Transcript KEPLERx

Bellwork
1. Who is credited with the revolutionary model
of a HELIOCENTRIC solar system?
A. Aristotle
B. Ptolemy
C. Galileo
D. Copernicus
2. The planets loop backwards in their orbits.
A. TRUE
B. FALSE
3. During which months is Earth closest to the
Sun?
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The story so far….
• Ancient Greeks had a GEOCENTRIC model of the solar
system with Earth in center and Sun and planets in
perfect circles.
• Ptolemy add many epicycles to explain the looping of
planets during retrograde motion.
• Galileo used a telescope to see phases of Venus,
Jupiter’s moons, rotating sunspots
• Copernicus made a HELIOCENTRIC model of the solar
system with the Sun in the center so the planets were
NOT looping backwards, Earth’s faster orbit was
‘passing’ the slower outer planets.
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http://www.classzone.com/books/earth_science/terc/content/investigations/es2603/es2603page01.cfm
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Month
Distance (AU)
January
February
March
April
May
June
July
August
September
October
November
December
0.9840
0.9888
0.9962
1.0050
1.0122
1.0163
1.0161
1.0116
1.0039
0.9954
0.9878
0.9837
Distance from the Sun in AU’s
Earth’s Distance From the Sun
1.019
1.016
1.013
1.01
1.007
1.004
1.001
0.998
0.995
0.992
0.989
0.986
0.983
0.98
Earth’s Orbit around the Sun is NOT a Perfect circle!
None of the planets orbit in perfect circles!!
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Kepler’s Model of the Solar
System
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Johannes Kepler’s (1600)
Kepler ‘inherited’ years of astronomical observation data
after the sudden death of Tycho Brahe
Mathmatician - Kelper's mathematical
skills were extraordinary.
He could not get Tycho's very careful
observations to fit Copernicus’ model.
He constructed 3 Laws about planets
orbits:
SHAPE
SPEED
TIME
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1st Law: Ellipses!
The SHAPE of the orbital paths of each planet is
an ellipse (NOT a perfect circle)
(with the Sun not exactly in the center, but at one focus)
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Eccentricity = (how flattened – not perfect
circle the orbit)
= Distance between foci / major axis
Major axis
13. Which planet’s orbit is closest to a perfect circle?
14. Which two planets have the most eccentric orbits?
15. Which planets eccentricity is closest to Earths?
Planet orbit Eccentricity
Mercury .210
Venus .006
Earth
.017
Mars
.093
Jupiter .048
Saturn .055
Uranus .047
Neptune .008
Pluto
.250
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Eccentricity of outer planets, Pluto,
comets orbits
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Object
Eccentricity:
Countdown Time
Area swept out
Distance from Sun
(same or varies)
(same or varies)
((same or varies)
Speed
(appears to be
constant or varying)
Earth
Venus
Pluto
Comet
http://highered.mcgrawhill.com/olcweb/cgi/pluginpop.cgi?it=swf::800::600::/sites/dl/free/007299181x
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2nd Law: SPEED of the planet
An imaginary line connecting the Sun to any planet
sweeps out equal areas in equal time.
Area 1
90 days
Planets vary in
their orbital
speed
and distance
Area 2
90 days
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If the orbit of the planet is NOT a perfect circle, but an ellipse,
Then is the SPEED (velocity) of the planet the same as it orbits?
Examine the figure of a planet; orbiting the Sun and fill in the blanks with the correct letter:
A
o
o
o
o
o
o
o
Focus ____
Aphelion ____
Perihelion ____
Increasing speed: ____ to ____
Decreasing speed: ____ to ____
Planet has greatest speed ____
Planet has lowest speed ______
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1. Which orbit would experience the largest change in orbital speed?
2. Which would have the smallest change in orbital speed?
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Which planet has the shortest year (orbital period)?
Which has the longest?
Why??
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Kepler’s 3rd Law:
a planet’s orbital TIME is proportional to its distance
from the sun.
In other words……the farther away the planet, the longer its ‘year’
P2 (years) = A3 (AU)
1 Astronomical Unit = The Earth-Sun Distance (93 million miles)
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P2 (years) = A3 (AU)
Object
P (year)
A (distance)
P2
A3
Mars
1.88
1.52
3.51
3.52
Jupiter
11.9
5.20
141
142
a planet’s orbital TIME is always proportional
to its distance.
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Kepler’s Third Law
Object
a (AU)
P (year)
a3
Mercury
0.387
0.241
0.058
=
0.058
Venus
0.723
0.615
0.378
=
0.378
Earth
1.00
1.00
1.00
=
1.00
Mars
1.52
1.88
3.51
Jupiter
5.20
11.9
141.
Saturn
9.54
29.5
868.
Uranus
19.2
84.0
7,080.
P2
=
=
=
=
=
Neptune
30.1
165.
27,300.
Pluto
39.5
248.
61,600. =
3.53
142.
870.
7,060.
27,200.
61,500.
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Use Kepler’s 3rd Law to find the orbital period (years) of a planet
If a planet is 5 AU’s distance from the Sun,
HOW many years is it’s orbital period?
P2 (years) = A3 (AU)
P2
= (5
P2
= 125
P
AU)3
2
= 125
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Use Kepler’s 3rd Law to find the distance of a planet
If a planet takes 5 years to orbit the Sun
(orbital period),
What distance is it from the Sun?
P2 (years) = A3 (AU)
(5)2
= AU3
25
= AU3
3
25 = AU
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