# Homework assignment 2: Detecting planets via radial velocity variations

Items marked with Bonus! are extra-credit questions. They are not necessary to score 100 percent, but they can increase your score if you choose to do them.

1. Joe Spectrograph studies the star Gliese 33 = HD 4628. He has heard that an exoplanet has been discovered around this star, due to radial velocities which follow this ephemeris:

where

T    =  2457083.15992     (Julian Date)
P    =        5.2616      (period in days)
K    =       69           (m/s)
vsys  =   ???              (systemic velocity of the star)

1. What is the value of vsys for this star?
2. What is the mass of this star?
3. Make a graph showing the radial velocity predicted by this formula over three consecutive cycles
4. Joe uses his telescope, in Rochester, NY, to measure the spectrum of this star on the following nights: Oct 1, 2, 7, 9, 12, all in 2015. On each night, he measures the spectrum three times: at 10 PM, midnight, and 2 AM, each time with an exposure time of 10 minutes. He calibrates his spectrum against a neon-helium lamp inside the dome each time.

5. Bonus! Make a graph showing the radial velocities Joe will measure from his spectra, relative to the lamp in the dome.
6. What is the distance of this planet from its host star?
7. What is the mass of this planet?

Joe figures out that he should use standard stars to remove most of the radial velocity variations due to the Earth's rotation and orbital motion. He modifies his procedures and now produces nice tables of radial velocities which show only the change due to the star's own motion.

The following three questions are based on his observations of new objects -- NOT the same as the star in Question 1.

Hint: the periods in the questions below should all be in the range of 1 - 20 days. If you are using a tool to find the period, it is a good idea to search using a step size <= 0.01 days

1. Over a period of several years, Joe measures the radial velocity of one particular star. He sees pretty clear evidence for an exoplanet. His measurements are in the file http://spiff.rit.edu/classes/extrasol/homework/hw_4/rv_2.dat
1. What is the period of variations in this star's radial velocities?
2. Assuming that this is a Sun-like star, what is the orbital radius and mass of the planet?
3. Bonus! This is a real exoplanet. Which one?

2. Joe finds another star with RV variations. These are less obvious. See http://spiff.rit.edu/classes/extrasol/homework/hw_4/rv_3.dat
1. What is the period of variations in this star's radial velocities?
2. Assuming that this is a Sun-like star, what is the orbital radius and mass of the planet?
3. Bonus! This is a real exoplanet. Which one?

3. Bonus! Joe thinks that maybe, just maybe, there might a signal in the measurements of another star. He's not sure. http://spiff.rit.edu/classes/extrasol/homework/hw_4/rv_4.dat
1. What do you think?