Universal Gravitation

Wait a minute, Doc, are you trying to tell me that my mother has got the hots for me? Precisely. Whoa, this is heavy. There's that word again; "heavy". Why are things so heavy in the future? Is there a problem with the earth's gravitational pull?

Topics  Introduction Introduction  Kepler’s Laws Kepler’s Laws Kepler’s Laws  Universal Gravitation Universal Gravitation Universal Gravitation  Planetary and Satellite Motion Planetary and Satellite Motion Planetary and Satellite Motion  Different Views: Newton v. Einstein Different Views: Newton v. Einstein Different Views: Newton v. Einstein

A little history…  Ancient Greece  Things rose or fell according to what they were  Smoke rises  Objects fall  Gave birth to the terms  Levity (lightweight)  Gravity (heavy)

Stargazing  Always the popular past time, early humans noticed that celestial bodies moved in regular patterns  Planet = “wanderer”  Tycho Brahe ( )  Extremely detailed measurements of planetary motion  Built first observatory (an entire island! ~Hven)  Had precise instruments constructed

Johannes Kepler  One of Brahe’s assistants and a brilliant mathematician  Used heliocentric (sun-centered) model and Brahe’s measurements to discover basic descriptions for the behavior of every planet and satellite (moons, comets, etc.)  “fatal” blow to church-enforced geocentric description  Verified Copernicus’ ideas  Those 3 descriptions are now known as…

Kepler’s Laws of Planetary Motion  First Law  The paths of the planets are ellipses, with the sun at one focus.

Kepler’s Laws of Planetary Motion

 Second Law  An imaginary line from the sun to a planet sweeps out equal areas in equal time intervals.

Kepler’s Laws of Planetary Motion  Third Law  The square of the ratio of the periods of any two planets revolving about the sun is equal to the cube of the ratio of their average distances from the sun T = Period r = average distance from the sun

Kepler’s Laws of Planetary Motion  Notice that the first two laws pertain to individual planets or satellites  The third law relates the motion of different planets or satellites!

The falling apple  About 45 years after Kepler  Isaac Newton saw an apple fall, and also observed the moon in the daytime sky  What’s keeping the moon from flying off into space?  Force that makes the apple fall must be causing the moon to continually “fall” toward Earth

Universal Gravitation  If the planets travel in ellipses, then the distance between the planets and the sun changes.  If this distance changes, then the amount of force on the planet from the sun must change

A universal force  He named this force gravity, and he said it existed between every single object!  The amount of force depends on:  How massive the objects are  More mass = more force  The distance between the objects  Closer together = more force

Inverse Square Law  Inverse relationship between gravitational force and the square of the distance between two objects  The sign means “proportional to”

Law of Universal Gravitation  m 1 and m 2 = masses of two objects  d = distance between objects’ centers of mass  G = gravitational constant  6.7 x N·m 2 /kg 2

Revolutionary Idea  We can use the Law of Universal Gravitation to figure out how long it takes a satellite to complete its orbit around the sun.  m s = mass of the sun  This can be modified to orbit anything (i.e. moon around sun)!

Satellites AND Set them equal to each other…

Gravitational Field  Friction – block on an inclined plane  Normal force – standing on the ground  Both are contact forces  How can the sun exert a force on Earth, even though we’re millions of miles away?

Newton’s Ideas  Great for explaining planetary motion  Gave us accurate, precise method for predictions  Couldn’t answer the question “how?”

Faster than Superman…  Newton said that gravitational forces permeated instantly…  Suppose the sun disappeared…  Einstein said that gravitational effects would take time to feel

Einstein’s Ideas  Gravity is not a force, but a “bend” in space  More massive bodies will cause a greater bend

Tested and “true”  Both of Einstein’s theories have been tested time and time again, and have been extremely accurate in their predictions  New discoveries may necessitate revision of his theories, nonetheless!