08 Universal Gravitation

The Earth-centered Universe of Aristotle and Ptolemy dominated Western thought for nearly 2000 years.
In the 16th century, Polish astronomer Nicholas Copernicus introduced a revolutionary idea.

Background:
- Full name: Mikotaj Kopérnik
- Studied at the University of Kraków and later in Italy, focusing on various subjects including astronomy, mathematics, and medicine.
- Settled in Frauenburg, East Prussia, where he practiced medicine and fulfilled canonical duties.
Major Work:
- Authored "De revolutionibus orbium coelestium" which laid foundation for modern astronomy.
- Completed around 1530 but published in 1543, posthumously.

In "On the Revolutions of the Heavenly Bodies":
- Proposed the Sun as the center of the Solar System, termed heliocentric system.
- Ordered the planets in a modern context: Earth as the third planet from the Sun, with the Moon orbiting Earth, while stars are distant objects not revolving around the Sun.
- Earth believed to rotate every 24 hours, making it seem as though stars revolve around it.

Known for accurate astronomical observations that influenced future scientists.
Advocated a geocentric model with Earth at the center, where the Sun, planets, and stars revolve around it.
Established an observatory on the Island of Hven, utilizing large instruments for observation for 20 years.

Overview:
- German astronomer and assistant to Tycho Brahe, an ardent supporter of the heliocentric view.
- Focused on mathematical relationships governing planetary motion.
Key Contributions:
- Emphasized the significance of planetary orbits through mathematical laws.
- Published first two laws of planetary motion in "New Astronomy" (1609) and the third law in "The Harmonies of the World" (1619).

Law 1: Planets/comets orbit the Sun in elliptical paths, with the Sun's center of mass at one focus.
Law 2: A line connecting a planet to the Sun sweeps out equal areas in equal time intervals.
Law 3: The squares of the periods of planets are proportional to the cubes of their average distances from the Sun.

Contributions:
- Utilized Kepler's laws to define gravitational force, stating it varies inversely with the square of the distance between a planet and the Sun.
- Inspired by the observation of an apple falling, which led him to consider the attraction between Earth and other celestial bodies.

Defines gravitational force between two spherical masses:
- Equation involves:
  - r: distance between centers of masses
  - m1, m2: mass of the objects
  - G: universal constant

Background:
- Attended Cambridge University but did not graduate. Wealthy, yet lived frugally, focusing on scientific studies.
- Known for measuring Newton's gravitational constant.
Apparatus:
- Developed a device involving a 6-foot rod with metal spheres to measure gravitational attraction.
- Determined gravitational force through the twisting of the rod, balancing torsional force with gravitational force to measure distances and masses.
- His experiment yielded a value for G approximating 6.75 x 10^-11 N m^2/kg^2, later refined to 6.67259 x 10^-11 N m^2/kg^2.