KEPLER’S SECOND LAW

QUESTIONS ABOUT KEPLER’S SECOND LAW

1-For an ellipse, what is the eccentricity? What is the smallest possible value for
eccentricity? How would you describe an ellipse that has a very small eccentricity?
2-From the information gathered from the planetary orbital eccentricity data table, would you describe the shapes of the planet’s orbits to be very round or very elongated? How did you draw this conclusion?
3-Figure 7 shows a schematic of Earth’s orbit around the Sun. When does perihelion occur for the Earth? What about aphelion? Do you think this perihelion/aphelion effect is the cause of the seasons? Why or why not?
4-Figure 8 shows a schematic of Kepler’s first law. Do you think this representation is accurate for a planet in our Solar System? If you could change this figure to be more accurate for a planetary orbit, how would you change it?
5-Where in a planet’s orbit does it experience maximum orbital velocity, at perihelion or aphelion? Where is its orbital velocity the smallest?
6-The main dividing points of the year are the two solstices (the longest day in summer and longest night in winter) and the two equinoxes (when night and day are equal). These are the starting points of summer, winter, spring and fall, and it is generally assumed that they are equally spaced.
But are they?
Spring equinox in 2003 was on March 21, while fall equinox was on September 22, 184 days later. In 2004, a leap year, spring equinox occurs March 20, and if you count the days, you will see that to get there only takes 181 days more from September 22. The two intervals are not equal!
Equinox positions are on opposite sides of the Earth’s orbit, 180° apart, yet getting through (northern) winter takes Earth 3 days less than getting through summer.
How can that be?
(Interesting note: the above asymmetry was known to the ancient Babylonians, was measured by Hipparchus around 140-130 BC, and was also quoted by Ptolemy.)
7-Halley’s Comet is a short period comet that is visible to us on Earth every 76 years. It is the only known short-period comet that is regularly visible to the naked eye from Earth, and the only naked-eye comet that might appear twice in a human lifetime (You may have witnessed Halley’s Comet if you were around in 1986)Would you describe the eccentricity of the orbit to be closer to zero or closer to one? When does Halley’s comet speed up in its orbit and when does it slow down? Would you say that Halley’s comet spends more time closer to perihelion or closer to aphelion?
8-According to Kepler’s third law, there is a relationship between the time a planet takes to revolve around the Sun and its
a. size
b. period of rotation
c. distance from the Sun
d. eccentricity
9- I’ll download below.

Sample Solution

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