Transcript Chapter 2-Kepler to Einstein

Tycho Brahe (1546-1630) best observer of his day
Made most accurate measurements of his time
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Tycho’s Observatory at Uraniborg
• He developed new instruments
and new techniques for
conducting observations.
• Kepler used his observations to
derive his laws of planetary
orbits.
• It was the precision of Brahe's
observations that enabled
Kepler to determine that the
orbits of the planet’s are ellipses
with the Sun at one focus.
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Johannes Kepler (1571-1630)
Developed three laws of planetary motion.
Was able to describe how the planets moved.
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First law: The orbits of the planets are ellipses.
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Eccentricity (e) is a number between 0 and 1 that
tells you how elliptical an orbit is.
Some sample eccentricities:
Earth’s orbit: e = 0.017 (only slightly off-circular)
Pluto’s orbit: e = 0.248 (more elliptical)
Halley’s comet: 0.967 (very elliptical)
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Kepler’s second law:
Planets sweep out equal areas in equal times
-means planets orbit at varying speeds, faster
closer to sun, slower further from sun
(Kepler didn’t know why)
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Kepler’s Third Law: Kepler found
a simple relationship between a planet’s
orbital period (P) and its average distance
from the Sun (A)
P2Planet = A3Planet
P = period of planet’s revolution in years
A = average distance of planet from sun in
A.U.
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Solar System
• note: Uranus,
Neptune & Pluto were
discovered much later
(during 1800-1900s)
with advent of more
powerful telescopes
• presence predicted
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Isaac Newton (1642 – 1727)
developed laws for physical matter
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Law of INERTIA
person moving at a constant speed
car stops but person keeps moving
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Newton’s Second Law: When forces act on a body, they change
the (speed & direction) motion of the body: acceleration, deceleration
Velocity – rate of motion (speed: 35 mph; 5 m/s) with direction
Acceleration – rate of change of motion (could be speed or direction!)
F=m*a
Gravity causes an acceleration!
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Newton’s Third Law
• For every action (force) there is an
equal and opposite reaction (force)
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Newton’s Laws explain that something must
be acting on the planets to keep them in orbit
According to the law of inertia planets should fly off in a straight line
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What determines how strong
the force of gravity is ?
Mass of object (being acted on)
Mass of object (acting on)
Distance between them!
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Newton’s Law of Universal Gravitation
Two bodies attract each other with a force that is
proportional to the mass of each body and inversely
proportional to the square of the distance between
them.
Where the gravitational constant G = 6.67 · 10-11 N m2/kg2
and r is the distance between the objects with masses m1
and m2.
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Newton’s law of gravitation for the Solar
System
m
M
r
M is the mass of the Sun
m is the mass of a planet (i.e., Earth)
r is the distance between them
Example: What if you discovered
a planet TWICE as far from the
Sun as the Earth – how would its
gravitational pull compare to
Earth’s?
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• What does it mean for an object to be in
orbit?
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Is there gravity beyond the Earth’s surface?
“weightless” : not beyond influence of gravity
• treat astronaut as any other orbiting body
• Earth’s pull is what keeps astronaut in orbit
• feels ‘weightless’ because she and spacecraft are experiencing
gravity together
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