Equations

Question 1

Space time curvature

Answer 1

Gμv = κTμv

G is space time curvature
T is matter and energy

Question 2

Weak equivalence principle

Answer 2

mI = mG

Question 3

Fractional change in proper separation

Answer 3

ΔL/L = h/2

Question 4

Metric tensor in a nearly flat space time

Answer 4

gμv = ημv + hμv

Question 5

Optimum arm length

Answer 5

Lopt = λ/4

Question 6

Physical thickness

Answer 6

dQWL = λ/4n

Question 7

Relationship between mechanical loss and coating thermal noise

Answer 7

Sx(f,T) ∝ T ɸ(f)

Question 8

Detecting light

Answer 8

Use Poynting vector

S = E x H = 1/μ0 E x B

Question 9

Michelson interferometer power

Answer 9

PAS = P0 cos^2{ 2𝜋Δ𝐿/𝜆}

Question 10

Chirp mass

Answer 10

M = {(m1m2)^3/5}/{(m1+m2)^1/5}

Question 11

Bayes theorem

Answer 11

p(θ|d,H) = {p(d|θ,H) p(θ|H)} /p(d|H)

From left to right: posterior, likelihood, pities, evidence

Question 12

Matched filter SNR

Answer 12

p = (d|h)/sqrt(h|h)

Question 13

Compactness of the source

Answer 13

R = (GM/ω^2max)^1/3

compare with Schwarschild radius

r = 2Gm/c^2

Question 14

Hubbles constant

Answer 14

v = H0d