Astrophysics Concepts and Equations

This set of flashcards covers key concepts and equations from astrophysics, focusing on dynamics of planetary systems.

Radial Velocity Amplitude

K \approx \left(\frac{2\pi G}{P}\right)^{1/3} \frac{mp \sin i}{(M*)^{2/3}}

Minimum Mass (m_p \sin i)

m{p, min} = mp \sin i

Center of Mass Relation

M* a* = mp ap (where M and mp are masses of the star and planet, and a and ap are their respective distances from the center of mass)

Kepler's Third Law

P^2 = \frac{4\pi^2}{G(M*+mp)} a^3

Continuous Fourier Transform

F(\omega) = \int_{-\infty}^{\infty} f(t) e^{-i\omega t} dt

Discrete Fourier Transform

Xk = \sum{n=0}^{N-1} x_n e^{-i2\pi k n / N} for k = 0, \ldots, N-1

Transit Depth / Flux Ratio (\Delta F)

\frac{\Delta F}{F} = \left(\frac{Rp}{R*}\right)^2

Chi-Squared (\chi^2)

\chi^2 = \sum \left(\frac{y i - f(xi)}{\sigma i}\right)^2

Reduced Chi-Squared (\chi^2/\nu)

\chi^2\nu = \frac{\chi^2}{\nu} = \frac{1}{N-M} \sum \left(\frac{yi - f(xi)}{\sigma_i}\right)^2

Angular Frequency (\omega^2)

\omega^2 = \frac{G(M*+mp)}{a^3}