Gravity

Modern Physics offers a coherent if not unified description of nature from the sub-atomic length scales of 10 m to astronomical length scales of m. Obviously it was not always so. Through the middle ages natural philosophers had a disjoint perception of the Universe. Specifically there was little connection between the description of physical phenomena on earth and the description of the motion and properties of the ``heavenly bodies'' such as our sun, the planets and stars. This lack of a coherent understanding of our Universe is perhaps best exemplified by the belief which persisted until the middle ages that earth is the center of the Universe. Aristotle reached this conclusion in (350BC) based on the absence of visible parallactic shift of distant stars. Claudius Ptolemy 140AD cemented this view by developing an elaborate phenomenological description of the motion of the planets in circular orbits about points close to the center of the earth each with their specific epicycles. Up until the fifteenth century this world-view persisted. But to keep up with more accurate observations eventually the description became extremely complicated involving more and more epicycles and without a hope of understanding where all this came from on a more fundamental level.

Nicholas Copernicus (1473-1543) proposed that the earth orbits around the sun along with the other planets and was able to understand some of the stranger aspects of the planet motion across the night sky. This view was violently opposed by catholics and protestants alike and though Copernicus died a natural death followers of his were actually burned on the fire as heretics.

Tycho Brahe (1546-1601) put the ideas to experimental scrutiny by far improving the available data on planetary motion through measurements taken with the naked eye from an observatory on a small island. Brahe managed to place the other planets in their right sequence from the sun but he could not convince himself that the earth moved. It was his assistant Johannes Kepler (1571-1630) who determined to find some systematics poured over the treasure trove of data for 20 years and finally derived his three laws of planetary motion :

1. Planets move in elliptical orbits with the sun at one focal point
2. equal areas are swept out by a line from sun to planet in equal times
3. for all planets in our solar system (a is semi -major axis of the elliptical orbit and is a constant).

Galileo Galilei (1564-1642) paved the way to complete the Copernican revolution. by inventing the telescope and discovering four satellites orbiting Jupiter and thus proving that not all bodies orbit earth. He was an avid proponent of the Copernican view of our solar system and for that reason was perceived as a threat by the pope who forced him to denounce his heretic views and placed him in house arrest.

Isaac Newton (1642-1727) at age 24 provided an explanation for Kepler's laws and thereby tied together astronomical and terrestrial physics. He recognized that there was no apparent weakening of the gravitational pull of the earth on a body as you move that body from sea level to the highest tower or mountain and so said why should this force not also be responsible for forcing the moon to orbit the earth? To explained Kepler's three laws based on his own three laws of motion and the additional assumption that a central force acts between all massive bodies:

where r is the distance between the bodies with mass and . We now see how Kepler's laws drop out from Newton's simple Universal frame-work.

 
• Kepler's first and third law
• Kepler's second law
• Newton and the apple
• Example: Motion of a Asteroid
• Potential and Kinetic Energy in Orbit
  • Escape Velocity