Formulas

Question 1

z =

Answer 1

λ(obs)-λ(em)/λ(em)

Question 2

v(rec) =

Answer 2

H(0)d

Question 3

v(obs) =

Answer 3

H(0)d + v(pec)

Question 4

r(t) =

Answer 4

a(t) x s

Question 5

H(t) =

Answer 5

a(dot)/a

Question 6

a^3(t)p(t) =

Answer 6

a^3(t(0))p(t(0)) = p(0)

Question 7

Ω(t) =

Answer 7

p(t)/p(c)(t)

Question 8

p(dot) + ∇ . (pv(v)) = - P/c^2 ∇ . v(v)

Answer 8

where RHS is the relativistic correction
p = p(0) + U/c^2

Question 9

mass continuity

Answer 9

p(dot) + 3(p + P/c^2)H = 0

Question 10

equation of state P(p) =

Answer 10

{Kp^5/3 adiabatic case
{Kp isothermal case

Question 11

Visible stars in the Milky way p =

Answer 11

N(stars) x M(sun) / volume of Milky Way

Question 12

Keplers third law

Answer 12

GM(gal)P^2 = 4π^2a^3

Question 13

<v^2> =

Answer 13

<v(radial)^2> = 3σ^2

Question 14

v^2(rot)/R =

Answer 14

GM/R^2

where M = 4/3 π p R^2