Introduction to Astrophysics/Laws and Formulae

Kepler's Laws

 * 1) The orbit of each planet is an ellipse which has the sun at one of its foci.
 * 2) Each planet moves in such a way that the line joining it to the sun sweeps out equal areas in equal times.
 * 3) The squares of the periods of revolution of the planets about the Sun are proportional to the cubes of their mean distance from it.

Newton's gravitational law
$$F = G\frac{m_1 m_2}{r^2}$$

Black body radiation
Wein’s displacement law(only for black bodies)

λmax = W/T

Wein’s constant(W)= 2.90 &times; 10&minus;3 m K

T= temperature of the black body

Stefan's Law
$$E = {\sigma}{T^4}$$

Apparent Magnitude
$$m = -2.5 \log_{10} I + K$$

Pogson's Formula
$$m_1 - m_2 = 2.5 \log_{10} \left(\frac{I_2}{I_1}\right)$$

Absolute Magnitude
$$m - M = 5 \log_{10} \left(\frac{d}{10}\right)$$