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