Equations Flashcards
(24 cards)
Parallax
p [rad] = Radius / Distance
Kepler’s third law
T^2 = 4π^2*a^3/(GM)
Redshift
z = (λ_obs - λ0)/λ0 = v/c
Lorentz factor
γ = 1 + z
Doppler-Fizeau Effect
D = (δλ/λ) * (c/H0)
Hubble-Lemaître Law
v = H0 * D
Hubble constant
H0 = 70 km/s/Mpc
Angular diameter formula
ø = D_A * θ
D_A = angular diameter distance
θ = angle in radians
Flux
F = L/(4π*D^2)
F = E_rec / (A * t)
Apparent and absolute magnitude,
distance modulus
m = -2.5log(F/F0)
μ = m - M = 5log(D/10pc)
Apparent velocity (approaching cloud)
v_app = v*sinθ / (1-v/c * cosθ)
Receding cloud
v_r= v*sinθ / (1 + v/c * cosθ)
Gravitational potential energy
U = -GMm/R
Escape velocity
v_esc = sqrt(2GM/R)
Compactness
𑄺 = R_s/2R
Schwarzschild radius
R_s = 2GM/c^2 = 2.9*(M/M⊙) km
Accretion luminosity
L_acc = 𑄺ṁc^2 = GMṁ/R
Eddington luminosity
LEdd = 4π * G * M* c* mp/σ
L_Edd = 1.26 * 10^31*(M/M⊙) Watt
Collapses
Rotational properties
(Ω/Ω0) = (R0/R)^2
Conservation of magnetic flux
(B/B0) = (R0/R)^2
Lifetime of a star
τ ∝ 1/M^2
Energy from fusion
E_tot = η * m_core * c^2
η = 0.007 (efficiency of fusion of H)
m_core = 0.1M⊙
Energy & luminosity
dE/dt = L => E = L*t
Orders of magnitude
MASS
M⊙ = 2 * 10^30 kg
M⊕ = 6 * 10^24 kg
M(WD) = M⊙
M(NS) = 1.4M⊙
M(quasar) = 10^6 - 10^10 M⊙
M(microquasar) = 3-20 M⊙
RADIUS
R⊙ = 7 * 10^5 km
R⊕ = 6 367 km
R(WD) = 10^4 km
R(NS) = 10 km
LUMINOSITY
L⊙ = 3.83 * 10^26 W
L⊕ = 10^-9 L⊙
L(WD) = 10^-3 - 10^-2 L⊙
L(NS) = 10^-5 - 10^-1 L⊙
L(quasar) = 10^12 - 10^14 L⊙
Astronomical unit
Parsec
1 AU = 1.49 * 10^8 km
1 parsec = 3.26 ly = 3 * 10^13 km
