Physics 681: Solar Physics and Instrumentation –

Lecture 2

Carsten Denker

NJIT Physics DepartmentCenter for Solar–Terrestrial

Research

September 6, 2005 Center for Solar-Terrestrial Research

Kepler’s 3rd Law(1 ) (perihelion)

(1 ) (aphelion)p

p p a aa

r a ev r L rv r v r v

r a e

2 21 1 1 and

1 2 (1 ) 2 (1 )p

p aa

v e M Mv G v G

v e a e a e

2 21 1 and

1 1p a

GM e GM ev v

a e a e

2(1 )p pL r v GMa e

2 1 21 1

2 2 2 2pp

mmM ME v G G G U

r a a

Virial Theorem

September 6, 2005 Center for Solar-Terrestrial Research

Kepler’s 3rd Law (cont.)21

2 2

M ME G v G

a r

21 2

2 1( )v G m m

r a

0 0 0

1 1 1

2 2 2

P P PdA L L LA dt dt dt P

dt

2 2 2 2 2 2 2 2 2 2

2 32 2 2

2 4 4 4

1

A a b a bP a

L L GMGMa e

Virial Theorem: For gravitationally bound systems in equilibrium, it can be shown that the total energy is always one-half of the time averaged potential energy.

September 6, 2005 Center for Solar-Terrestrial Research

Hertzsprung-Russell Diagram

http://www.physics.sjsu.edu/tomley/Planck.html

September 6, 2005 Center for Solar-Terrestrial Research

Sun – OverviewMass (kg)

1.99e+30

Mass (Earth = 1) 332,830

Equatorial radius (km) 695,000

Equatorial radius (Earth = 1) 108.97

Mean density (gm/cm3) 1.410

Rotational period (days) 25-36

Escape velocity (km/sec) 618.02

Luminosity (ergs/sec)3.827e3

3Magnitude -26.8

Mean surface temperature 6,000°C

Age (billion years) 4.5

Principal chemistry

Hydrogen Helium Oxygen Carbon Nitrogen Neon Iron Silicon Magnesium All others

92.1%7.8%

0.061%0.030%

0.0084%0.0076%0.0037%0.0031%0.0024%0.0030%

September 6, 2005 Center for Solar-Terrestrial Research

Parameters Astronomical unit [AU]: A = 149,597,870 ± 2 km (perihelion

in January: 1.471 × 1011 m; aphelion in July: 1.521 × 1011 m) Travel time: τA = 499.004782 ± 0.000006 s Velocity of light: c = 299,792,458 m s–1

Constant of gravitation: (6.67259 ± 0.00085) × 10–11 m3 kg–

1 s–2

Mass of the Sun: m = (1.9889 ± 0.0003) × 1030 kg Radius: r = (6.960 ± 0.001) × 108 m Mean density: ρ = 1.408 g cm–3

Gravitational acceleration: g = 274 m s–2

Solar constant: S = 1367 ± 3 W m–2

Luminosity: L = (3.844 ± 0.010) × 1026 W Magnitude: M = 4.74 (absolute) and m = –26.74 (apparent) Effective temperature: Teff = 5778 ± 3 K

September 6, 2005 Center for Solar-Terrestrial Research

Electromagnetic SpectrumGroup Problem:

List a few solar phenomena that you know!

Where in the solar spectrum would you try to observe these solar phenomena?

September 6, 2005 Center for Solar-Terrestrial Research

Solar Spectrum

http://www.spacewx.com/solar_spectrum.html

http://www.noao.edu/image_gallery/html/im0600.html

September 6, 2005 Center for Solar-Terrestrial Research

Planck Function (

http://scienceworld.wolfram.com/physics/PlanckLaw.html)

Wavelength form:

Frequency form:

Wien displacement law:

Rayleigh-Jeans law:

Wien law:

Stefan-Boltzman law:

2 5

/

2 /( )

1hc kT

hcB T

e

3 2

/

2 /( )

1h kT

h cB T

e

3

max

2.898 10 K m

4.965 T

hc

kT

2 2( ) 2 / for ( )B T kT c h kT

3 2 /( ) (2 / ) for ( )h kTB T h c e h kT

4 5 4 2 3 with 2 /(15 )F T k c h