TEACHER ANSWER KEY
Venus year is 224.7 days.
Earth's year is 365.256 days.
How many days are in 2 Venus 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 Venus and Earth.
Number of Year |
Venus' number of days |
Earth's number of days |
1 |
224.7 |
365.256 |
2 |
449.4 |
730.512 |
3 |
674.1 |
1095.8 |
4 |
898.8 |
1461.0 |
5 |
1123.5 |
1826.3 |
6 |
1348.5 |
2191.5 |
7 |
1572.9 |
2556.8 |
8 |
1797.6 |
2922.0 |
9 |
2022.3 |
3287.3 |
10 |
2247 |
3652.6 |
11 |
2471.7 |
4017.8 |
12 |
2696.4 |
4383.3 |
13 |
2921.1 |
4748.3 |
What is Venus' rate per day? ( 1 / 224 . 7 )
What is Earth's rate per day? ( 1 / 365 . 256 )
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)
((1 / 224 . 7 0 - ( 1 / 365 . 256 )) * T = 1
0.0017126 T = 1
T = 583.9169 days
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)? 5 * 583.9169 = 2919.548 days
How does this answer compare in years with the number of Earth days in the table above?
8 * 365. 256 = 2922.048 days
Therefore, Venus has 5 * 583.9169 = ___2919.585______
And Earth has 8 * 365.256 = ___2922.048____
It can be determined that the Earth lags behind by ____2.4______ days every fifth junction.
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. Determine the dates of the transit that may be viewed during your lifetime. The first few have been completed. In addition, can you determine the two transits that occurred prior to 1631? 1518 and 1526
1631 1639
1761 1769
1874 1882
2004 2012
2117 2125
2247 2255
Is there an observable pattern in the years that the transits occur? If so, describe the pattern you observe.
1761 - 1639 = 122 years
1874 - 1769 = 105 years
2247 - 2125 = 122 years , therefore by working to fill in the pattern
1882 + 122 = 2004 year of transit
2004 + 8 = 2012 year of transit and as a check:
2117 - 2012 = 105 years
In addition, there are eight years between the transit pair years.
Extensions:
The following is a table of the Mercury Transits.
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 |
There is no apparent pattern evident.
The following is a list of the years when Earth transits the Sun as viewed from Mars.
1516 |
1984 |
1595 |
2084 |
1621 |
2163 |
1700 |
2189 |
1800 |
2268 |
1879 |
2368 |
1905 |
2394 |
There is an evident pattern.
1595 - 1516 = 79 1621 - 1595 = 26 1700 - 1621 = 79 1800 - 1700 = 100
1879 - 1800 = 79 1905 - 1879 = 26 1984 - 1905 = 79 2084 -1984 = 100
2163 - 2084 = 79 2189 - 2163 = 26 2268 - 2189 = 79 2368 - 2268 = 100