Download Astronomy Assignment #8 Exoplanets II

Astronomy Assignment #8 Exoplanets II
Solutions
Answer the following questions in complete sentences.
1. Go to the Exoplanet Catalog web site at http://exoplanet.eu/catalog/ and copy down the following information
that can be found above the data table
a. How many exoplanetary systems are currently known?
There are 1103 exoplanetary systems are currently known.
b. How many exoplanets are currently known?
There are 1,780 exoplanets are currently known.
c. How many multiple-planet exoplanetary systems are known?
There are 460 multiple-planet exoplanetary systems currently are known.
2. There are 950 exoplanets known with reliable measures of both the minimum mass of the exoplanet and the semimajor axis of its orbit. This data can be found in HOT TIPS under Exoplanet Catalog 01 April 2014. A graphic
summary of the properties of these 950 exoplanets is in HOT TIPS under Exoplanet Summary April 2014 (PPT
presentation). Please answer the following questions using the graphics in the Exoplanet Summary April 2014
presentation.
A. On the Mass Histogram:
a. On the histogram of masses of exoplanets, what is the most common mass range? What percentage of
exoplanets fall in this most common mass range?
The most common mass range for exoplanets with known masses and semi-major axes is between 100
MEarth and 1,000 MEarth. The 465 exoplanets that fall in that mass range comprise 49% of the 950
exoplanets with known masses and semi-major axes.
b. On the histogram of masses of exoplanets, how many planets are 1 Earth mass or less? What percentage
of exoplanets fall are1 Earth mass or less?
Of the 950 exoplanets with known masses and semi-major axes, only 4 exoplanets have masses of 1 MEarth
or less. This constitutes only 0.4% of the total.
B. On the Semi-major Axis Histogram
a. Exoplanets are most commonly found in two regions around stars. What are the two most populated
semi-major axis bins for these exoplanets?
The two most populated semi-major axis bins for exoplanets with known masses and semi-major axes is a
less than 0.1 AU and a greater than 1 AU but less than or equal to 5.0 AU.
b. What percentage of exoplanets have semi-major axes as close, or closer, than 1 AU from their central
star?
There are 592 exoplanets with semi-major axes as close, or closer, than 1 AU from their central star in the
950 exoplanets with known masses and semi-major axes. These exoplanets comprise 62% of the total.
C. On the Eccentricity Histogram
a. In our Solar System, only one planet has an eccentricity greater than .1 (Mercury, e = 0.22). So only 1
out of eight or 12.5% of our planets have eccentricities greater than 0.1. What percentage of exoplanets
have eccentricities greater than 0.1?
There are 366 exoplanets with known masses, semi-major axes and eccentricities whose eccentricity is
0.1 or less. These exoplanets comprise 47 % of the total. The percentage of exoplanets whose
eccentricity is greater than 0.1 is 53%.
b. Comparing only the eccentricities of our Solar System planets to these other exoplanets, how are the
exoplanet orbits different from the orbits of our planets?
In our solar system there is only one planet of eight (12%) with an eccentricity greater than 0.1. The
percentage of exoplanets with e greater than 0.1 is over 50%. Over half of the exoplanets orbits are
significantly non-circular.
c. One of the high eccentricity exoplanets is HD 166724 b whose semi-major axis is 3.53 AU and
eccentricity is 0.73. What is the perihelion distance of HD 166724 b from its star? Hint: Recall
e 1
rP
a
Solve the equation above for rp.
e  1
rP
a
rP
 1 e
a
rP  1  e   a

rP  1  0.73  3.53 AU
rP  0.95 AU
The perihelion distance of HD 166724 b from its star is 0.95 AU.
d. If HD 166724 b had an Earth-like planet orbiting it at 1.0 AU from the star, what might happen to it given
the answer to part c of this series of questions.
If HD 166724 b had an Earth-like planet orbiting it at 1.0 AU from the star, its orbit would be very close
to the perihelion distance of one of its other planets (assume it is of Jovian mass). This is a very unstable
situation and the assumedly smaller Earth-like planet would be either destroyed or ejected by the larger
Jovian mass planet as it swung into perihelion. Simply put, no terrestrial planets could exist in this
planetary system with a Jovian mass planet swinging in to a perihelion distance of less than 1 AU.
D. On the total cumulative number of exoplanet histogram
a. I started teaching at OCC in 1995. How many exoplanets were known at the end of that year? What
factor have the number of exoplanets increased since I started working at OCC?
In 1995 there were 5 known exoplanets. Now, in 2014 there are 950 exoplanets with known masses and
semi-major axes. This represents an increase in the number of exoplanets of a factor of 190 or 19,000%
E. On the semi-major axes versus mass scatter plot
a. It appears that exoplanets are falling into one of three regions on this plot. Describe those three regions
that exoplanets seem to be grouping in based on this scatter plot.
#2
#1
#3
The 950 exoplanets with known masses and semi-major axes.
Region
1
2
3
Mass Range, MJupiter
Between 0.2 and 4 MJupiter
Between 0.2 and 80 MJupiter
Between 0.005 and 0.1 MJupiter
Range of Semi-major axis, AU
Comments
Between .02 and 1.5 AU
Masses greater than 63 Earth masses
Between .5 and 9 AU
Masses between 1.6 and 32 Earth
Between .003 and .25 AU
masses
The regions most populated by exoplanets appear to be
1. Very close to the star with a between .02 and 1.5 AU and with planet masses greater than 63 Earth
masses. This is the location of terrestrial planets, but clearly the masses of these planets indicate that
they are Jovian planets.
2. Not so close to the star with a between .5 and 9 AU and with planet masses greater than 63 Earth
masses and up to very large masses of 80 Jupiter masses. This is region crosses the boundary
between the location of terrestrial planets and Jovian planets. Many of the planets in this region are
Jovian planets in Jovian planet locations as predicted by the Solar Nebula Theory.
3. Relatively small planets with masses less than 32 Earth masses in pretty close with a between .003
and 0.25 AU. These are could be either small Jovian planets or large terrestrial planets in terrestrial
planet locations.
4.