Nicholas Copurnicus
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Wanderers (Planets)
Inferior
Nearer the Sun than the Earth
Morning Star/Evening Star
Superior
Farther from the Sun than the Earth
Loops
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Movement of Mars
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Motion of the Sun Moon
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Ptolemy’s explanation
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Glory Years
of
Astronomy
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Motion of Mars by Copurnicus
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Galileo Galilei
Outstanding scientist of his
era
Bought and built telescopes
Observed
Venus in gibbous phase
moons around Jupiter
millions of stars in the Milky
Way
spots on the Sun
craters, highlands and seas
on the Moon
etc.
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Venus by Ptolemy
Venus by Copunicus
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Tycho Brahe
Invented wonderful
observing tools
Twenty years of
observations
Hired Kepler
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The Solar system by Tycho
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Kepler’s 1st Law
Every Planet
revolves
around the
Sun in an
orbit that is
an ellipse
with the Sun
at one focus
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Kepler’s 2nd Law
A line from the
planet to the
Sun will
sweep out
equal area in
equal time
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The square of
the period of a
planet is equal
to the cube of
the semi-major
axis
Kepler’s 3rd Law
2
3
P=a
Yr
AU
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Sir Isaac Newton
Newton was a
genius whose
work in
mathematics,
theoretical
mechanics and
optics completely
revolutionized
physics
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Gravity
Every object anywhere in
the Universe attracts every
other object in the
Universe by a Force which
Mm
F=G r2
is proportional to the
product of their masses
and inversely proportional
to the distance separating
them.
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Gravity
The equation for
the intensity of
light has a similar
form to the gravity
equation so we
can use light to
demonstrate the
Inverse Square
Law.
Inverse Square Law
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Laws of Motion
Newton’s 1st Law
Newton’s 1st Law
A body at rest will
remain at rest and a
body in motion will
remain in motion in a
straight line until
acted upon by a
force.
In the absence of
a force the
velocity (V) will
not change
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Laws of Motion
Newton’s 2nd Law
The acceleration of a
body is proportional to
the force applied and
inversely proportional to
the mass of the body.
F=ma
Newton’s 2nd Law
The change of
velocity = acceleration (a) = Force /
mass
a = F/m
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Laws of Motion
Newton’s 3rd Law
For every action there is an
equal and opposite reaction
m1 v 1 = m 2 v 2
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From this law we derive Thrust which
makes possible Jet Engines and Rockets
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Orbital Mechanics
Knowing that a bullet shot
out of gun is pulled to the
ground by gravity, Newton
envisioned this experiment
on the top of the highest
mountain. From this
experiment Newton
related the motion of the
Moon to the motion of a
falling apple.
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Orbital Mechanics
An object is space has a
velocity. During a given time
the object would move from A
to B. But in the same time the
gravity from the sun causes it
to fall toward the sun the
distance from A to D. The
resulting trajectory of the
object is from A to C. If the
object is a planet in orbit we
note that the distance from C
to the Sun is just the same as
the distance A to the Sun.
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Kepler’s 3rd Law as Modified
by Newton
Newton discovered while working from ‘first
principles’ that Kepler’s 3rd Law needed to be
modified. Leaving out constants…
2
(M1+M2) P = a
3
Masses must be measured in Solar masses, period in
Earth years and the distance between masses in
Astronomical Units
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Tides
Many books explain
tides this way. Moon
pulls on the water on
the Moon side causing it
to bulge up a little. The
Moon pulls the center of
the Earth away from the
water on the far side
causing it bulge up a
little on that side.
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Tides (an alternate explanation)
The Earth and the Moon revolve around the common
center of mass for the system (Barycenter). The tide one
Moon side is due to gravitational force but the tide on the
other side is due to centrifugal force.
Barycenter
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End Chapter 3
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