Friday, September 18, 2015

Homework 3

1)     0.2 arcsec = 206265 (a/5 pc)
        a = 0.000004848 pc = 0.999999059 AU
        contrast = planet's flux / star's flux (0.25*pi*totalstarflux*0.2*Rp^2/(0.5*pi*a^2)) / (totalstarflux) = 0.5*0.2*(Rp/a)^2 = 1x10^-10
        Rp = 0.000031623 AU = 4730.695 km = 0.067 RJ = 0.7425 RE

2)     0.2 arcsec = 206265 (a/5 pc)
        a = 0.000004848 pc = 0.999999059 AU

3)     Probability = Rs/a = 0.5*0.004649 AU/0.999999 AU = 0.0023 = 0.23%

4)     P = sqrt(a^3)=0.999985 years
        t = (P/pi)*((Rs+Rp)/a) = (0.999985 years/pi)*(0.5*0.004649 AU + 0.000031623 AU)/0.999999 AU 
        t = 0.0007499 years = 6.56 hours

5)     depth = (Rp/Rs)^2 = (0.000031623 AU / (0.5*0.004649 AU))^2 
        depth = 0.000185 = 0.018 % = 185 ppm
        detectable from space but probably not from the ground

6)     P = sqrt(a^3)= sqrt((0.999999 AU)^3) = 0.999985 years
        You would have to observe it for 0.999985 years to see one full orbit

7)     Planet is at quadrature, phase = 0.25 or 0.75
        time till transit = 0.25*P or 0.75*P
        time till transit = 0.24999 years or 0.749888 years = 91.06 days or 273.183 days

8)     Vp = 2*pi*Rp/P = 2*pi*4730.695 km/0.999985 years = 29728.29 km/year = 0.0009446 km/s
        Mp = Ms*Vs/Vp = 0.5*1 solarmass * 0.0005 km/s / 0.0009446 km/s = 0.264 solar mass
        Mp = 88130.86 ME = 277.33 MJ 

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