51 Pegasi: The Discovery of a New Planet

Location of 51 Peg in the constellation Pegasus.

Summary
The student discovers a planet orbiting another star and compares the results of the discovery with planets in our solar system.

Materials

Graph Paper
Scientific Calculator

Background and Theory
In just the past few years, astronomers have announced discoveries of at least 250 planets orbiting nearby stars! You can examine the data up close and personal at http://exoplanet.eu 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. We cannot see these planets. 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. The planet makes the star "wobble."

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 (the light is redshifted) and sometimes approaching (the light is blueshifted) our frame of reference. This wobble of the star was the first indication that the star 51 Peg had an invisible companion.

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

Note: The days of the observations in this table are expressed in the number of days, or fraction thereof, from when the astronomer first started observing. That is, the dome of the telescope was first opened at Day = 0.

Table 1 lists the observed radial velocities. These were obtained by measuring the Doppler shift for the absorption lines using the formula:

Solving for the radial velocity v of the star:

Here, c is the speed of light,

is the laboratory wavelength of the absorption line being measured, and

is the difference between the measured wavelength of the line and the laboratory value.

Procedure

Print out the worksheet.

Plot the 32 data points on graph paper, setting up your scale and labels. Use the observed radial velocities (in m/s) versus the day of the observation.
Draw a SMOOTH CURVE (do not simply connect-the-dots) through the data. The curve is a sine curve (ask if you don't know) and thus will always reach the same maximum and minimum values and have the same "number of days" between each "peak" and "valley". You should interpolate between data where points are missing.
Thought 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.)