EXTENSION WORKSHEET

Mercury year is 87.969 days.

Earth's year is 365.256 days.

1. How many days are in 2 Mercury years? How many days are in 2 Earth years? Complete the table below and make a conjecture (guess) as to which two years are close to the same number of days for Mercury and Earth.

 Number of Year Mercury's number of days Earth's number of days 1 87.969 365.256 2 175.938 730.512 3 4 5 6 7 8 9 10 11 12 13

2. What is Mercury's' rate per day?

3. What is Earth's rate per day? Howe much time will it take Mercury to overtake Earth?

(Hint: (Mercury's rate - Earth's rate) rotations per day in decimal form and use D = RT where T = time interval)

(Mercury's Rate - Earth's Rate) * T = 1

4. How does this answer compare in years with the number of Earth days in the table above?

5. It can be determined that the Earth lags behind by __________ days every fifth conjunction.

As a result, a transit (when the planet Mercury crosses across the face of the Sun) is visible from Earth.

6. The table below lists the transits for Mercury. Is there an observable pattern in the years that the transits occur? If so, describe the pattern you observe.

 1907 1957 2003 2052 1914 1960 2006 2062 1924 1970 2016 2065 1927 1973 2019 2078 1937 1986 2032 2085 1940 1993 2039 2095 1953 1999 2049 2098

7. The following is a list of Earth Transits from Mars. Is there an observable pattern evident in these transit years? If so, describe the pattern that you observe.

 1516 1984 1595 2084 1621 2163 1700 2189 1800 2268 1879 2368 1905 2394

Venus Transit Graphing Calculator Instructions

(PART ONE)

The graphing calculator can make some tedious calculations much easier through the spreadsheet capabilities of the calculator. These directions allow for some exposure to this feature.

• Enter the number of years into the calculator into list one. In order to get to the list:  When entering a data value, type the data value and press enter. For example,

This would complete the data for List 1.   The spreadsheet capabilities allow the students to complete multiple calculations in a minimal amount of time. The students can now complete their table of values based on the data displayed in the lists on the calculator.

CALCULATOR INSTRUCTIONS

(PART 2)

This option is designed to introduce the graphing calculator as a tool to uncover patterns in the data. The spreadsheet capabilities allow the students to view evident patterns or to rule out a pattern using technology.

• Enter the data values from the table into the calculator. The first column will be in List 1 and the second column will be in List 2. To enter the data;

• When entering a data value, type the data value and press ENTER. For example,

To enter the data into the calculator for List 2:

Now it is time to look for a pattern. We will look for a direct variation constant, a value that is constant between List 1 and List 2.

The constant that appears in List 3 indicates that there is a constant difference of eight years between the data values in List 1 and the data values in List 2. There is an evident pattern.

To view this constant rate of change, look at the graph:

The data points appear to be linear and have a constant difference of eight years. Notice the gap in the points. This gap is the years of the Venus Transit that will be visible in coming years. Compete the table of values to determine the years of the Transits.