Our model fit for the amplitude of all the effects, \(A_\textrm{dop}\), \(A_\textrm{ell}\), \(A_\textrm{ell}\), \(A_\textrm{ecl}\), and an overall flux adjustment term. With this information, the geometric albedo, \(A_\textrm{g}\), can be determined from
\[\label{eqn:A_ecl} A_\textrm{ecl} = A_\textrm{g} \bigg(\frac{R_\textrm{p}}{a}\bigg)^2. % Geometric albedo\]
We assume that both the planet and the star can be described as a black body, \(B_\lambda\), where \(c\) is the speed of light in vacuum, \(h\) is Planck’s constant, \(k_\textrm{B}\) is Boltzmann’s constant, and \(\lambda\) is the wavelength
\[B_\lambda(T_\textrm{B}) = \frac{2hc^2}{\lambda^{5}}\frac{1}{e^{\big(\frac{hc}{k_\textrm{B}T_\textrm{B}\lambda}\big)}-1}, % Planck function\]
the brightness temperature of the object, \(T_\textrm{p}\) for the planet, can be determined with the use of the Kepler transmission function, \(T_\textrm{K}\), and the known temperature of the star, \(T_\star\).
\[\label{eqn:A_ecl2} A_\textrm{ecl} = \bigg(\frac{R_\textrm{p}}{R_\star}\bigg)^2 \frac{\int B_{\lambda}(T_\textrm{p}) T_\textrm{K} d\lambda}{\int B_{\lambda}(T_\star) T_\textrm{K} d\lambda}. % Brightness temperature\]
We use a built-in Python minimizer, scipy.optimize.leastsq() to solve this equation for the temperature of the planet, \(T_\textrm{p}\).
The result of these calculation is shown in Table \ref{tab:results} as well as published values.