cosmology

Question 1

equation for t? (γ, t0)

Answer 1

t = γt0

where t = time of event when event is not stationary (eg, spaceship w lightclock moving past you) or “time for outside observer” and t0 = time of event when event is stationary (where you are on spaceship with lightclock watching the lightclock) or “time for observer in same inertial frame of reference”

Question 2

equation for lorentz factor (γ)? (v, c)

Answer 2

γ = 1/√(1 - [v^2/c^2])

Question 3

equation showing doppler effect (z)? (λ, f, v, c)

Answer 3

z ≈ Δλ/λ ≈ Δf/f ≈ v/c

where v = recessional velocity

Question 4

equation for recessional velocity (v) of planet/galaxy?

Answer 4

v = H0d

where H0 = hubble’s constant and d = distance from observer

Question 5

how to work out age of universe?

Answer 5

t0 = 1/H0

where t0 = time that galaxies have been receding from us

Question 6

equation for measuring distance to object using RADAR?

Answer 6

distance to object = (speed of light x total travel time)/2

Question 7

equation for relative velocity of body using RADAR?

Answer 7

[relative] velocity = Δd/(t2-t1)

Question 8

doppler shift for REFLECTED signal when v &laquo_space;c (eg, car moving past traffic camera)? (v, c, f)

Answer 8

2v/c ≈ Δf/f

(2 bc wave shifts twice, before hitting car + after hitting car when returning back to camera)

Question 9

equation for distance (d) of nearby planet/star from earth using parallax method (in degrees)? (θ)

Answer 9

d = 1 AU/tanθ

where θ = apparent angle (parallax angle) that planet moved through as planet observed from earth over course of long period of time

or if its not from earth:
d = r/tanθ in radians

where r = average distance from star at centre of solar system and the planet that the other planet/star is being observed from

Question 10

what is 1 arc-minute in degrees?

Answer 10

1 arc-minute = 1/60 of a degree

Question 11

what is 1 arcsec in degrees?

Answer 11

1 arcsec = 1/3600 of a degree

Question 12

distance of planet/star from earth using parallax angle in radians? (θ)

Answer 12

d = 1 AU/θ in radians

or if its not from earth:
d = r/θ in radians

where r = average distance from star at centre of solar system and the planet that the other planet/star is being observed from

Question 13

what is 1 parsec (pc)?

Answer 13

1 parsec = 3.09 x10^16

Question 14

equation for intensity (I)? (P, A)

Answer 14

intensity = power/cross-sectional area

Question 15

equation for intensity (I) from a point source?

Answer 15

intensity = power/4π(r^2)

Question 16

how can you measure distance (d) from earth/a planet to a point source of radiation using standard candles? (I, P)

Answer 16

I = P/4π(d^2)

where P = power or luminosity of standard candle (object w known luminosity) and I = intensity (aka brightness) received on earth/planet

Question 17

length contraction equation? (l, γ, l0) <- those are lowercase L

Answer 17

l = (1/γ)l0

where l = apparent length of moving train (frame of reference of someone standing outside train) and l0 = length of ‘stationary’ train (frame of reference when you’re on train)

Question 18

relativistic mass equation? (m, γ, m0)

Answer 18

m = γm0

where m = mass of moving object (train, ball, etc when you are stationary outside of train/are ball) and m0 = mass of ‘stationary’ object (train, ball, etc when you are on train/are ball)

Question 19

equation for wein’s law?

Answer 19

(λ max)T = 2.898 x10^-3

(basically λ max x T = constant)

where λ max = wavelength of peak power/intensity emitted by body and T = temp of body

Question 20

equation for stefan-boltzmann law?

Answer 20

L = Aσ(T^4)

L ∝ T^4

(luminosity has positive correlation with temp)