Transcript Gravitation

 System consisting of three
stars: Alpha Centauri A,
Alpha Centauri B, and
Proxima Centauri
 Alpha Centauri A and B
(depicted at left) form a
binary star system
 Binary star system: two
stars orbiting around their
center of mass
 Video animation recorded
at a speed 1,000,000x
faster than real time
What force is responsible for
the motion of Alpha Centauri A
and Alpha Centauri B?
 Neglecting air resistance, all objects near the surface of
the Earth are in free-fall
 Know the acceleration due to gravity on the earth’s
surface is 9.8 m/s2
 Discuss the historical development of the law of
universal gravitation.
 Understand how Newton’s law of universal gravitation
explains both the motion of falling objects and the
orbits of satellites and planets.
 Understand how the acceleration due to gravity acting
upon a mass is affected by the location and mass of the
other object in question.
 Quantitatively apply Newton’s law of universal
gravitation to solve problems.
 Fiction: Newton was sitting under an apple tree. Upon
being struck upon the head by an apple, Newton
realized gravity.
 Fact: Newton observed an apple falling to the ground
while sitting in his garden. He then reasoned that the
same force that pulls an apple toward the ground is the
same as the force that holds celestial objects in orbit.
 Gravitational force – a force of mutual attraction
between masses separated by a certain distance.
 Newton knew that the Moon was 60x farther from the
center of Earth than it was from the Earth’s surface.
 If the force decreased at an inverse square rate, the
gravitational force at the surface of the Moon would be
1/602 times the gravitational force on Earth’s surface.
 During Newton’s time, the period of the Moon ( 27
days) and the mass and radius of the Earth were
known. Using these values, Newton was able to
determine the acceleration of gravity on the Moon.
 Newton’s value was not exactly correct since the
known values were not known to great precision.
Using values known today, Newton would have been
correct.
 Commonly referred to as the Principia
 Published July 5, 1687
 Newton discusses:
 the Laws of Motion
 the Law of Universal Gravitation
 the derivation of Kepler’s Laws
 harmonic oscillation
 Detailed the law of universal gravitation in the third
volume of the book - De mundi systemate (on the
system of the world)
 Gravitas, Latin: “weight”
 G: universal gravitation constant
G = 6.67 x 10-11 N m2/ kg2
 m: mass of an object
 r: the distance between the center of mass of the two
objects
 Fg is an attractive force that always exists between two
masses, regardless of:
 the medium separating them
 their size or composition
 A satellite in orbit around a planet can be considered
as a point mass and a sphere.
 Fg is the same as if all the mass of the sphere was
concentrated at its center (the center of mass).
 The gravitational forces that any two masses
exert on each other are always equal in
magnitude and opposite in direction.
 The gravitational forces are an example of an
action-reaction pair.
 G = 6.67 x 10-11 N m2/ kg2
 Since G is a very small number
 gravity has the lowest relative strength of the four
fundamental forces
 force of gravity is negligible unless a very large mass
involved
 Know that the gravitational forces acting on two
masses are equal and opposite.
 The resulting acceleration of each mass is not
necessarily equal and opposite.
 Consider the gravitational force that arises due to your
interaction with the Earth using Newton’s Second Law
of Motion, F = ma.
 The most important of the fundamental forces at long
distances because of it’s infinite range
 Explains free-fall motion on Earth, planetary orbits, and
large-scale order of galaxies.
 Can analyze the orbits of celestial objects to determine
it’s distance from other celestial objects (the Sun)
 Allows researchers to detect the presence of matter that
cannot be detected by telescopes – dark matter
 Acts universally on all matter
 Unlike the electromagnetic force, the gravitational force
acts universally on all matter since it does not depend on
a mass’ electric charge.
 Gravity is a field force
 Gravitational field strength g
where g = Fg/m
 Gravitational field is a vector
with magnitude g pointing in
the direction of Fg
 Gravitational field strength
equals free-fall acceleration
The blue arrows correspond
to the magnitude of the
gravitational field vectors of
Earth’s gravitational field at
that point.
 The acceleration due to gravity decreases slowly with
increasing height (altitude or distance between the
center of mass of the Earth and the object in question)
 At distances comparable to or greater than the radius
of the Earth, the acceleration due to gravity decreases
at a faster rate.
 An object’s inertial mass is the same regardless of the
acceleration due to gravity.
 “Weight” = mass x gravitational field strength
 on earth, weight = mass x 9.8 m/s2
 dependent upon gravitational field strength therefore
weight changes with location

 m: your mass; M: mass of planet; r: planet radius
 your weight on the surface of any planet will depend
upon the planet’s mass and radius
 The gravitational force is a field force that always exists
between two masses, regardless of the medium that
separates them.
 The same law of gravity applies everywhere in the
universe.
 The magnitude of the gravitational force between two
masses is given by the formula:
 Fg between two masses is an action-reaction pair;
however, the resulting acceleration of each mass due to
Fg will differ (if unequal masses).
 Holt, Rinehart, & Winston: Chapter 7
 Read pages 263 – 264
 Complete problems: 39, 40
 Worksheet
 Complete problems 19, 25, 27, 29