Download WEEK 4 1/30/12 Kepler`s 3 Laws The 3 rules of planetary motion

WEEK 4
1/30/12
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Kepler’s 3 Laws
○ The 3 rules of planetary motion inferred by Johannes Kepler from the data
acquired by Tycho Brahe
Kepler’s 1st Law: Planets move in elliptical orbits, with the Sun at one of the foci
o Planet’s distance from the Sun changes over time due to its
elliptical orbit
o Perihelion- when the planet is the closest to the Sun
o Aphelion- Point where planet is farthest from the Sun
§ Semi-major axis
§ Semi-minor axis
Kepler’s 2nd Law: Equal areas of the orbit are ‘swept out’ by a planet, in equal periods
of time (translation A1 and A2 have the same area and are covered in the same amount
of time (i.e. 1 month))
○ Law of Equal Areas
○ A line drawns from the Sun to a planet sweeps out equal areas in equal times as
the planet orbits the Sun
o
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o Both take the same amount of time to occur, and are of equal
areas
§ Think of triangles: either long Base and short Height, or small Base and long
Height etc.
o Planet’s speed change in their orbits depending to their
proximity to the Sun:
§ Perihelion (closer)=Faster, Aphelion (farther)=Slower
o WHY?
§ Kepler didn’t know: assumed it had something to do with being close to the
Sun (didn’t understand gravity yet—Newton)
§ Zeitgeist was that the movement of heavenly bodies had nothing to do with the
movement of worldly bodies
Kepler’s 3rd Law: Period²= Semimajor Axis³
○ Harmonic Law
○ the square of the period of a planet’s orbit, measured in
years, is equal to the cube of the semimajor axis of the
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planets orbit measured in AUs
o Semimajor axis is average distance away from sun (radius)
o Keeping the same units
§ Calibration constant (AU³) is actually 1 yr²/AU³
§ Can use any other form of distance, but we would have to adjust the
calibration unit
o Implication
§ A planet moves slower the farther from the Sun- echo from second law
These laws introduced a shift in the zeitgeist that allowed the Industrial Revolution
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Newton’s 3 Laws
Newton’s 1st Law: things in motion stay in motion at constant velocity, UNLESS a force
is applied
o Object will remain at rest until acted upon as well
o Inertia: an object wants to keep doing what it is doing, unless
acted upon by an outside force
Newton’s 2nd Law: Force= Mass x Acceleration
o Heavier objects are harder to move
Newton’s 3rd Law: Every action has an equal and opposite reaction
o Forces ALWAYS come in pairs
o If I push a car, the car is pushing back on me; moves when one
force is greater than the other.
Newton was more general than Kepler
o Newton’s laws apply to EVERYTHING, Kepler’s only to the 5 known
planets of the time
2-1
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Newton
o Studied Galileo’s notes and was able to get most of his
knowledge thanks to the groundwork of Galileo
o It was previously thought that if you wanted something to keep
moving, then you had to keep pushing it (didn’t fully understand
friction)
F= m x a
o Mass- quantity of matter in an object
§ Unit of mass is the kilogram
§ 1 kg = about 2.2 lbs (technically incorrect) comparing mass and weight
§ Weight is a force
§ Mass does not change, weight does since it is dependent upon gravity
o Acceleration
§ (Change in speed) divided by the (change in time)
§ We cannot ‘feel’ constant velocity. But we can feel acceleration
Flying in airplane vs. slamming on breaks
§ Acceleration at surface of earth is 9.8 m/s²
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Force
o Units are Newton’s (Nt or N)
§ Kg x m/s²
Newton’s Law of Universal
Gravitation
o G= (Newton x meters²)/ kg²
OR
o m³/(s² x kg²)
o G= 6.67 x 10-¹¹ Nt m²/kg²
■ G is calibrated to meters and must make sure other distances in equation
are meters as well.
Newton can explain every single motion at his time with the application of these 4 laws
o Then we discovered Mercury was slightly off of where it was
predicted to be
§ Red flag that the theory is not 100% accurate
Newton’s theories break down when we are really close to a massive object (Sun/star)
or moving really fast (close to speed of light)
2-3
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Using Newton’s law of gravitation
o Radius of earth is 6378 km from center of earth
o a= (G m1)/r²
Law of Inertia
o Tendency of objects to continue what they are doing
o Resist to a change in motion
Gravitational mass
o Quality to attract another object with mass
Newton assumed that Gravitational and Inertial Mass were equal
o He realized that they were two separate forces, and for some
unknown reason they were equivalent
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Centripetal acceleration
o Anything moving in a circular orbit must be accelerating
towards the center of the orbit
o a= v²/ r
o At any single point the orbiting body wants to shoot off, but
gravity keeps pulling on it towards the center of the object to
keep it going in a circle
§ Spinning a ball attached to a string over your head
The string is the ‘gravity’ that is pulling it towards the center. If you were to cut the string
then the ball would shoot off in a straight line in the direction that it was travelling
o Mass and radius determine if an orbiting body will remain in
orbit or exit/fall
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a= ∆v / ∆t
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Gravitational constant G= 6.67x10^-11
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F= G m1 m2
r²
Contributing Group Members: Caitlyn Daniels, Chase Duff, Oliver Davis, Silas DeLuca,
Whitney Dekle, Cole Downing, Ryan Cunningham