Velocity =

(in terms of frequency and wavelength)

v = f λ (ms^-1)

(1.1)  pg 16

Velocity of light in a vacuum

C =

(in terms of frequency and wavelength)

C = f λ

(ms^-1)

(1.2) pg 16

Velocity of Light in a vacuum

C =

(value ms^-1)

C = 3 x 10⁸ ms^-1

Energy of a photon

ε =

(related to frequency)

ε = h f

(measured in joules,j, where h= planck constant)

(1.3) pg 17

Planck constant

h =

(in joule seconds)

Planck constant

h = 6.63 x 10^-34 Js

Planck constant

h =

(in electronvolts)

Planck constant

h = 4.14 x 10^-15 eV

Wien's (displacement) law

λ_peak =

(in terms of temperature)

Wien's (displacement) law

λ_peak = 2.90 x 10^-3

        T

(λ_peak in metres, T in kelvin)

(1.4) pg 22

absorption of a photon

f_fi =

(in terms of energy change of a photon)

f_fi = 1 (E_f -E_i)

   h  

 f_fi = specific frequency of electromagnetic radiation for changed energy levels

(E_f - E_i) = final - initial state of energy of a electron = ε_fi the energy of the photon [in eV]

h = Planck constant = 6.63 x 10^-34Js

(1.5) pg 25

emission of a photon

f_fi =

in terms of energy change of a photon

f_fi = 1 (E_f -E_i)

   h

 f_fi = specific frequency of electromagnetic radiation for changed energy levels

(E_f - E_i) = final - initial state of energy of a electron = ε_fi the energy of the photon [in eV]

h = Planck constant = 6.63 x 10^-34Js

(1.5) pg 26

photon energy emitted by any thermal source of temperature T (in joules)

ε ~

photon energy emitted by any thermal source of temperature T

ε ~ k T   (J)

k = Boltzmann contant =1.38 x 10^-23JK^-1

(1.6) pg 32

photon energy emitted by any thermal source of temperature T (in electronvolts)

ε ~

photon energy emitted by any thermal source of temperature T (in electronvolts)

ε ~ k T   (eV)

k = Boltzmann contant =8.61 x 10^-5 eV K^-1            

(1.6) pg 32

(1.6)

Boltzmann contant

k =

(expressed first in Joules, then in electronvolts)

Boltzmann contant

k = 1.38 x 10^-23    J K^-1

k = 8.61 x 10^-5 eV K^-1

the latter found by dividing first value by energy of electronvolt:

k  =1.38 x 10^-23      J K^-1

      1.602 x 10^-19    JeV^-1

Luminosity of the Sun

L_ʘ =

(in watts)

Luminosity of the Sun

L_ʘ = 3.84 x 10²⁶ W

Conservation of energy

E =

(in terms of mass and speed of light in a vacuum)

Conservation of energy

E = m c²

c = 3.00 x 10⁸ ms^-1

(2.1) pg 50

Distance from Earth to Sun

Astronomical Unit = AU =

(in metres)

Distance from Earth to Sun

1 AU =1.5 x 10¹¹ m

transverse velocity of a star

v_t=

(in terms of distance to the star and proper motion)

 proper motion = star's intrinsic motion

transverse velocity of a star

* v_t = d x μ (km s^-1)

d = distance to the star (km)

μ = proper motion (arcsec yr^-1)

*from equation V_t = d x sin μ since sin μ is small

(3.1) pg 87

wavelength of sound

λ =

in terms of speed of sound in air and frequency of wavelength

wavelength of sound

λ = c_s

      f

c_{s = speed of sound}

f = frequency

(3.2) pg 89

Doppler effect (sound)

radial velocity V_{r =}

in terms of speed of sound and change of frequency

(transverse velocity produces no Doppler effect)

Doppler effect (sound)

radial velocity

V_r = c_{s x (f - f’)}

               f’

c_s = speed of sound in air

f = frequency

f’ = observed frequency

(3.3) pg 89

Doppler effect (light/em spectrum)

radial velocity V_{r =}

in terms of speed of light and change of wavelength

Doppler effect (light/em spectrum)

radial velocity 

V_r = c _x  (λ' - λ)

               λ

c = speed of light in a vacuum

λ = frequency

λ' = observed wavelength

(3.4) pg 89

(Doppler Shifts)

Space Velocity

v =

(in terms of transverse and radial velocities, of roughly same order of magnitude and specify overall motion of star through space with respect to us)

(think pythagoras)

(Doppler Shifts)

Space Velocity

v = √(v_t² + v_r²)

v_t = transverse velocity

v_r = radial velocity

(3.5) pg 90

(stellar) parallax

distance to a close star

d =

measured in astronomical units

(stellar) parallax

distance to a close star

d  =   1 

        p

p is angle of parallax, measured in radians

(3.6) pg 91

(stellar) parallax

distance to a close star

d =

measured in parsecs

(stellar) parallax

distance to a close star

d  =   1 

        p

d is measured in parsecs (pc)

p is angle of parallax, measured in arcseconds (arcsecs)

 
(3.7) pg 91

definitition of

parsec

The parsec is defined as the distance, d, corresponding to a stellar parallax of 1 arcsec

since there are 206 265 arcsecs in a radian

1 pc = 206 265 AU

1 pc = 3.09 x 10¹³ km

definition

Light Year

A Light Year (ly) is the distance that electromagnetic radiation would travel in a vacuum in a year.

1 ly = 0.307 pc

≈ 9.49 x 10¹² km

star's radius

(stars with large angular diameter)

R =

in terms of angular diameter (obviously small) and distance

star's radius

(stars with large angular diameter)

R = α x d

 2

d =distance

(3.8) pg 99

Harvard Spectral Classification

(spectral class letters?)

0 B A F G K M (L)

(hot)........................................(cool)

30,000 K +................................3000 K -

power, l,  radiated by unit area of a black body

at an absolute temperate T

l =

(in terms of temperature and the Stefan-Boltzmann constant, σ)

power, l,  radiated by unit area of a black body at an absolute temperate T

l = σ T⁴

T = temperature (K)

σ = Stefan-Boltzmann constant =5.67 x 10^-8 W m^-2-4 K

Luminosity

L =

(in terms of radius, temperature and using Stefan-Boltzmann constant)

Luminosity

L = 4 Π R² σ T⁴

R = radius of star (m)

T = temperature (K)

σ = Stefan-Boltzmann constant =5.67 x 10^-8 W m^-2-4 K

(3.9) pg 106

spectral flux density

(the rate at which energy from a source crosses a unit area facing the source)

F =

(in terms of Luminosity, L, and distance, d)

spectral flux density

F =      L   

        4Πd²

L = Luminosity (watts, W)

d = distance (m)

(3.10) pg 107

Luminosity

L =

(in terms of distance to the star, d, and flux density, F)

Luminosity

L =  (4Πd² )F

L = Luminosity (Watts, W)

F = flux density (W m^-2)

d = distance (m)

(3.11) pg 107

distance to star

d =

(in terms of flux density, F, and Luminosity, L)

distance to star

[image]

   L = luminosity (W)        F = flux density (W m^-2) 

(3.12) pg 107

Luminosity of visual band of light

L_v =

(in terms of distance to the star, d, and flux density of the visual light, F_v)

Luminosity of visual band of light

L_v =  (4Πd² )F_v

 L_v = Luminosity (Watts, W)

F_v = flux density (W m^-2)

d = distance to star (m)

(3.13) pg 108

distance to star

[image]

L_v = luminosity visual band(W)

F_v = flux density visual band (W m^-2) 

(3.14) pg 108

Luminosity of Sun

L_v =

Luminosity of Sun  (pg 108)

L_v = 4.44 x 10²⁵ W

compared to total luminosity of sun

(mostly visual and IR from photosphere):

L_sun = 3.84 x 10²⁶ W     (pg 43)

difference in magnitude of two stars

m₁ - m₂ =

in terms of apparent brightness of the stars

difference in magnitude of two stars

m₁ - m₂ = -2.5 log (b₁ / b₂)

m₁ and m₂ = apparent magnitudes of the two stars

b₁ and b₂ = apparent brightness of the two stars (flux density, or any other unit as here the unit cancels)

 
(3.15) pg 110

Absolute magnitude of a star

M =

(in terms of apparent magnitude and distance)

Absolute magnitude of a star

M = m - 5 log d + 5

M = magnitude

m = apparent magnitude

d = distance (parsecs, pc)

(3.16) pg 111

magnitude of gravitational force, F,

between two celestial objects

F =

(in terms of gravitational constant, mass and distance between the two objects)

magnitude of gravitational force, F,

between two celestial objects

F = GMm

       r²

G = gravitational constant

M = mass of of one object, m = mass of other object

r = radius of relative orbit = distance between the two objects

(3.17) pg 120

orbital period, P

P =

(in terms of orbital radius (distance between the objects), Gravitational constant and the masses of the two objects)

orbital period, P

P = 2 Π  √             r³         

        √       G (M + m)  

(3.18) pg 121

orbital period, P, of an ellipse

P =

(in terms of semi-major axis (distance between the objects), Gravitational constant and the masses of the two objects)

orbital period, P, of an ellipse

P = 2 Π   √               a³         

           √          G (M + m)     

a = semimajor axis, G = Grav constant, M and m = masses

(3.19) pg 121

gravitational constant

G =

gravitational constant

G = 6.67 x 10^-11 N m² kg^-2

sum of masses

of two objects in orbit around each other

M + m =

(in terms of semimajor axis, gravitational constant and orbital period)

sum of masses

of two objects in orbit around each other

M + m = 4Π²a³

              G P²

(3.20) pg 121

ratio of two masses

in binary system

M =

m   

ratio of two masses

in binary system

M = d_m

m    d_M

M and m = masses of the objects

d_m and d_M = distances of masses from centre of mass

(3.21) pg 122

orbital speed of stars in binary system

V_M =   and       V_m = 

orbital speed of stars in binary system

V_M = 2Πd_M    V_m = 2Πd_m

        P                  P

(3.22) pg 124

ratio of velocities

of stars in binary system

V_m =

V_M    

ratio of velocities

of stars in binary system

   V_m =  d_m =  M

   V_M      d_{M      m}

(3.23) pg 124

distance between two stars

in a binary system, r

r =

(in terms of semimajor axis as well as

in terms of distances of each mass from the centre of mass)

distance between two stars

in a binary system, r

r = a = d_M + d_m

(spectroscopically,  the oscillation period, P is observable, so d_M & d_m can be individually found from this equation.  Therefore, using (3.20) and (3.23) the masses can be calculated)

(3.20) pg 124

eclipsing binary

diameter of smaller star

d_s = 2R_s =

in terms of velocity, v,  and difference between time of start of eclipse, t₁ and full eclipse, t₂ , using eclipsing binary chart

and using

distance travelled = speed x time

using distance travelled = speed x time

d_s = 2R_s = v x (t₂ - t₁)

t₁ = time of start of eclipse and t₂ = time of full eclipse, using eclipsing binary chart

(3.25) pg 124

eclipsing binary

since small star moves R_S + R_L +R_L + R_S

in time small star, S, eclipses large star, L

2R_S + 2R_L =

in terms of speed, v, and change in time between time small star emerges from eclipse, t₄ and time small star begins eclipse, t₁

eclipsing binary

2R_S + 2R_L = v x (t₄ - t₁)

t₄ = end of eclipse, t₁ = start of eclipse

(3.26) pg 124

eclipsing binary

diameter of larger star

d_L = 2R_L =

eclipsing binary

diameter of larger star

d_L = 2R_L = v x (t₄ - t₂)

(3.27) pg 124

( for use with cards #46 - 48 )

[image]

t₁ = start of partial eclipse

t₂ = start of total eclipse

t₃ = end of total eclipse

t₄ = end of partial eclipse