Transit Method

EXOPLANET DISCOVERY LAB

INSTRUCTIONS

In this lab, you will be learning about transit photometry, a method commonly used to discover planets outside our solar system. Please write your answers in the boxes that are provided. You also will be asked to complete several graphs. You may either draw directly on your word document using the Draw tab in the ribbon menu of your iPad Word app, or print, complete your assignment by hand, and scan your document for submission.

INTRODUCTION

Exoplanets are planets found outside our solar system orbiting stars other than our sun. The Kepler space observatory was launched by NASA in 2009 to aid in the discovery of exoplanets. More specifically, the Kepler Mission is designed to find near-Earth size planets that reside within a star’s Goldilocks zone. The ultimate goal is to identify exoplanets that are potentially habitable—though, Kepler cannot detect whether an exoplanet is actually inhabited.

Kepler fulfills this mission by searching for planetary transits. Let’s consider an example to understand the concept of transiting. Imagine you are looking into the beam of a brightly lit flashlight. Now, imagine that a small bug flies between you and the flashlight. The beam will be dimmer, perhaps imperceptibly, to your eyes. Scientists can measure the change in the brightness of light due to the transit of the bug. Similarly, when a planet passes in front of a star as viewed from Earth, the event is called a planetary transit (see Figure 1). When such transits occur, the star’s brightness also dims.

Figure 1. Like the change brightness given from the flashlight in our example, scientists can also measure the change in brightness given from a star during a planetary transit. To give you a better idea of what this looks like, consider the image above of the 2012 Venus transit across the Sun. The small dots show Venus’s path as it passed between the Earth and the Sun. For observers on Earth, the sun’s brightness measurably dipped on that day. Credit: NASA/SDO

The changes in brightness are graphed on a light curve, where time is graphed on the x-axis and brightness is on the y-axis. Before the transit, the brightness is measured as 100%; meaning the observer sees the star giving off its normal, maximum amount of light. However, once the transit begins, the brightness decreases. This continues until the planet passes, and the brightness reverts to its maximum (see Figure 2). View a NASA animation showing the construction of a light curve in real time.

Figure 2. Light curve of a transiting star. In reality, light curves do not look quite so smooth. Click here to see the first light curve captured for an exoplanet.

Light curves are rich in information. For example, scientists can figure out how close a planet is to its star based on its transit time. Johannes Kepler’s laws of planetary motion state that distant planets, those with large orbits, move more slowly about their sun than those that are close. So, a slower transit indicates the planet is further from its star. The mass of the star can also be derived based on the magnitude of the dip in the brightness curve. Taken together, distance and mass point to whether the exoplanet of the right size and distance to reside within the Goldilocks zone, meaning it could potentially harbor life. Repeated transits are identified as candidate exoplanets for further investigation. As of August 2017, the Kepler space observatory has identified 2,337 confirmed exoplanets and an additional 4,496 candidate exoplanets. Those that are confirmed, are of near-Earth size, and lie within their star’s Goldilocks zone dwindles to just 30 planets.

HYPOTHESES

For the following questions, draw your answers on the provided graphs and explain your reasoning in the blank boxes.

1. Compared with the graph above, what will the brightness curve look like for a larger planet?

2. Explain the reasoning behind your predicted curve.

3. What will the brightness curve look like for an exoplanet that has a shorter orbital period?

4. Explain the reasoning behind your predicted curve.

RESULTS AND ANALYSIS

The following tables represent idealized data collected from a photometer, a light meter, focused on a set of stars every 4 hours over a period of 36 hours. You will use these data to calculate the % brightness and plot these data in the provided graphs. To calculate the brightness, use the initial value for comparison. Each additional reading will be divided by the initial value (the photometer reading taken at time zero). To obtain the percentage, multiply by 100. (NOTE: These data show magnitude changes in brightness much larger than would be observed. Once you’ve completed the lab, try to think about why these data may not be realistic).

So, % brightness = (measured value at each time point/initial value) x 100%

Then you will answer the questions about each graph in the subsequent boxes.

STAR 1
Time (in hours)	Measured value	% brightness
0 (Initial)	56448	(56448/56448) x 100 = 100%
4	56438	(56438/56448) x 100 = 99.98%
8	53938	(53938/56448)*100=95.55%
12	34912
16	27044
20	20976
24	29045
28	50784
32	54618
36	56438

We can use Excel to create our graphs for us! I will give you the steps to do so.

1. Copy and paste the data given the chart into Excel.

Star 1
Time (in hours)	Measured value	% brightness
0	56448
4	56438
8	53938
12	34912
16	27044
20	20976
24	29045
28	50784
32	54618
36	56438

2. In column C (the % brightness column) in cell C2, enter the brightness formula given in the example.

a. Remember the formula is: (Brightness value at each time point/Initial brightness value) * 100

b. Click on C2, then press the equal = sign, then hit the ( symbol.

c. Click on B2 to highlight the initial measured value, then click on the / sign

d. Enter $B$2, then ) * 100,

e. Your entire formula in Cell C2 should look like this:

i. =(B2/$B$2) * 100

ii. Now hit enter

iii. The value should be 100

f. Why the $ sign? It is because we don’t want Excel to do relative calculations, we want it to do an absolute calculation. In other words, we always want it to use cell B2, the initial brightness value, as the divisor (the bottom number).

g. Now you can click Fill and drag down the rest of the table to fill in the rest of the values. If you grab the small green square in the corner of C2, it will fill in our formula down the rest of the column.

h. COPY AND PASTE YOUR TABLE HERE:

i. Click on Column C then column A, then click on InsertChartsScatter with lines. It will look like dots connected by lines.

j. COPY AND PASTE YOUR GRAPH HERE:

3. Now following steps 2a-h above, do the same for starts 2-4.

a. Remember to always use the $ signs around your initial value or it won’t calculate correctly. (so it is $cell letter$cell number, EG $B$2).

b. I recommend putting each Star on a separate sheet in your excel document to make your life easier!

c. Remember to copy and paste both your table and your graph here for full credit.

STAR 2
Time (in hours)	Measured value	% brightness
0	56443
4	56468
8	56453
12	56453
16	56458
20	56453
24	56458
28	56443
32	56463
36	56448

STAR 3
Time (in hours)	Measured value	% brightness
0	56458
4	53703
8	19734
12	50819
16	56458
20	53703
24	19734
28	50819
32	56468
36	53718

STAR 4
Time (in hours)	Measured value	% brightness
0	56468
4	56468
8	3615
12	9939
16	7554
20	471
24	496
28	28491
32	56468
36	56463

DISCUSSION

5. What is the difference between the planets orbiting around stars 1 and 3? Specifically refer your results to support how you arrived at your conclusion.

6. What is the difference between the planets orbiting around stars 1 and 4? Specifically refer your results to support how you arrived at your conclusion.

7. What can you conclude about star 2? Why didn’t we observe a transit? (Hint: there is more than one possible explanation!)

8. The orientation of a planet’s orbit can also affect its light curve. Consider the following example. Compared with the upper transit, what would the light curve look like for an orbit that is shifted with respect to its viewer? You may draw both curves on the provided graph to show contrast. Be sure to either use different colors or dashes to distinguish the two lines.

9. Explain the reasoning behind your predicted curve.

______________________________________________________________________________

Adapted from:

Seth, A. & West, A. (2011, February 11). Transiting Planet Experiment. The University of Utah Department of Physics. Retrieved from http://www.physics.utah.edu/~aseth/teach/life/transitplanet.pdf