Transcript Lecture 5 - University of Maryland: Department of Astronomy

Lecture 5
Newton -Tides
ASTR 340
Fall 2006
Dennis Papadopoulos
ACCELERATING MOTION
Motion at constant acceleration a in meters/sec2
Start with zero velocity. Velocity after time t is v(t)=at.
The average speed during this time was vav=(0+at)/2=at/2
The distance traveled s=vavt=at2/2
Suppose you accelerate from 0 to 50 m/sec in 10 secs
The distance s will be given by
S=(1/2)(5 m/sec2)102= 250 m
The general formula if you start with initial velocity v(0) is
s=v(0)t+(1/2)at2
Conservation Principles
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•
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N1 with v0 comes directly from Aristotle’s
concept (object at rest remains at rest) by
applying Galilean Relativity: change to frame
with initial v=0 ; F=0 so object remains at rest;
change frames back and v= initial v
N3 is exactly what’s needed to make sure that
the total momentum is conserved.
So… Newton’s laws are related to the symmetry
of space and the way that different frames of
reference relate to each other.
Action=Reaction
If friction and pull balance exactly cart moves with constant
velocity otherwise it slows down or accelerates depending on
what dominates
Force and acceleration

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Forces between two bodies are equal in magnitude,
but the observed reaction --the acceleration -depends on mass
If a bowling ball and ping-pong ball are pushed apart
by spring, the bowling ball will move very little, and
the ping-pong ball will move a lot
 Forces in a collision are equal in magnitude, too
Circular or Elliptical
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Velocity, as used in Newton’s
laws, includes both a speed
and a direction. V and also F
and a are vectors.
Any change in direction, even
if the speed is constant,
requires a force

In particular, motion at
constant speed in a circle must
involve a force at all times,
since the direction is always
changing
Motion
What happens when there is
no force
NEWTON’S LAW OF
UNIVERSAL GRAVITATION
Newton’s law of Gravitation: A particle
with mass m1 will attract another
particle with mass m2 and distance r
with a force F given by
Gm1m2
F
2
r
Notes:
1.
2.
“G” is called the Gravitational constant
(G=6.6710-11 N m2 kg-2)
This is a universal attraction. Every particle
in the universe attracts every other particle!
Often dominates in astronomical settings.
Gravitational Mass
3.
4.
vs. Weight
Defines “gravitational mass”
Using calculus, it can be shown that a
spherical object with mass M (e.g. Sun,
Earth) gravitates like a particle of mass M at
the sphere’s center.
F
GMm
r2
Measuring G
Gravitational forces
Same as
if all the
mass was
at O
Total
force
zero
First Unification
in Physics
1/3600 g
First grand unification
Moon
Moon falls about 1.4 mm in one sec away from straight line
Apple falls 5 m in one sec
Earth
REM/RE=60
Inverse square law
Orbital and Escape Velocity
Vorb=7.8 km/sec
Vesc = 11 km/sec
Vesc=(2GME/RE)1/2
g ( R)  GM (r  R) / R 2
Weight ( R)  mg ( R)
g ( R)  GM (r  R) / R 2
Weight ( R)  mg ( R)
g ( R)  GM (r  R) / R 2
Weight ( R)  mg ( R)
KEPLER’S LAWS EXPLAINED

Kepler’s laws of planetary motion
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Can be derived from Newton’s laws
Just need to assume that planets are attracted to the Sun by
gravity (Newton’s breakthrough).
Full proof requires calculus (or very involved geometry)
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Planets natural state is to move in a straight line at constant
velocity
But, gravitational attraction by Sun is always making it
swerve off course
Newton’s law (1/r2) is exactly what’s needed to make this
path be a perfect ellipse – hence Kepler’s 1st law.(use
calculus)
The fact that force is always directed towards Sun gives
Kepler’s 2nd law (conservation of angular momentum)
Newton’s law gives formula for period of orbit
2
4

P2 
R3
G( M sun  M planet )
TIDES
Daily tide twice Why?
1/R2 law
Earth
Moon
Water pulled
stronger than
the earth
Earth pulled
stronger than
the water
TIDES
Twice monthly Spring Tides (unrelated to Spring) and
Twice monthly Neap Tides
Full moon – extra low tides
Earth
moon
Sun
Earth
moon
New moon
Extra high tides
TIDES
Twice monthly Neap Tides
Sun moon at right angles
Earth
Earth
First Quarter
Last quarter