Gravitation Chapter 7, section 3

Geocentric Models Aristotle (384 – 322 BC) taught that the earth was surrounded by crystalline spheres on which the planets and stars were located Ptolemy (100 – 170) taught the planets and sun orbit the earth in the order Mercury, Venus, Sun, Mars, Jupiter, Saturn

Heliocentric Model Nicholaus Copernicus (1473 – 1543) proposed the sun was the center of the solar system explaining the motion of the planets Tyco Brahe (1546 – 1601) made a long series of observations trying to resolve the debate between the two models. He hired Johannes Kepler to analyze the data

Kepler’s Laws of Planetary Motion Johannes Kepler (1571 – 1630) Used observations of Tyco Brahe to analyze planetary motion 1 st Law: planets follow elliptical paths with sun at one focus 2 nd Law: planets move so that imaginary line from planet to sun sweeps out equal areas in equal time intervals

Kepler’s Laws 3 rd Law: The square of a planet’s orbital period is proportional to the cube of its mean distance from the sun Newton was able to use his laws of motion and gravitational law to prove Kepler’s laws Laws apply to all satellites

Isaac Newton Lived 1642 – 1727 First formulated theory of gravity in 1666 Published in Principia Mathematica in 1686

Isaac Newton and Gravity Newton realized an apple falls because of force of gravity Analyzed motion of the moon--it follows a circular path, so a force is needed Newton first to realize gravity causes both. Newton extended gravitation theory to all objects, realized gravitational attraction is property of all mass

Universal Law of Gravitation First formulated by Newton, based on the work of Kepler and others G = 6.67 x Nm 2 /kg 2, the constant of universal gravitation, first measured by Henry Cavendish in 1798 r is the radial distance between the centers of mass of the two objects

Gravitational Force Mutual force of attraction between particles of matter Attractive force is universal—all matter attracts all other matter Very weak force, only noticeable when large quantities of matter are present Attractive forces are equal and opposite between two objects

An Inverse-Square Law Gravitational force is inversely proportional to the square of the distance between objects. Doubling the separation distance produces one-fourth the force If the distance is reduced by one-half, force is four times as great

Gravitational Fields Gravitational force acts over a distance without contact Caused by interaction with gravitational field Field can be thought of as lines of force radiating from objects Strength of field is force per unit mass exerted on object: g = F/m

Gravity and the Earth To find the gravitational force on earth, use the radius of the earth for the distance and the mass of the earth as one of the bodies. Since the gravitational force is weight, therefore, g is strength of gravitational field

Satellite Motion Satellites are “falling” but tangential motion keeps them in orbit Gravitational force acts a centripetal force changing direction of motion so In circular orbit, speed is constant, altitude depends on orbital speed

Satellite Motion Geosynchronous satellites have 24 hour orbital period and remain “motionless” in sky If speed is greater or less than needed for circular orbit, elliptical orbit results Speed is not constant in elliptical orbit but greatest when satellite is closest to earth (perigee) and least when farthest away (apogee) Total energy is constant, transferring from kinetic to potential and back again

Gravitational Effects Tides—caused by the moon’s gravitational pull on the earth Stars form when clouds of hydrogen gas coalesce because of gravitational attraction, compressing until nuclear fusion occurs Black Holes—created when large stars exhaust their nuclear fuel and undergo gravitational collapse

Gravity and the Universe “Big Bang” theory says universe hurled outward from big explosion Universe is expanding, only pull of gravitation can stop it. Unknown whether enough matter exists to stop expansion and begin contraction leading to “Big Crunch” and another big bang-expansion-contraction cycle.

General Relativity Einstein explained the pull of gravity with his theory of general relativity The attractive force is the result of the warping of the fabric of space-time by large amounts of mass Like a heavy weight on a trampoline, smaller objects are pulled toward a large mass