STUDENT WORKSHEET for _______________________

One Venus year is 224.7 days.

One Earth year is 365.256 days.

1. How many days are in 2 Venus years?
2.

3. How many days are in 2 Earth years?
4.

5. Complete the table below and make a conjecture (guess) as to which two years are close to the same number of days for Venus and Earth. Note: The days will appear at different years for Venus and Earth in the table.

 Number of Year Venus' number of days Earth's number of days 1 224.7 365.256 2 449.4 730.512 3 4 5 6 7 8 9 10 11 12 13

Next, complete the questions below to verify your conjecture.

4. What is Venus' rate per day?

5. What is Earth's rate per day?

6. What time in days will Venus overtake the Earth?

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

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

7. The answer in terms of days will be what is called the Synodic period for Venus. What is 5 * (the number of days in your answer)?

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

9. Therefore, Venus has 5 * 583.9169 = _____________

10. And Earth has 8 * 365.256 = _________________

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

As a result, a transit (when the planet Venus crosses across the face of the Sun) is visible from Earth. The transit occurs in pairs that are separated by eight years.

12. Determine the dates of the transit that may be viewed during your lifetime. In the table below, the first few have been completed. In addition, can you determine the years for the two transits that occurred prior to 1631?

____ ____

1631 1639

1761 1769

1874 1882

____ ____

2117 2125

2247 2255

13. Is there an observable pattern in the years that the transits occur? If so, describe the pattern you observe.