Equations

Question 1

Keplers 3rd Law

Answer 1

a^3 / P^2 = G(m1 +m2) / (4*pi^2)

Question 2

Virial Thm

Answer 2

1/2 d^2 I / dt^2 = 2K + U

= 3 integral PdV + U

Question 3

Magnetic Pressure

Answer 3

P_b = B^2 / (8 Pi)

Question 4

Radiative Transfer Equation - General

Answer 4

dI_nu/dTau_nu = -I_nu + S_nu

Question 5

Planck Blackbody

Answer 5

B_nu = (2 h v^3 / c^2) * 1/(exp(h nu / k T)-1)

Question 6

Stellar Mass Conservation

Answer 6

d M / d r = 4 Pi r^2 rho

Question 7

Stellar Energy Conservation

Answer 7

d L / d r = 4 Pi r^2 rho epsilon

Question 8

Stellar HSE

Answer 8

d P / d r = - G M rho / r^2

Question 9

Stellar Radiative Energy Transp.

Answer 9

dT / dr = - 3 Kappa rho L / (4 a c T^3 4 Pi r^2)

Question 10

Lamor

Answer 10

dE / dt = 2 q^2 a^2 / (3 c^3)

Question 11

Fluid - continuity

Answer 11

drho / dt + del dot (rho u) = 0

Question 12

Fluid - momentum

Answer 12

d(pu) / dt + del dot (rho u u + P - pi) = rho g +f

Question 13

fluids - energy

Answer 13

dE / dt + del dot [u(E+P)] = -rho u dot del Phi

d(p v^2 / 2 + E) +del dot [v(p v^2 / 2 + (P + E) -
pi + F_c] = rho v Fi / m

Question 14

eqn of state

Answer 14

P = rho k T / m_bar

Question 15

Convective energy transport

Answer 15

dT/dR_ad = (1-1/Gamma)T/Pg dP/dr

Question 16

PE of sphere

Answer 16

• 3 / 5 G M^2 / R

Question 17

M of elliptical gal or glob cluster

Answer 17

M = 5 (sigma_los)^2 * R / G

Question 18

FE - a

Answer 18

a_dot^2 - 8 Pi G rho / 3 * a^2 = -kappa c^2

Question 19

FE - omega

Answer 19

H_0 ^2 (omega_0-1) = kappa * c^2

Question 20

Luminosity (T)

Answer 20

4 Pi R^2 Sigma T^4

Question 21

Diffraction Limit (Beta)

Answer 21

1.22 Lamda / D

Question 22

ISM - J to L

Answer 22

4 Pi J = L / (4 Pi d^2)

Question 23

Isothermal Slab

Answer 23

I = I0 exp(-Tau) + B(1-exp(-Tau))

Question 24

Relationship Tau and Sigma

Answer 24

Tau = sigma n d

Question 25

RJ Limit B

Answer 25

b = 2 nu^2 k T / c^2

Question 26

Weins Law

Answer 26

lamda = 2900 um K / T

Question 27

Tb

Answer 27

Tb = c^2 I / (2 k nu^2)

Question 28

Fermi momentum

Answer 28

p_f = (3 n h^3 /(8 pi))^1/3

Question 29

Fermi Pressure

Answer 29

P_f = 8 pi / 15 * (pf^5/m_e h^3) goes as n^5/3

Question 30

Photon momentum

Answer 30

p_gamma = E / c = h nu / c

Question 31

Bernoullis eqn

Answer 31

v^2/2 - G M / R + integral(P/rho) = const

Question 32

t_relax

Answer 32

t_relax = N / (6 ln(N/2)) * R / v

Question 33

kramer opacity

Answer 33

kappa = rho T^(-7/2)

Question 34

ideal gas adiabatic dT / dr

Answer 34

dT / dr_ab = 2 T / (3 rho) * d rho / d r

Question 35

ideal gas energy

Answer 35

u = 3 k T / (2 m_bar)

Question 36

ideal gas sound speed

Answer 36

C_s = ( 5 k T / 3 m_bar)^1/2

Question 37

fundamental plane

Answer 37

R I sigma = const. (approx.)

Question 38

schechter function

Answer 38

phi = phi_0 (L/L_star)^alpha exp (-L/L_star) d(L/L_star)

Question 39

sersic profile

Answer 39

I = I_e exp(-b[(R/R_e)^1/n -1])

Question 40

Cosmology Fluid Equation

Answer 40

u_dot a / a_dot = -3 (u + P)

Question 41

Cosmology acceleration eqn

Answer 41

a_dbldot / a = - (4 pi G / 3) * (rho + 3P/c^2)

Question 42

H J K J

Answer 42

``` H = F / 4 pi J = c / 4 pi * u = 1/2 (I_plus + I_minus) K = c / 4 pi * p = 1/4 (I_plus + I_minus) J = 3H (Tau + 2/3) = sigma T^4 / pi ```

Question 43

T = f(Tau)

Answer 43

T = T_eff ( 3/4(Tau + 2/3))