Chapter 1

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We are covering 1.1-5

Heliocentrism vs Earthcentrism

Helios - Sun

Retrograde motion

...needs to be explained.

This is the motion *relative* to the stars of the "wanderers" visible to the naked eye: Mercury, Venus, Mars, Saturn, Jupiter.

Greek model - Earth centered

Retrograde motion explanation:

• Planets move on circular epicycles,
• each epicycle is centered on an orbit,
• the center of each epicycle follows a circular orbit around Earth.

By the 1500s, The Greek model with Earth at the center, as capped off by Ptolemy (2nd century AD), had been around for nearly 1800 years. It did a good job of explaining the observations of...

• motion of constellations across the sky
• motion of sun and moon around Earth
• retrograde motion of the planets against the background of stars

Greek Metaphysics

• Imperfect earth below with irregular mountains/valleys/oceans   VS
• Perfect realm above with perfectly round moon, & planets orbiting in precise combinations of circles.

  Ptolemy's own claim to fame was the equant (the $\cdot$ in the picture): From this point, the planetary epicycles appear to move at a constant angular speed.

  He introduced equants to get even better agreement between the Greek model and the observed paths of the planets. But with each tweak, the model was becoming more complicated...

  The zodiac constellations

  The 5 planets that the Greeks could see with the naked eye are Mercury, Venus, Mars, Jupiter and Saturn.

  In SkyView, look for those 5 planets, and the sun, and note what the nearest constellation is for each one.

  We noted that all of these are currently located in front of one of the 'Zodiac' constellations, such as Aquarius, Pisces, Taurus...

  The 'ecliptic'

  All the planets and the sun are in more or less the same plane, or the "disk" of Earth's orbit. So, planets will always be located somewhere near the "path in the sky" traversed by the sun. The constellations of the zodiac are the ones located along that path.

  The ecliptic is the apparent path across the sky of the sun. In Skyview:

  1. Search for the Sun.
  2. It's path across the sky will show up as a gray-blue band (where it was) and a dotted line (where it will be). This is the ecliptic
     
     

  Right now (Late January, 2024) you can see that the Sun is in front of the constellation Capricornus. And a number of planets show up nearby, close to its path!

  This display is a bit deceptive. It looks like the Sun will move past Capricorn as the day progresses. But in fact, if you look a bit later today you'll see that Capricorn has moved *with* the sun. Only gradually, over the course of the next few weeks, will the Sun move to being in front of...What's the Zodiac sign after Capricorn?

  This image shows the "view from the North Star" down towards the Sun
  
  University of Hong Kong, Department of Physics, via Western Washington University.
  Since "this month's" constellation (Capricorn) is so close to the Sun, it will be partially visible when the Sun is just barely below the horizon: Either soon before sunrise or shortly after sunset. See:

  • The Zodiac (Spanel Planetarium).
  • The plane of the ecliptic (NASA).

  Copernicus proposes heliocentrism (1543)

  ...in De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres).

  

  What instrument is Copernicus shown using to make observations with?

  In "The Book Nobody Read" [Good Library] by Owen Gingerich (Harvard Physics prof and GC grad) Copernicus' heliocentric model tended to be passed over by the scholars of the time, who were more interested in his new, equant-free, simpler methods for calculating planetary position.

  The [unsigned] preface to "De revolutionus..." argued that no one really knows the truth, and that astronomers are free to use any model they like to make the calculations as easy as possible. Including the heliocentric model which, as it happened, did not require epicycles, nor equants to calculate the positions of planets.

  But according to recent scholarship the preface was inserted by Andreas Osiander, a colleague to whom Copernicus had entrusted the publication of his manuscript.

  Can heliocentrism explain retrograde motion?

  You've examined that in Concept Checks #5 and #6...
  - Answers to Concept Checks #5 #6
  Here is an animation that demonstrates retrograde motion in the heliocentric model.

  Other Concept Checks:

  1. d. For a circle, "fixed point" and "distance" refer to center and radius.
  2. No, the Moon is only partially lit, in a way that suggests it's reflecting the light from the sun, *Not* as if its a source of light.
  3. d. According to Ptolemy, Venus [is never seen at midnight] because the center of its epicycle is on the line from Earth to the sun.
  4. The sun "rises" in the East because Earth rotates Eastward.

  Conceptual exercises

  1.) All the star move together, as if stuck to a crystal sphere, but do not move relative to each other. Planet are bright spots, like stars, but over the course of many nights, they move relative to the stars.

  4.) Retrograde motion of some planet relative to the stars can be seen, which would not be predicted if planets orbited around Earth on simple circles (without epicycles).

  6.) The greeks had an affection for circles. And having the planets move on epicycles, on circles around Earth gave a completely predictable pattern, of when you would see things like retrograde motion: The planets are slowing and reversing according to a discernable pattern, and not just "randomly".

  Copernicus vs. Ptolemy

  Tycho Brahe got excited about looking for evidence which could be used to decide between Copernicus' and Ptolemy's models.

  He designed and built a new instrument (still not a telescope) which allowed him to make extraordinarily precise measurement of the planets' and stars' positions.

  Which model did his observations agree with better?

  

  The disagreement between Copernicus' heliocentric model and Brahe's measurements was about 8 arc min = 8/60 of one degree

  Johannes Kepler

  ...was a student of Brahe's. He took this 8 arc min discrepancy seriously.

  After 16 years of effort trying different models, he found that Brahe's measurements agreed almost exactly with a model in which planetary orbits were ellipses, not circles with the sun at one focus of the ellipse.

  
  Astronomia Nova, 1609.

  All this time, Kepler, Brahe and other astronomers earned money partially through their astrological publications!

  One amazing thing about our solar system: In that picture...*Everything* is spinning / orbiting counterclockwise...

  • The earth around its axis,
  • The Moon around Earth.
  • The Moon around its axis.
  • All the planets around the sun.
  • All of the asteroids in the asteroid belt

  ...and they're all very nearly in the same plane.

  Wonder about why that might be...