chapter 8 notes - School District of La Crosse

Download Report

Transcript chapter 8 notes - School District of La Crosse

• I. Kepler's Laws of planetary motion.
A. Was seeking an explanation of why
Mars orbit was off of path of a circle as
predicted by Brahe.
B. Brought astronomy from a qualitative/
observational science to a quantitative/
measurement science
• The planets move in elliptical orbits with
the sun as 1 foci
Kepler’s second law-Law of areas
• Planets will sweep equal area in equal
square of the periods is
proportional to the cube of the
average radius of the orbit
B SAMPLE PROBLEM- The moon Io is 4.2
units from the center of Jupiter. It has a period
of 1.8 days. The measurement of Ganymede’s
orbit is 10.7 units, find the period
A. Showed that if the planets are moving in elliptical orbits
the net force acting on the planet must vary proportionally
with the inverse square of the distance
1. F 1/d2 d is the average distance between the 2
B. The product of the 2 masses involved also play a role.
1. Noted the falling of an apple from a tree and
surmised that the earth is attracting the apple, but the apple is
also attracting the earth...even if it is very little
2. Noted that the force of attraction is directly
proportional to the product of the masses.
C. Law of Universal Gravitation- The force
of attraction is proportional to the product
of the masses and inversely proportional to
the square of the distance.
1. F=G M1M2/r2
a. G= 6.67x10-11NM2/Kg2
b. Cavendish experiment
determined the value of G
 The apparatus constructed by Cavendish was a
torsion balance made of a six-foot wooden rod
suspended from a wire, with a 2 inch diameter
1.61 pound lead sphere attached to each end.
Two 12 inch 348 pound lead balls were located
near the smaller balls, about 9 inches away, and
held in place with a separate suspension
system. The experiment measured the faint
gravitational attraction between the small balls
and the larger ones.
 III. Using the law of universal gravitation
A. Planets and satellites
B. Newton reasoned if a bullet shot out of a gun with enough
force from a high mountaintop it would go into orbit about the earth
1. The parabolic motion of the projectile would be identical to
the curvature of the earth.
2. An object with a horizontal velocity of 8Km/s will keep the
same altitude and circle the earth.
C. V=
D. Finding the velocity of a satellite-A satellite is 225Km above
the earth’s surface. What is the orbital velocity?
E. Able to derive Keplers 3rd law
Theoretical concerns
 There is no immediate prospect of identifying
the mediator of gravity. Attempts by physicists
to identify the relationship between the
gravitational force and other known
fundamental forces are not yet resolved,
although considerable headway has been
made over the last 50 years (See: Theory of
everything and Standard Model). Newton
himself felt the inexplicable action at a distance
to be unsatisfactory (see "Newton's
reservations" below).
Newton's theory requires that gravitational
force is transmitted instantaneously. Given
classical assumptions of the nature of
space and time before the development of
general relativity, a propagation delay
leads to unstable orbits.
• Disagreement with observation
• Newton's theory does not fully explain the
precession of the perihelion of the orbits
of the planets, especially of planet
Mercury. There is a 43 arc second per
century discrepancy between the
Newtonian prediction, which arises only
from the gravitational tugs of the other
planets, and the observed precession
The predicted deflection of light by gravity
using Newton's theory is only half the
deflection actually observed. General relativity is
in closer agreement with the observations.
The observed fact that gravitational and
inertial masses are the same for all
bodies is unexplained within Newton's
system. General relativity takes this as a
postulate. See equivalence principle