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Astronomy 114
Lecture 6: Newton’s Laws of Motion and Gravity
Martin D. Weinberg
[email protected]
UMass/Astronomy Department
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—1/17
Announcements
Problem Set #2 posted today, due next Friday
Grade/homework posting release form
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—2/17
Announcements
Problem Set #2 posted today, due next Friday
Grade/homework posting release form
Newton’s Laws
Physical laws, Fundamental forces
Explain Kepler’s Laws and Galileo’s observations
in one theory
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—2/17
Newton (1642-1727)
Recognized importance of Galileo’s
contribution
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—3/17
Newton (1642-1727)
Recognized importance of Galileo’s
contribution
Laws of Motion
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—3/17
Newton (1642-1727)
Recognized importance of Galileo’s
contribution
Laws of Motion
Law of Gravitation
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—3/17
Newton (1642-1727)
Recognized importance of Galileo’s
contribution
Laws of Motion
Law of Gravitation
Explained all of planetary motion
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—3/17
Newton (1642-1727)
Recognized importance of Galileo’s
contribution
Laws of Motion
Law of Gravitation
Explained all of planetary motion
Explains much of all motion in the
Universe
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—3/17
Principia Mathematica, 1687
Unified observations of
Kepler and Galileo
Invented Calculus to
solve the problem
Beginning
physics!
A114: Lecture 6—09 Feb 2007
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of
modern
Astronomy 114—4/17
Newton’s 3 Laws of Motion (1/5)
1. Law of Inertia: A body remains at rest, or moves in a straight
line at a constant speed, unless acted on by an outside force
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—5/17
Newton’s 3 Laws of Motion (1/5)
1. Law of Inertia: A body remains at rest, or moves in a straight
line at a constant speed, unless acted on by an outside force
2. Second Law: Acceleration of an object is proportional to the
force acting on that object
F=ma
m is mass
a is acceleration
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—5/17
Newton’s 3 Laws of Motion (1/5)
1. Law of Inertia: A body remains at rest, or moves in a straight
line at a constant speed, unless acted on by an outside force
2. Second Law: Acceleration of an object is proportional to the
force acting on that object
F=ma
m is mass
a is acceleration
3. Third Law: When one body exerts a force on a second body,
the second body exerts an equal and opposite force on the first
body
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—5/17
Newton’s 3 Laws of Motion (2/5)
First Law: Law of Inertia
The motion of an object has speed and direction
An object’s resistance to changes in motion is known
as inertia
Contradicted the still popular theories of Aristotle that
objects will eventually come to rest
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—6/17
Newton’s 3 Laws of Motion (3/5)
Second Law of Motion
F= ma
F describes the force acting
m is the mass of the object
a is its acceleration, the change in its motion.
Like motion, force has both a value or strength, and a
direction in which it acts.
Acceleration refers to any change (“speeding up”,
“slowing down”, or change of direction)
Implies First Law of Motion
A114: Lecture 6—09 Feb 2007
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Astronomy 114—7/17
Newton’s 3 Laws of Motion (4/5)
Second Law of Motion: examples
The larger the force the larger the acceleration
For equal force, a larger mass must have a smaller
acceleration
Larger mass has greater inertia. Can use this to
measure mass of an object
Unit of force (metric) is called a Newton (N):
1 Newton is equal to 1 kg · m/s2
Inertial mass
A114: Lecture 6—09 Feb 2007
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Astronomy 114—8/17
Newton’s 3 Laws of Motion (5/5)
Third Law: equal and opposite force
Example: smack an object
Object moves as a result
Your hand also feels a force and bounces back
(and hurts)
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—9/17
Newton’s 3 Laws of Motion (5/5)
Third Law: equal and opposite force
Example: smack an object
Object moves as a result
Your hand also feels a force and bounces back
(and hurts)
Example: small object hits a large object
If the forces are equal, why does the smaller
object bounce back faster?
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—9/17
Newton’s 3 Laws of Motion (5/5)
Third Law: equal and opposite force
Example: smack an object
Object moves as a result
Your hand also feels a force and bounces back
(and hurts)
Example: small object hits a large object
If the forces are equal, why does the smaller
object bounce back faster?
msmall asmall = F = mlarge alarge
mlarge
alarge
asmall = m
small
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—9/17
Fundamental Forces (1/2)
Physicists have identified four natural forces
Gravity
Holds the Sun and planets together in the solar
system
Holds stars together in galaxies
Things fall “down” on Earth
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—10/17
Fundamental Forces (1/2)
Physicists have identified four natural forces
Gravity
Holds the Sun and planets together in the solar
system
Holds stars together in galaxies
Things fall “down” on Earth
Electromagnetism: a force between objects with
electric charge
Holds atoms together
Responsible for chemical reactions
Friction of book on table
Magnets
A114: Lecture 6—09 Feb 2007
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Astronomy 114—10/17
Fundamental Forces (2/2)
Strong force
Holds nuclei of atoms together
Generation of energy in stars, supernovae
Power, bombs
A114: Lecture 6—09 Feb 2007
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Astronomy 114—11/17
Fundamental Forces (2/2)
Strong force
Holds nuclei of atoms together
Generation of energy in stars, supernovae
Power, bombs
Weak force
Radioactive decay
Also energy in stars, supernovae
A114: Lecture 6—09 Feb 2007
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Astronomy 114—11/17
Newton’s Law of Gravity (1/6)
Newton described the force of gravity mathematically
Every body in the Universe attracts every other body
with a force proportional to the product of their
masses and inversely proportional to the square of
the distance between them:
Fgravity
Gm1 m2
=
r2
G is the same here as it is in a distant galaxy. It is a physical
constant of the Universe.
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—12/17
Newton’s Law of Gravity (2/6)
Gravity is an attractive force, and in accordance with
Newton’s Third Law, the two masses feel equal and
opposite forces
Gravity is relatively weak because of the small value
of the gravitation constant G; in metric units:
G = 6.7 × 10−11 N · m2 /kg2
Large masses are required to provide an appreciable
force, e.g. the mass of the Earth is 6.0 × 1024 kg
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—13/17
Newton’s Law of Gravity (3/6)
On the surface of a planet:
Fgravity
Fgravity
Gm2
= m1 × 2
r
= m1 × aEarth’s surface
Acceleration caused by the Earth on any object placed on its
surface is the same: its value is 9.8 m/sec/sec.
Acceleration on the surface determines weight of
object
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—14/17
Newton’s Law of Gravity (3/6)
On the surface of a planet:
Fgravity
Fgravity
Gm2
= m1 × 2
r
= m1 × aEarth’s surface
Acceleration caused by the Earth on any object placed on its
surface is the same: its value is 9.8 m/sec/sec.
Acceleration on the surface determines weight of
object
On another planet
2
mplanet
rEarth
aplanet
=
× 2
aEarth
mEarth
rplanet
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—14/17
Newton’s Law of Gravity (3/6)
On the surface of a planet:
Fgravity
Fgravity
Gm2
= m1 × 2
r
= m1 × aEarth’s surface
Acceleration caused by the Earth on any object placed on its
surface is the same: its value is 9.8 m/sec/sec.
Acceleration on the surface determines weight of
object
On Mars
2
0.11
mMars
rEarth
aMars
1
=
=
× 2
×
aEarth
mEarth
1
0.53
rMars
A114: Lecture 6—09 Feb 2007
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2
= 0.39
Astronomy 114—14/17
Newton’s Law of Gravity (4/6)
Velocity
Planet
Acceleration
Combined with Laws of
Motion: explains orbits
Kepler’s Three Laws
Resulting
trajectory
A114: Lecture 6—09 Feb 2007
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Astronomy 114—15/17
Newton’s Law of Gravity (5/6)
Newton discovered that orbiting bodies may follow
any one of a family of curves called conic sections
The ellipse is only one possibility
A114: Lecture 6—09 Feb 2007
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Astronomy 114—16/17
Newton’s Law of Gravity (6/6)
Planets obey the same laws as objects on Earth
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—17/17
Newton’s Law of Gravity (6/6)
Planets obey the same laws as objects on Earth
Kepler’s laws: explained by force of gravity
Planets orbit around the center of mass of the
Solar System
Since most of the mass is the Sun, Sun is very
close to center of mass
Third law depends on the sum of the two masses:
P2 =
A114: Lecture 6—09 Feb 2007
"
4π 2
G(m1 + m2 )
Read: Ch. 4
#
a3
Astronomy 114—17/17
Newton’s Law of Gravity (6/6)
Planets obey the same laws as objects on Earth
Kepler’s laws: explained by force of gravity
Planets orbit around the center of mass of the
Solar System
Since most of the mass is the Sun, Sun is very
close to center of mass
Third law depends on the sum of the two masses:
P2 =
"
4π 2
G(m1 + m2 )
#
a3
New types of unbound orbits — hyperbolas and
parabolas — in addition to ellipses
A114: Lecture 6—09 Feb 2007
Read: Ch. 4
Astronomy 114—17/17