13: Equations

Question 1

Ratio of Δλ to λ

Answer 1

Δλ/λ = v/c, if v &laquo_space;c

Δλ = difference between the observed wavelength and emitted wavelength
λ = emitted wavelength
v = velocity if the source
c = speed of light
the double less than means ‘much less than’
the velocity of something must be much less than the speed of light to avoid relativistic effects

Question 2

Velocity = (Hubble’s constant)

Answer 2

v = H₀d
v = recessional velocity
H₀ = Hubble's constant
d = distance

Question 3

In the equation v = H₀d, what unit is velocity?

Answer 3

kms⁻¹

Question 4

In the equation v = H₀d, what unit is Hubble’s constant?

Answer 4

kms⁻¹Mpc⁻¹

Question 5

In the equation v = H₀d, what unit is distance?

Answer 5

Mpc, megaparsec

Question 6

What is 1 Mpc in m

Answer 6

3.09 * 10²²

Question 7

Relativity t =

Answer 7

t = λτ

where t = actual time (longer)
τ = expected time w/o relativity (shorter)
λ = relativistic factor (always greater than 1)

Question 8

equation with radar for working out distance to object

Answer 8

2d = ct

Question 9

break down realivistic factor t = (1)t0 / sqr(1 - v²/c²)

Answer 9

t = longer interval
t0 = proper time
v = constant velocity
t0 can also be 1

Question 10

how to calculate age of universe in years if given a value for hubbles constant of 300km s^-1 mpc^-1
mpc^-1 = 3.1 * 10^22

Answer 10

first convert that velocity into ms^-1 and divide by value of megaparsec to get hubble’s constant in seconds
then do timescale = 1 / hubbles constant to get age of universe in seconds
then divide this timescale in seconds by 3.16 * 10^7 (seconds in year) to get timescale for age of universe in years