Title: System consisting of three stars: Alpha Centauri A, Alpha Centauri B, and Proxima Centauri
1Alpha Centauri
- 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?
2Universal Gravitation
3Gravity on Earth
- Neglecting air resistance, all objects near the
surface of the Earth are in free-fall - Know the acceleration due to gravity on the
earths surface is 9.8 m/s2
4Objectives
- Discuss the historical development of the law of
universal gravitation. - Understand how Newtons 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 Newtons law of universal
gravitation to solve problems.
5Newton and the apple
- 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.
6Inverse Square Relationship
- Newton knew that the Moon was 60x farther from
the center of Earth than it was from the Earths
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 Earths surface. - During Newtons 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. - Newtons value was not exactly correct since the
known values were not known to great precision.
Using values known today, Newton would have been
correct.
7Philosophiae Naturalis Principia Mathematica
- Commonly referred to as the Principia
- Published July 5, 1687
- Newton discusses
- the Laws of Motion
- the Law of Universal Gravitation
- the derivation of Keplers 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
8Universal Gravitation
- 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
9The Gravitational Force Between a Point Mass and
a Sphere
- 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).
10The Gravitational Force
- 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.
11Universal Gravitation Constant
- 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
12The Gravitational Force and Newton's Second Law
of Motion, F ma
- 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 Newtons
Second Law of Motion, F ma.
13The Gravitational Force and Newton's Second Law
of Motion, F ma
14The Gravitational Force
- The most important of the fundamental forces at
long distances because of its 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 its 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.
15Gravitational Field
- 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 Earths
gravitational field at that point.
16Gravitational Field Strength
- 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)
17Gravitational Field Strength
- At distances comparable to or greater than the
radius of the Earth, the acceleration due to
gravity decreases at a faster rate.
18Weight
- An objects 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 planets mass and radius
19Summary
- 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).
20Assignment
- Holt, Rinehart, Winston Chapter 7
- Read pages 263 264
- Complete problems 39, 40
- Worksheet
- Complete problems 19, 25, 27, 29