Download The Sun and Planets Homework 9.

The Sun and Planets
Homework 9.
Spring Semester 2017
Prof Dr Ravit Helled
Due by: 13.05.2017
TURN IN YOUR SOLUTIONS NEXT WEEK IN CLASS
or
EMAIL THEM AS A PDF
Exercise 1.
Detection Methods
1. Briefly explain the radial velocity method for detecting extrasolar planets. Why
does this technique work best for detecting massive planets, and those in short period
orbits around their host star? What planetary parameters can you determine using
this technique?
2. Briefly explain the transit method for detecting extrasolar planets. What type of
planets is this technique most sensitive to? What planetary parameters can you
determine using this technique?
3. What do we mean when we say that we observed a system “edge-on” or “face-on”?
Draw a diagram to help explain your answer.
4. What additional planetary parameters can I determine by combining radial velocity
and transit measurements? What does this tell me about the planet(s)?
5. Go to http://exoplanet.eu/catalog/. How many planets have been discovered
using the radial velocity method? How many planets have been discovered using
the transit method? What are these numbers as a percentage of the total number
of known planets? You can filter the planets in the catalog by detection method
using the drop-down menu labeled Detection. For the transit method, select only
“Primary Transit.”
6. What is the significance of the “sin(i)” term (where i is the inclination of the planet’s
orbit) in radial velocity measurements? What limitation does this place on our
understanding of the planet? Can we overcome this limitation? If so, how?
Exercise 2.
Radial Velocity
In the exercise class, we showed you how to calculate a planet’s mass given its radial
velocity curve. Using the equation for conservation of momentum (Mp vp = M? v? ), we
showed that the equation for the planet’s mass can be given as
Mp =
M? v?
vp
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where M is mass, v is orbital velocity, and the subscripts ? and p indicate the host star
and planet, respectively. As we showed in class, in order to calculate the planet’s mass
from the radial velocity data, you need Kepler’s third law and the equation for orbital
velocity
P2
4π 2
=
a3
GM?
r
v=
GM?
a
(Kepler’s 3rd law)
(orbital velocity)
Recall that the radial velocity of the star, as seen from the observers perspective, is
K = v? sin(i), where i is the inclination of the system relative to the observer’s line-ofsight.
1. In the figure below is a radial velocity curve for a planet orbiting a 1.72 M star.
What is the radial velocity, K, period of the star, P? , and the semi-major axis of
the planet, ap ?
Figure 1: Radial velocity data for a planet orbiting a 1.72 M star.
2. Calculate the minimum mass of the planet.
3. Now that you know the orbital distance (i.e., semi-major axis) of the planet and its
minimum mass, what can you say about the kind of planet this is?
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