using a Bose-Einstein condensate and lasers to atoms almost to the point where atoms are completely still.
Electricity and the Proportionality Constant:
* Ever notice how similar the force of gravity and the force of electricity are similar? For gravity, F = G*m*M/r^2 and for electricity, F = k*q*Q/r^2.
* If you want a good mnemonic for the equation of work, just get mad: W = m*a*d.
* Using the relationship of a monatomic molecule’s transitional energy and it’s kinetic energy, Ludwig Boltzmann solved for his constant (k) by solving 3/2*k*T = 1/2*m*v^2
Efficiency of the Hydrogen Fusion:
* I’m thankful that hydrogen fuses at a constant rate (.007 weight loss per nuclei). If it didn’t, life may have not been possible.
* Measuring the fusion came first came from Lord Kelvin asking “How does the sun keep shining?” The greatest contributions came during the decade of 1895-1905, and a value was finalized before the beginning of World War II.
If you want a good read, check “Cosmic Numbers” out.
This blog is property of Edward Shore. 2015.