Paraphrase a Lab Report on planets and orbits for a physics discussion

    Question description

    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.

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