Homework 1 Question 2 Figures: William Matzko

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HW5 Q2, Q3, Q5 (William Matzko)

2. We know the phase amplitude is  ε = A*g*(R/r)^2, where A is the geometric albedo, R is the radius of the planet, r = a(1-e^2)/(1+ecos(f)), and g = 10^(-0.4*m). Here, m is just  m = 0.09( α/100) + 2.39( α/100)^2 - 0.65( α/100), where  α is in degrees (the 100's in the denominator are likewise in degrees). We are working with a Venus analog, so we can assume, in this part, that e = 0, so that r = a. The phase amplitude will be maximum when  α = 0. So, our maximum phase amplitude is then  ε = (0.67) (1)(6050km/108E6km)^2, where I have plugged in the geometric albedo of Venus, the radius of Venus, and Venus' semimajor axis. This yeilds  ε = 2E-9.  Now, we are to assume i = 40 degrees and w = 270 degrees. The effect of w is to orient the orbit such that we have a maximum phase angle at f = 0 . We know the relation between  α and these orbital elements: cos( α) = -sin(i)sin(w+f). Plugging in the numbers and solving for  α yields  α = 50 d...
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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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Homework 5 (Jocelyn)

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Astrometry  Estimate the semi-major axis beyond which astrometry (orbit face-on) becomes more sensitive than radial velocity searches (orbit edge-on). Exoplanet Phase Variations What is the maximum phase amplitude we would observe for the planet? What eccentricity will produce the same maximum phase amplitude as that calculated from part (a)? Exoplanet Demographics  What were two early surprising features of exoplanetary systems? Ultra short period planets and Super Earths  What correlation of planet size with occurrence have Kepler results demonstrated? The planetary radius gap is real How is the Habitable Zone around a star define? It is the region around a star which Earth like planet can possess liquid water on its surface  Stellar Parameters  For a typical star with uncertainties of 10% for both the mass and radius, what does this imply for the uncertainty in the mass and radius of the ...
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