Introduction to Astrophysics/Laws and Formulae

Gravitation

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

$F = G\frac{m_1 m_2}{r^2}$

F =	The gravitational force between two bodies.
G =	Universal gravity constant, 6.67 x 10−11 N m2 kg−2
m1 =	The mass of the first body.
m2 =	The mass of the second body.
r =	The distance between the centres of mass of two bodies.

Black body radiation

temperature of the black body.

w = 2.90 × 10⁻³ m K

Stefan's Law

E = σT⁴

E =	Rate of energy radiated from the surface of a black body per unit area.
σ =	Stefan's constant, 5.67 × 10−8 W m−2 K−4
T =	Surface temperature of the black body.

Stellar Magnitude

Apparent Magnitude

m = − 2.5log ₁₀I + K

m =	Apparent magnitude of star.
I =	Intensity of light received.
K =	a constant

Pogson's Formula

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

m1 =	Apparent magnitude of first star.
m2 =	Apparent magnitude of second star.
I1 =	Intensity of light received from first star.
I2 =	Intensity of light received from second star.

Absolute Magnitude

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

m =	Apparent magnitude of star.
M =	Absolute magnitude of star.
d =	Distance to star in parsecs.