1. Plot the Positions of the Sun and Mercury
(45 points — 5 points/week penalty after deadline)
You are given a table with the positions of the Sun and Mercury on 135 dates. Plot dots to represent the position of the Sun on each of the dates, and draw a smooth curve through the dots to show the motion of the Sun along the Ecliptic. On the same graph, plot dots to represent the position of Mercury on each of the dates, and draw as smooth a curve as possible through the dots to show the motion of Mercury during the same time period. Label the dots for Mercury with the Julian Date corresponding to each dot, and the dots for the Sun with the celestial longitude that the Sun had when at each dot, rounded off to degrees and tenths of a degree. Grades are based only on the accuracy with which the dots and curves are plotted. No grade is given for the labeling.
2a. Measure the Positions of Mercury
(no grade — graded with parts 2b and 2c)
Use the corner of a piece of graph paper to measure the position of each Mercury dot, relative to the Ecliptic, and the nearest dots for the Sun. Make a table showing the measured and calculated celestial latitude and longitude of Mercury for each of the 135 dates, and use the position of the Sun on those same dates to calculate the elongation of Mercury on those same dates.
2b. Plot the Celestial Latitudes of Mercury
(15 points — 2 points per week late penalty after due date)
Plot a graph showing the measured latitudes, using the same scale as on the original graph. The grade for this part includes the grade for that part of Part 2a in which you obtained the numbers that are plotted in part 2b.
2c. Plot the Elongations of Mercury
(30 points — 4 points per week late penalty after due date)
Plot a graph showing the calculated elongations, using the same scale as on the original graph. The grade for this part includes the grade for that part of Part 2a in which you obtained the numbers that are plotted in part 2c.
3a. Use Nodal Passages to Calculate the Orbital Period of Mercury
(7 points — no late penalty)
Using the original graph of Mercury's motion, and the graph of its celestial latitude, estimate the dates of ascending and descending nodal passages. From the difference between each nodal passage and the subsequent nodal passage of the same type, calculate the orbital period of Mercury, as an average and standard deviation of ten separate values.
3b. Construct the Orbits of the Earth and Mercury
(25 points — no late penalty)
On a sheet of polar coordinate paper (for practice, you can use the Polar Coordinate Graph Paper
page, but I will provide a high-quality graph, 12 inches square, for the actual project), construct a circle to represent the orbit of the Earth, then use the positions of the Sun and the elongations of Mercury and a protractor and straight edge to graphically construct the orbit of Mercury. After obtaining 22 dots to represent the motion of Mercury during its 88 day orbital period, draw a smooth curve through the dots and correct any errors in their position.
3c. Measure the Orbit of Mercury
(13 points — no late penalty)
Perform measurements upon your orbit for Mercury (from part 3b) to estimate certain numbers, called the elements of the orbit, and to evaluate the accuracy of your results.
3x. Calculate the Eccentricity and Perihelion for the Earth
(7 points extra credit)
Use the celestial longitudes of the Sun to show that the orbit drawn for the Earth (in part 3b) represents the actual motion of the Earth.