Isaac Newton's Study Guide: Cartesian Cosmology

• This study guide covers the material for Isaac Newton Parts 1-9.
• The guide helps identify content for an quiz or test.

The Cartesian Cosmology

• The Church of England (Protestant) encouraged innovation, unlike the Roman Catholic Church
• The Church of England did this to support naval warfare and shipping
• Heliocentrism is concluded by Descartes through logical reasoning.
• Descartes reasoned that celestial bodies are in an invisible fluid, arguing that empty space doesn't exist
• Planetary orbital motion is driven by the spin of celestial bodies, with planets moving like objects being caught in a tornado.
• Every star is its own center with other planets caught in vortexes, according to Descartes

Robert Hooke and the Royal Society

• Robert Hooke was the Curator of Experiments with duty to critically examine experiments that tested theories
• Hooke presented tested theories in many branches of science, and the society would discuss conclusions.
• The Royal Society aimed to distinguish philosophy vs science, and played roles getting scientists funding
• Hooke attributed planetary motion to an invisible attractive force (gravitational attraction)
• The Royal Society asked Hooke to prove gravitational attraction
• William Gilbert proposed the the earth has an invisible magnetic field that induces motion across empty space
• Hooke demonstrated "attractive" force coming from the sun by a string.
• Bodies have gravitational attraction, larger bodies attract smaller ones, used to explain all motion.
• Gravity is a force that acts between all masses in the universe, its effects have no distance limit.
• The strength of gravity decreases with distance
• The fundamental force governs the structure and behavior of the cosmos.
• The Moon increasing in orbital speed if it moved closer to the Earth is because of the increasing gravitational pull

Isaac Newton and the Reflecting Telescope

• Newton invented Calculus, math that describes how quantities change and describes motion of planets with infinitesimal precision
• Dispersion occurs when light passes through a prism producing a light spectrum (rainbow)
• Sunlight is composed of all rainbow colors and glass bends each color of light by different refraction angles
• White light is composed of different colors, and a prisim doesn't create colors but separates the existing ones
• Newton constructed a telescope with mirrors to avoid dispersion, which blurs colors in telescopes with glass lenses
• Reflecting telescopes (Newtonian reflectors) use mirrors, avoiding dispersion by passing light through the primary mirror, then reflecting through a secondary mirror.

Newton's Law of Gravity

• Gravity weakens by the squared amount of the distance away you are apart from what it is attracting
• If an object doubles its distance from a source of gravity, gravity weakens by 4
• If distance is tripled, gravity becomes 1/9 (0.1333).
• Hooke suspected gravity obeys an inverse-square law because light follows the inverse square law
• The inverse square law leads to Kepler's 3rd law
• Kepler's 3rd law is the relationship between orbital period and radii between planets
• Inverse square law leads to elliptical motion
• Newton proved gravity with Calculus (which he invented); he proved Kepler's 1st and 3rd laws

The Universality of Kepler's 3rd Law

• Principia Mathematica (1687) is Newton's book that proved gravity, using Calculus and his 3 laws of motion.
• Newton proved that gravity is universal, so all orbital motion obeys Kepler's laws
• Newton measured the masses of Jupiter and Saturn using the moons' orbit and movement around the two (more gravity = faster moons move)
• Jupiter is 300x more massive than Earth
• Saturn is 9.5x larger than Earth
• Newton was able to measure the masses of Jupiter and Saturn by observing the motion of their moons.
• Jupiter is both largest and has a more than 300 times that of Earth, while Saturn is still over 90 times more massive than Earth.
• Knowing the mass and size can tell density, calculating it as mass divided by volume.
• Jupiter and Saturn have lowdensity (gas giants) and have largest volumes
• Jupiter and Saturn are mainly composed of gaseous vapor and have small solid cores.

Newton Explains the Earth's Precession

• Newton used precession of equinoxes to show a spinning sphere has an outwards “centrifugal” push pushing from the equator
• Newton's 3rd law: for every action there is an equal and opposite reaction
• Centrifugal force is the force of a spinning sphere pushing outwards as it spins
• The Earth bulges since volumes push outwards from the equator, thus is at strongest there
• Gravity force is less strong at the equator (time passes slower) because the equator is farthest from the center
• The Earth equatorial bulge changes pendulum clocks by making them feel weaker, thus moving slower.
• Disc shapes galaxies happen like this: Andromeda, stars flung outward into disc shapes
• Earth's precession is due to gravitational pulls of the Sun, Moon's and Planets on Earth's equatorial bulge + the Earth's own mass gravitational pull, causing a wobble
• It takes 26,000 years for Earth's spin axis to precess in a complete circle

Newton Explains the Earth's Tides

• High tide = the coastline disappears
• Low tide = the coastline appears
• Earth's ocean layer experiences a tug from the Moon + centrifugal force (bulge) around the equator
• Together they produces a flat elongated bulge of water moving with the moon
• The Moon's gravity is 6x weaker than Earth (so the moon orbits the earth), but has still pulls on our oceans
• Affecting the monthly cycle, the Moon pulls on the ocean, and the sun exerts influence too.
• "Spring" tides are the deepest high tides, while “neap” tides are shallowest
• When the Sun, Moon, and Earth are parallel, the gravity adds up causing the spring tides
• Spring tides occur during new and full moons
• Neap tides occur during the 1st and 3rd quarter due to the Sun, Moon, and Earth being perpendicular

Newton Explains the Moon's Orbit

• The body with the most gravity is the one being orbited
• The moon orbits around the “center of mass,” an average location of all mass around the system.
• With two equal bodies, the center of mass is exactly in the middle - both bodies exert equal gravitational force.
• In bodies of unequal mass, the center of mass will be nearer to the body with the more mass, because the force of gravity is more potent.
• Both the Earth and Moon orbit around their center of mass (offset around the Earth but inside Earth), describing the Moon's orbit
• Planets orbit bodies around the center of mass.
• The Earth's moon system wobbles around the Earth's center of mass at 1/80 seconds off
• The sun’s orbital wobble of the sun with the earth/sun system is 1/80,000

Halley's Comet and the Proof of Gravity

• Comets have elongated elliptical orbits (like 1680's great comet)
• Comets can obey Kepler's law and follow an elliptical path/orbit with the sun at one focus point.
• Orbits of comets are elongated, explaining long orbital periods (thousands of years)
• We rarely see the same comet twice in a lifetime because they're only visible a few months when they get closer/reflect sunlight
• Halley suspected the comets of 1456, 1531, 1607 and 1682 were the same because sightings:
  • Had all comet sightings moving in retrograde position (night to night they moved backwards, east to west) w/similar sky appearances
  • Experienced equal time intervals (76 years/orbital period).
• The comet of 1758 was named "Halley's Comet" proved Newton’s law applied to Earth and the sky
• Next Halley comet appearance: 2061

Newton's Law

• Newton's law of gravity is not truly universal because some phenomena don't obey Newton's law:
  • Something moving near speed of light
  • Approaching a black/worm hole
  • A planet with closer orbit around a star
• Einstein's general relativity applies more universally compared to Newton's rules.

Study guide covering Isaac Newton Parts 1-9. Includes Cartesian Cosmology, the Church of England's support for innovation and naval warfare, and Descartes' heliocentrism conclusion. Also covers Robert Hooke and the Royal Society.