gravitation chapter 7, section 3. geocentric models aristotle (384 – 322 bc) taught that the earth...
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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
• 1st Law: planets follow elliptical paths with sun at one focus
• 2nd Law: planets move so that imaginary line from planet to sun sweeps out equal areas in equal time intervals
Kepler’s Laws
• 3rd 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 x10-11 Nm2/kg2 , 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
221
r
mGmFg
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
mgr
mGmF e
g 2 2r
Gmg e
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
2
2
r
GmM
r
mvFF gc
r
GMv
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.