Graded Assignment Lab Report for Discussion Answer the following questions before you participate in the discussion. Note: You will not turn in this report to your teacher. 1.  Look at the shape of Mercury’s orbit. Is it a circle? (The polar graph paper is a perfect circle.) 2.  If the shape of Mercury’s orbit is not a circle, then how would you describe the shape? Does it have a geometric name? 3.  Where is the position of the sun within the orbit? Is it at the center? If not, how would you describe the sun’s location? Answer: Mercury's orbit isn't a circle. It actually has an egg-like shape. It's geometric name would be an ellipse.  The sun's position within the orbit isn't at the center. It is located at one of the foci of the ellipse. The focus of an ellipse is a point that isn't the center but located  some distance away from the center and close to the vertex or edge of the ellipse. From it's location its closest vertex is 0.31 AU away and the farthest vertex is 0.47 AU away. 4.  How far away from the sun was Mercury at aphelion? On what day did aphelion occur? 5.  How far away from the sun was Mercury at perihelion? On what day did it occur? 6.  How many days elapsed between aphelion and perihelion? What percent of the time to complete one orbit was this? 7.  What was the average radius of Mercury in its orbit that you calculated? How does it compare to the accepted value of 0.387 AU? Calculate the percent error using the following equation. Show your work. [img width="323" height="44" src="file:///C:/Users/Spare/AppData/Local/Temp/msohtmlclip1/01/clip_image003.png" v:shapes="_x0000_i1025"> Answer: At aphelion mercury was 0.47 AU away from the sun. This happened during  35 and day 41. At perihelion the sun was 0.31AU away from the sun. This happened during days 81 and 85.  Once perihelion happens it takes  about 35 days until aphelion happens. Then again perihelion takes place 34 days after aphelion. In totals 69 days elapse between aphelion and perihelion. This is about 77.5 % of days that Mercury takes to finish one revolution. The average radius of Mercury's  orbit  that I calculated is 0.39 AU. % error =  ( | 0.39 – 0.387| / 0.387) *100  = 0.775% 8.  How do the three areas that you calculated in Step 3 compare to each other? 9.  Complete the following sentence: An imaginary line from the planet to the sun sweeps out __________ areas in __________ time intervals. 10.  The length of the arc in the wedge near the perihelion is longer than the length of the arc in the wedge near aphelion, but the time intervals are the same. What does this tell you about the velocities of the planet at different times in its orbit? Are they the same? Are they different? If the velocities are different, then when are they fastest and slowest? Answer: The three areas that I calculated based on the information provided every twenty day of the revolution. The first area was close to the aphelion and had the magnitude of 0.1 AU. The second one was close to the perihelion and it also had a magnitude of 0.1AU. The third area measured was part of the orbit found between the aphelion and the perihelion and it also measured 0.1 AU. An imaginary line from the planet to the sun sweeps out equal areas in equal time intervals. The arc length of the arc near the sun is bigger than the length of the arc far away from the sun. However the planet seems to travel those two different distances in same time intervals. This indicates that the velocity of Mercury isn't uniform through out its orbit around the sun. It seems like Mercury travels at  faster velocity when  it is around the sun. It slows down when it is far from the sun. 11.  Look in your table from Part 4 for the Mercury columns. When you compare the columns for Mercury’s p and a, are there any values that are the same? If so, which ones? 12.  Look in your table from Part 4 for the Mars columns. When you compare the columns for Mars’s p and a, are there any values that are the same? If so, which ones? 13.  What is the general relation between the orbital period of a planet and the orbital radius? Answer: Mercury  p (years) Mercury a (AU) Mars p (years) Mars a (AU) Saturn p (years) Saturn a (AU) Value 0.24 0.39 1.88 1.52 29.46 9.54 Value squared 0.06 0.15 3.5 2.3 868 91 Value cubed 0.01 0.06 6.6 3.5 25568 868 When we see the table for p and a values of Mercury some values are the same. The p value squared is equal as the a value cubed.  This also applies to Mars p and a. The value of p squared is equal to the value of a cubed. A planet's orbital periods squared are equal with a planet's orbital radius cubed. Kepler used this in his third law, saying that T^2 / r^3 = 1  so given the orbital radius a planet's period can be known. This law also holds true for other satellites that orbit planets or stars.

read character analysis for instructions Partial Rough Draft:Wed, Nov. 13, hard copy due at the beginning of class; please DOUBLE SPACEAt least 500 words (2 double-spaced pages) and no more than 750 words (3 double-spaced pages)Final Draft:Monday, December 2 by Noon, through submission to Turn It In (see instructions below)1400 words/ 5.5 pages (MINIMUM; no maximum) Typed, double-spaced11-12 point font YOU MAY NOT USE OUTSIDE SOURCES FOR THIS ESSAY.