GEOL1415-01: Transit of Venus - Observations of Tycho Brahe - Geology Assignment Help

Assignment Task:

TRANSIT OF VENUS1

Planetary transit occurs when a planet moves directly between a star and the earth (see figure to the right). It is one of the most popular method to detect exoplanets. During a transit the brightness of the star decreases, which can be detected using a space telescope. This drop in brightness plays a vital role in determining the orbital period and the size of the exoplanet.

For our solar system, transit occurs for inferior planets (Mercury and Venus) and played an important in determining the length of the Astronomical Unit (AAAA). 1 AU is the average distance between the earth the sun. The accepted value for 1 AU is 150∗10⁶ km or 1.50∗10⁸ km

The orbital plane of Venus is titled at angle of 3.4o, which results in transit of Venus a very rare event (less than twice a century). On the other hand, Transit of Mercury is relatively common, occurring one or twice a decade. The first recorded observation of the transit of Venus was in 1639. Since then only six transit of Venus has occurred in 1761,1769,1874,1882,2004 and 2012, while the next transit will not occur until 2117.

Using observations of Tycho Brahe, Johannes Kepler described the motion of planets around the sun. The three scientific laws are called Kepler’s Law of planetary motion and were used to determine the relative scale of orbital size of planets in terms of the distance between the sun and the earth. The average distance between the earth and the sun was set to 1AU. However, Kepler was not able to measure the absolute scale of the solar system, i.e the value of 1AU in km or miles.

In 1715, Edmund Halley was the first to propose the idea to determine the Astronomical Unit using transit of Venus. If two observers at different location on earth observed the transit of Venus simultaneously then the apparent shift in the position of Venus, also called the parallax can be calculated. If the distance between the observers is known, then for the calculated parallax the distance between Venus and Earth can be calculated. If the distance between earth and Venus is known then the distance between earth and sun can be calculated, since the distance between sun and Venus was known in AU. However, for the lab today we will use a simpler form of the formula to calculate the length of the Astronomical Unit (AA) and is given below:

Objective:
1. Using Transit of Venus images, measure the parallax angle between two locations on the earth
2. From parallax, measure the length of Astronomical Unit

Procedure:
1. Open Transit Lab → Press Esc.
2. File → Login → Ok → Ok. This will open the Transit of Venus and Mercury exercise.
3. Run → 2004 Venus Transit.
4. File → Image Database → Image Directory → Load. This will open Select Site for Data window. This window consists of Venus transit images taken from three different locations on earth.
5. Double click Learmonth, WA Australia. This will open a list in the Image Database Directory.
6. Double click on the first image list. This will open an image of the sun, while Venus may not appear on the first few images. Go through the images until Venus (a black spot, see figure below) just starts to appear on the sun.
7. Go down the list till Venus completely appears on the sun (see figure below).

8. Record data and Plot. This is done as follows:
a. Click on the Venus spot and three windows will appear. Measurement Data, Spot Position and a magnifying window (see figure below).
b. Location of Venus is given in Spot Position window, while Measurement Data window will be used to record data to a file.

d. Click Record button in Measurement Data window. This will record the data to a file which will be accessed later.
e. Double click the next image in Image Database Directory and repeat steps 8-11. For every image you must click the Venus spot and the Record button to save a new data.
f. Repeat above steps for all the images in the list.
g. Once you finished recording the data for all the images, you can access the data from File → Measurement Data → View/Edit. This will open Venus Transit Measurements window. Close the window for later use
h. You can also plot the data from Analysis → Plot/Fit Data. This will open a plot window and show the recorded data from the first location. Close these windows for later use. Do not close the main CLEA Exercise -2004 Transit of Venus window.
i. We will repeat the above steps from the second location in the list. File → Image Database → Image Directory → Load. This will open Select Site for Data window. Double click Udaipur, India. This will open a list in the Image Database Directory.
j. Repeat steps 6-16 to record data for the Venus transit from the second location. For every image you must click the Venus spot and the Record button to save a new data. All data is written to the same file and all data are plotted on the same graph.
k. We will repeat the above steps from the third location in the list. File → Image Database → Image Directory → Load. This will open Select Site for Data window. Double click Teide, Canary Islands. This will open a list in the Image Database Directory.
l. Repeat steps 6-16 to record data for the Venus transit from the third location. For every image you must click the Venus spot and the Record button to save a new data. Ignore all the images after Venus touches the edge of the sun
m. After you have finished recording your data from all the three sites, show your data and plot to your instructor.
n. Save the data file, List → Save Data → As Displayed

9. You are now ready to do analysis on your data. This is done as follows
a. Analysis → Plot/Fit Data. This will open a plot for the recorded data from the three locations.
b. View → Detail. This will zoom in to your data points and three tracks are well separated.
c. Data → Curve Fit → Quadratic. This will add a quadratic fit to your data (lines will be smoother).
d. View → Print Window. Save your plot on the computer.

10. Calculate the parallax:
a. Our next objective is to calculate the parallax. That will be the shift in the position of Venus at a given time from the three locations we identified.
b. On your plot window, Data → Select Observation Time. A slider window appears with time as display.
c. Adjust the slider such that a circle appears on all the three transit tracks. Show the time to your instructor. This is time when the transit is visible from all the three sites
d. Click Ok. This will open a window with data, which must be recorded for all the three sites, Learmonth (LLL), Udaipur (U) and Teide (TTT). Record your data in table I under time I.
e. These values correspond to parallax in fractions of solar radius

12. Repeat steps 10-11 for two different times and records your data in table I and table II under time II and time III respectively

Answer the following questions:

2. Identify the formula to calculate the length of the astronomical unit. Also, identify every term in the formula along with the units
3. From table II time I, what are values of DD_EEEEand DD_EEEE

7. Attach the graph/plot from step 9d

8. In minimum 300 words describe a conclusion for the lab.

Your conclusion should elaborate on the following points
a. What were the main objectives of the lab?
b. How was data collected and how was it analyzed?
c. What were the main results of the lab?
d. Was the lab a success or a failure and support with arguments.
e. What were the main difficulties/precautions of the lab?

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