51 Pegasi Discovery of a New Planet S23

1 51 Pegasi: Discovery of a New Planet In this lab you will discover a planet orbiting another star and compare the results of the discovery with planets in our solar system. In the last few decades, astronomers have announced discoveries of thousands of planets orbiting nearby stars. These discoveries seem to finally answer the question of whether or not our solar system is unique. We should note, however, that when astronomers state that they have discovered a new planet, what they are really saying is that their data can best be interpreted as a planet orbiting a star. One cannot "prove" that these other planets exist (short of actually going there to explore); one can only state that, until the hypothesis is disproved, a planet orbiting the star best explains the observations. Only a handful of planets can actually be seen with a telescope. We can only measure indirectly the influence each one has on its parent star as the star and planet orbit their common center of mass. Since the host star pulls on the planet, causing it to orbit, by Newton’s 3 rd Law the planet pulls on the host star, making it move in a small orbit around the center of mass of the system. The planet makes the star "wobble." The wobble can be detected by analyzing the spectrum of the star and noting a Doppler shift in the spectral lines that repeats in a regular cycle. We enter this realm of discovery by working with actual data from observations of the star 51 Pegasi (51 Peg) made at the Lick Observatory in California. These data are the measurements of the Doppler shift of the wavelengths of the absorption lines seen in the spectra of 51 Peg. Table 1 lists the measured radial velocities (RV) as a function of time (recorded in days). As you can see, the radial velocities are sometimes positive and sometimes negative indicating that sometimes the star is receding from Earth (the light is redshifted) and sometimes approaching Earth (the light is blueshifted). This wobble of the star was the first indication that the star 51 Peg had an invisible companion. Plotting Procedure: Plotting Radial Velocity versus Time You will now plot the data points from the data Table1: 51 Peg Radial Velocity Data. You will use Excel to make your plot. You may want to refer back to the Excel Tutorial on Graphing to refresh your memory on how to use Excel to make a graph. We are expecting the curve to be close to a sine curve so refer to the second part of that lab. Setting up your graph: 1. Open a new blank Excel spreadsheet. 2. Enter the data from the table of data on the next page. 3. Highlight the data you are going to plot and insert a scatter plot. The curve will not be a smooth one so don’t connect the dots. 4. The title for your graph should be “51 Peg Radial Velocity vs. Day”. 5. The X axis label is “Day (day)”. 6. The Y axis label is “Radial Velocity (m/s)”. 7. Once you have your properly labeled graph, print it as a PDF. This is what you will post to the appropriate Assignment box in the lab D2L. Your graph will count for 50% of the lab grade.

2 Question: Why are there data missing? Why are there sizable gaps in the data? (Hint, some gaps are a little over 1/2 day long and these are observations from the ground.) Table 1 lists the observed radial velocities. These were obtained by measuring the Doppler shift for the absorption lines using the formula: ∆𝜆 𝜆 ൌ 𝑣 𝑐 OBSERVATIONS: TABLE 1: 51 Pegasi Radial Velocity Data Day v (m/s) Day v (m/s) Day v (m/s) Day v (m/s) 0.6 -20.2 4.7 -27.5 7.8 -31.7 10.7 56.9 0.7 -8.1 4.8 -22.7 8.6 -44.1 10.8 51 0.8 5.6 5.6 45.3 8.7 -37.1 11.7 -2.5 1.6 56.4 5.7 47.6 8.8 -35.3 11.8 -4.6 1.7 66.8 5.8 56.2 9.6 25.1 12.6 -38.5 3.6 -35.1 6.6 65.3 9.7 35.7 12.7 -48.7 3.7 -42.6 6.7 62.5 9.8 41.2 13.6 2.7 4.6 -33.5 7.7 -22.6 10.6 61.3 13.7 17.6 If we had continuous data the curve would be a smooth sine curve. Since we don’t have continuous data, the curve is not smooth and is pointy. Nonetheless, we can extract information from the plot. You will have to make estimates of the values which introduces uncertainty in your numbers. As a result, we also need to estimate what that uncertainty is.  A period is defined as one complete cycle; that is, where the radial velocities return to the same position on the curve at a later time. How many cycles did the star go through during the 14 days of observations? Number of cycles = ___________  The period is defined as how long it takes to complete one cycle. Since our plot isn’t smooth, the best way to estimate the period is to measure as many periods as possible and average them. You should be able to measure at least four periods.