Homework 1 Question 2: Daniel LeBrun


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HW5 Q1 (William Matzko)

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1.  For radial velocities, we have the relation k = 28.4 (m/s) p^-(1/3)(M_p*sin(i)) (M_s)^(-2/3), where M_p is the planet mass in Jupiter masses, and M_s is the mass of the star in solar masses. For astrometry, we have  α  = (M_p/M_s)(a)(d)^(-1), where a is the semimajor axis in AU, and d is the distance to the system in parsecs. Just to make things easier to look at, we can make some simplifying assumptions. We are already told to assume sin(i) = 1 in all instances and M_s is the mass of the Sun. We might as well further assume that our target is one Jupiter mass. Further, we know P is proportional to a ^(3/2). The two above equations then reduce to α = 0.001 (a) (d)^-1 k = 28.4 (m/s) (a)^(-1/2) We are given that astrometry is sensitive to  α = 10 micro arcseconds and above, and radial velocities are sensitive to k = 1 m/s and above. Note that only the astrometry method depends on d. We must now find when the astrometry method becomes more sensitive than the rad...
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HW 5 Q6 (William Matzko)

6. (a)Usually, the temperature on a planet decreases with altitude. However, in inversion layers, this is not the case. In an inversion layer, temperature increases with altitude. Such a thing is important in the atmosphere of exoplanets because it can give insight into what that planet's atmosphere could be composed of. These inversion layers are usually composed of molecules that absorb UV radiation, so finding these inversion layers on exoplanets is desirable if we want to try and find life on them. (b) We know that P = P_0 exp(-z/H), where P is the pressure, P_0 is the pressure at the surface level, z is the altitude above surface level and H is the scale height. We are given that, on Earth z = 8.8 km and H = 8 km. This corresponds to a pressure of ~0.333*P_0. On a modified planet, to find the z at which we have the same pressure, we first must compute the scale height. We can express the scale height equation as H = k*T/(u*m*g), where k is the Boltzmann constant, T is the te...
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Homework 2 Question 1 (William Matzko)

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[Images were embedded into the actual document when I wrote this. Here, they are just included as an attachment] How big can a planet get? Title: Evidence of an upper bound on the masses of planets and its implications for giant planet formation Author: Kevin C. Schlaufman First Author’s Institution: Department of Physics and Astronomy, Johns Hopkins University. Status: Published in the Astrophysical Journal, January 20, 2018.                Just as there is a fine line between dwarf planets and small “real” planets, there is also a fine line between high-mass planets and brown dwarfs. This paper explores the boundary of the latter. Currently, the International Astronomical Union has a limit on the upper mass of a planet; anything above about 13 Jupiter masses should be considered a brown dwarf, because at this mass the body should be able to fuse deuterium in its core. Schlaufman raises an objectio...
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