YOUR extrasolar planet
corrected: october 12, 2012
NEW stuff added shows below in italics
For this homework, as for any assignment,
showing/documenting your work counts the vast majority of the
credit; correct answers are, of course, preferred also
Each of you has access to the answers that astronomers have
derived for your extrasolar planet, so you should be
constantly checking (at the end of each part) whether your
answers matches theirs. In all cases, however, your
homework should be completed with your answers (not the
answers that the astronomers derive).
Planets that are in non-circular orbits will show some small
differences between your calculations and the astronomers'
because they will have included effects due to orbit
eccentricity.
If there is a huge mass difference between what you derive
(based on the spectrum and luminosity class of your star) from
the first page of the buff book and what the astronomers used,
you are welcome to consult me (but not night before the
assignment is due). People who have subgiant stars
(class IV) should particularly do so.
Heavy penalties ensue if your calculated
values differ from those of the astronomers, without cause.
using ONLY the observable quantities:
period,
radial velocity curve of your planet's star,
spectral/luminosity class of the your planet's star)
IF your planet has more than one extrasolar planet,
you MUST find the
radial velocity curve for THAT particular planet.... each
planet will
have a different radial velocity curve; MAKE SURE that you
find the
correct one....
different planets are denoted by a letter following the
star name..... for example: 55 Cnc e means
that it's the 4th planet discovered chronologically around
star 55 in the constellation Cancer
1) attach a printed copy of your planet's star's radial
velocity curve with the star's name plainly visible as the
cover sheet to this assignment
2) a) Determine the vv
sin i (amplitude of the star's radial velocity curve) from
your print out (you may not use the astronomer's/catalog's
value but you MAY check to make sure yours matches theirs AS
YOU SHOULD FOR ALL OTHER PARTS OF THIS LAB..... ).... show
your work!
b) If your radial velocity curve is plotted vs. time, you
must also determine the period from your curve (and not use
the stated value on the web site)
3) Use the spectral and luminosity class of your planet's star
to determine its mass. Show work! You may NOT use
the value quoted in the catalog (although see previous
question's comment)
4) find the lower limit to your planet's mass (first in
solar masses, and then in Jupiter masses) in an organized
manner;
make sure it's clear why your value is a lower limit
(make sure that you provide some documentary evidence of how
you found this in addition to the answer, for example,
guess-and-check intermediate calculations; if you used a
graphing method on your calculator, show the graph and where
the solution is; do calculators now solve inequalities
directly.... i don't think they are there yet, but if so, give
me some evidence .....)
5) % difference between your value in #4 and the accepted
value (in one of the extrasolar planet catalogs; specify
which)
(the % should be less than 2% unless your orbit is
noticeably elliptical, in which case the difference might be
as much as 10% if extremely elliptical; if the difference is
not less than 2%, there's probably a mistake.... go find
it)
6) the planet's orbit size in au (this will NOT be JUST
a lower limit to the orbit size! make sure that you
calculations show why this is not a lower limit whereas the
mass was!!)
7) % diff of #6 compared
to extrasolar planet catalog (again, difference must be less
than 2% unless orbit is very elliptical)
8) a range for the planet's surface temperature (using a
reasonable range for your planet's albedo)
9) the
likely composition of your planet based on its formation
temperature (with complete justification! yes, the
last two questions are a review of the third week of
class.... i wonder why we're reviewing?)
reasoning by analogy will get very little credit here...
back in september, we used our solar system's planets'
formation temperatures compared to condensation
temperatures to determine the composition of the solar
system's planets;
you're doing the same thing here
be complete; don't just tell what materials will be part
of the planet (and why); tell what won't be in the planet
(and why)
10) Finally, it would be helpful if you could attach a
sheet, printed from one of the extrasolar planet catalogs,
that lists not only the information that you are allowed
to use (radial velocity curve amplitude,
spectral/luminosity class of the star, and orbit period)
but also other information (mass of star, luminosity of
star, eccentricity of orbit, etc.) if such a page
exists.
11) Also attach the proof of the equation we used in
class [by starting with Kepler's third law (special
units), the center of mass condition, and the formula
for speed in circular orbits].... it should be about 6
lines of algebra