Calculating The Cosmos: How Mathematics Unveils The Universe, Ian Stewart, c. 2016.

Calculating the Cosmos: How Mathematics Unveils the Universe, Ian Stewart, c. 2016. 523.1STE.

Author: emeritus professor of mathematics at University of Warwick.

Prologue. Do you remember this?
November 12, 2014
landing a space probe on a coomet
the flight alone took ten years
the mother ship: Rosetta
the probe: Philae
the comet: 67P/Churyumov-Gerasimenko

Comets as a source of water for the origin of earth? Unlikely, based no results from that mission.

More likely: asteroids.

Newton's law of gravity lies at the heart of this book.

Chapter 1: why apples fall and the moon does not. It's the same reason, it appears why a bicyclist doesn't fall over either (as a rule; there are exceptions. President Biden may have been the most famous person to "break that rule"). 

Gravity: wee can calculate its effects with exquisite accuracy. Yet, we still don't understand it.

Key figures: leading roles in advance of astronomical knowledge: Galileo, Kepler, and Newton.

 So, why is it such a big deal that Sophia studies ellipses in middle school and high school math.

Aristotle
Nicolau Copernicus: heliocentric theory
Galileo: embraced Copernicus' theory
Kepler (1571 - 1630) -- Vermeer (1623 - 1675) -- Van Leeuwenhoek (1632 - 1723)

• his boss: Tycho Brahe
• made their "mark" studying Mars
• the ellipse
• major axis
• minor axis
• size and shape of an elliptical orbit: two numbers
• the major radius and the eccentricity
• from those two, the minor radius can be found
• spatial location of any other elliptical orbit about the Sun can be characterized by three more numbers, all angles:
• inclination of the orbital plane to the elliptic
• the direction of the major axis in that plane
• the direction of the line at which the two planes meet
• but, we need to know where the planet is in the orbit, which requires one further angle
• so, specifying the orbit of the planet and its position within that orbit requires two numbers and four angles -- six orbital elements.
• Kepler solved this with three laws of planetary motion;
• the orbit of a planet is an ellipse with the Sun at one focus
• the line from the Sun to the planet sweeps out equal areas in equal periods of time
• the square of the period of revolution is proportional to thee cube of the distance

Newton

• reformulated Galileo's observations from freey moving bodies as three laws of motion.
• bodies continue to move in a straight line at a constant speed (velocity) unless acted on by a force
• the acceleration of any body, multiplied by its mass, is equal to the force acting on it (F=ma)
• every action produces an equal and opposite reaction;
• 1687: he reformulated Kepler's planetary laws as a general rule for how heavenly bodies move -- the law of gravity, a mathematical formula for the gravitational force with which any body attracts any other

• one assumption, he deduced the following: the Sun exerts an attractive force, always directed towards its center:
• thus: the force is inversely proportional to the square of the distance

Credit for the law of gravity goes to Newton, but the idea wasn't original: Kepler deduced something similar by analogy with light.

Skipping ahead and random notes.

Spacetime continuum, p. 24: in Newtonian mechanics, none of these weird things happens. Space is space and time is time an ever the twain shall meet. In special relativity, space and time are to some extent interchangeable, the extent being limited by the speed of light. Together they form a single spacetime continuum. But most of the weird effects are apparent only at very fast speeds, so we don't notice them in everyday life.

Spacetime is already curved, an that curvature affects the path of a moving particle. No action at a distance is needed: spacetime is curved because that is what stars do to spacetime, and orbiting bodies reespond to nearby curvature. What we and Newton refer to as gravity, and think of as a force, is actually the curvature of spacetime.

Chapter 2: the formation of the solar system.

Chapter 3: why is the moon so large? The origin of the moon. That "impact" theory is not holding up well.

Chapter 4: the spacing of the planets.

• the Titius-Bode law
• predicting the existence of new / other planet
  

Chapter 5: the story of Ceres

• asteroids: originally planets, then minor planets, then "asteroid" (p. 73)
• the asteroid belt 
• three major clumps off asteroids
• Hildas, Trojans, Greeks, 
• the Kirkwood gaps, Daniel Kirkwood, 1866
  

Chapter 6: rings

• Saturn
• Uranus

Chapter 7: 

• planetary moons

Chapter 8:

• Halley's comet

Chapter 9: 

• chaos in the cosmos

Chapter 10: 

• the interplanetary superhighway 

Chapter 11:

• great balls of fire

Chapter 12:

• great sky river

Chapter 13:

• alien worlds

Chapter 14: 

• dark stars

Chapter 15:

• skeins and voids

Chapter 16:

• the cosmic egg

Chapter 17:

• the big blow-up

Chapter 18:

• the dark side

Chapter 19:

• outside the universe

Epilogue:

• why are we here? 
• wow, starts to get into the metaphysical, spiritual
• a lot of coincidences
• fine tuning
• physics depends on a number of fundamental constants
• the speed of light
• Planck's constant in quantum theory
• the fine structure constant, which determines the strength of the electromagnetic force
• these constants are generated by no accepted physical theory or preicted by any accepted physical theory: they could have been any number (does that also apply to pi? No, because pi can be generated / predicted by a simple algebraic formula)
• the chance of all this: one constant, six heads in a row
• there are at 26 constants
• 26 constants tossing 156 heads in a row: one in 10^-47 -- it ain'g gonna happen.

Three options:

• supernatural (Go)
• future physics will explain it
• the universe tries all possible values in turn ... until something works .... the metavers

Metaverse:

• the universe in its usual sense plus any number of hypothetical extras (alternate worlds; alternative, parallel worlds); p. 279
• in The Hidden Reality, Brian Green, describes nine different types of multiverse
• in this book, the author discusses four:
• quilted multiverse
• inflationary multiverse
• landscape multiverse
• quantum multiverse

Perhaps more later, but now I'm going to enjoy the book.