Astr 345 Assignment 4: Kepler’s method to find the orbit of Mercury
Due before midnight Fri, Sep 19, 2008 (full credit), before midnight Fri Sep 26, 2008 (half credit)
Introduction: Kepler’s method to find the orbit of Mercury uses the fact that we view Mercury’s orbit at a
tangent when the planet is at its maximum elongation from the Sun. Given several maximum elongations, we
can draw several tangent lines and therefore approximate the shape of the orbit. For this exercise, you will need a
protractor and a good sharp pencil. Perform the exercise slowly and deliberately, and be as accurate as you can.
Set-up: Start by drawing a large circle, perhaps 5 cm in diameter. This circle represents the orbit of the Earth.
Choose the center of the circle as being the location of the Sun (Earth’s orbital eccentricity is only 0.016, very
close to circular). Draw a radius pointing horizontally to the right (i.e., towards “3 o’clock”). This line
represents the direction of zero heliocentric longitude.
Draw tangent lines: Table 1 has 19 measurements of the maximum elongation of Mercury, every single
occurrence in the years 1967-9. First, locate the Earth: choose a date, and move counterclockwise around the
orbit by the number of degrees given. Place a dot to indicate the Earth’s location on that date.
Second, draw the tangent line. Draw a line away from Earth in a direction clockwise (west elongation) or
counterclockwise (east elongation), by the number of degrees listed on Table 1. Be sure to use the Earth-Sun
line as the zero for this angle.
The first date is done as an example in Figure 1.
Characterize the orbit: once you have drawn all 19 tangent lines, then sketch in Mercury’s orbit. Recall that the
Sun is located at one focus. Draw in the major and minor axes. Measure the length of the semi-major axis, and
scale this length to astronomical units (the Earth-Sun distance is 1 AU). Measure the eccentricity of the orbit.
Compare your measured values with the accepted values for aand e(cite your source of information).
Determine how close you are to the accepted values:
fractional dev iation =measured −accepted
accepted .
Submit your diagram and complete calculations.
Grading:
•You can share concepts, but all work must be completely original
•Write neatly and legibly
•Line up equal signs in a straight vertical column, and never have more than one equal sign on a line
•Define all non-standard variables
•Do not skip essential lines of algebra
•Develop ideas logically from start to finish
•Include a statement at the end of each problem interpreting the result
•Label your diagrams; all plots must be computer plots
•Take pride in your work
•All assignments are out of 30 points
