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Sketch an ellipse and label the major axis, minor
axis, and foci.
Ellipse Anatomy Review
Goal
1. Understand Kepler’s 2nd Law.
2. Begin to explore Kepler’s 3rd Law.
http://astro.unl.edu/naap/pos/animations/kepler.swf
Kepler’s Second Law
1.
2.
3.
4.
Find a partner, grab a computer.
Wait here. We will read through the
introduction as a class.
5. With your partner, work through the 10
exercises listed in the exercises tab.
(use diagrams to help if you like!) in your
notebook.
Kepler’s Third Law – The Math
Planet
P (years)
a (AU)
Mercury
0.241
0.387
Venus
0.615
0.723
Earth
1.000
1.000
Mars
1.881
1.524
Jupiter
11.862
5.203
Saturn
29.458
9.537
P2
a3
Kepler’s Third Law
Planet
P (years)
P2
a (AU)
a3
Mercury
0.241
0.387
0.0581
0.057961
Venus
0.615
0.723
0.3782
0.377933
Earth
1.000
1.000
1
1
Mars
1.881
1.524
3.5382
3.539606
Jupiter
11.862
5.203
140.71
140.8515
Saturn
29.458
9.537
867.77
867.4318
Kepler’s Third Law
P2
0.058
a3
0.058
0.378
0.378
1
1
3.538
3.539
140.71
140.85
867.77
867.43
a 3 = p2
a3 = 1
p2
a 13
p1 2
=
a 23
p2 2
a13 x p22 = a23 x p12
a13
a23
a1
a2
=
3
p12
p22
p
= 1
p2
2
( ) ( )
If Neptune lives at about 30.44 AU from the sun, what would
be its orbit period?
a1
3
= p1
2
(a ) ( p )
2
2
An asteroid orbits the sun with a mean orbital radius of 3.65 X
1011 m. One AU = 1.4957 x 1011 m. Calculate the period of
the asteroid.
a1
3
= p1
2
(a ) ( p )
2
2
The moon Io revolves around Jupiter in 0.0048 sidereal
years. Io has an mean orbital radius of 0.0028 Au’s. If
Europa (another one of Jupiter’s moons) has a period of
rotation of 0.0097 sidereal years, then how far away is
Europa from the center of Jupiter?
a1
3
= p1
2
(a ) (p )
2
2
HW
1. Vocab
–
–
–
–
–
Kepler’s Second Law
Kepler’s Third Law
Eccentricity
Period
Semi-major axis
*Don’t forget to observe the moon!
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