Chapter 3 - The System Sun-Earth

Question 1

What is the sun primarily made of?

Answer 1

75% hydrogen, 23% helium and 2% other elements.

Question 2

What is the definition of luminosity?

Answer 2

It is defined as the total radiation of sun radiated into solid angle omega = 4pi.

Question 3

What order of magnitude is the luminosity of the sun? (in terms of Watt)

Answer 3

10^26.

Question 4

What is the solar constant SC?

Answer 4

The solar constant is the absorbed power per unit area in the space outside the earth atmosphere by an ideal absorber under normal incidence.

Question 5

What is the value of the solar constant averaged over one year?

Answer 5

1370 W/m^2

Question 6

What is the relationship between the solar constant and the luminosity?

Answer 6

SC = 1/(4 π r_se^2) * L

SC = solar constant
r_se = radius sun-earth
L = luminosity

Question 7

What order of magnitude is the Sun’s mass? (in terms of kg)

Answer 7

(2* ) 10^30

Question 8

What is the annual weight loss of the Sun?

Answer 8

Approx 10^17 kg, so about 10^-13 of total sun mass.

Question 9

How is the Stefan-Boltzmann law defined?

Answer 9

Radiated power of body is:

P_em = e * A * sigma * T^4

e: emissivity (0

Question 10

Calculate the effective temperature of the Sun surface.

L = 3.82 * 10^26 W
R_sun = 7*10^8 m

Answer 10

P_em = L = 4 π R_sun^2 * sigma * T_eff^4

=> T_eff = 5780K

Question 11

What is the overall reaction of the energy production in the sun?

Answer 11

4p -> 4He + 2e+ + 2v_e + 26.73MeV

e+ : positron
v_e: neutrino

Question 12

What are the two major fusion reactions in stars? How much do they contribute in our star?

Answer 12

1) Direct p-p drain (mostly everything, 98% ish)

2) CNO-cycle (1.6%)

Question 13

Describe the direct p-p drain fusion reaction that occurs in the sun.

Answer 13

Fusion of protons to deuterons:

p + p -> d + e+ + v_e

Fusion of deutrons with additional protons:

d + p -> 3He + gamma + 5.49 MeV

Then there are several tertiary reactions. Two of them are:
3He + 3He -> 4He + 2p + 12.86 MeV (86%)
3He + p -> 4He + e+ + v_e + 18.77 MeV (2*10^-5 %)

Question 14

Describe the CNO-cycle, also known as the Bethe-Woizsäcker cycle.

Answer 14

Formation of 4He from p catalyzed by heavy elements CNO:

12C + p -> 13N + gamma (unstable, quickly:)
13N -> 13C + e+ + v_e

13C + p -> 14N + gamma
14N + p -> 15O + gamma (unstable, quickly:)
15O -> 15N + e+ + v_e
15N + p -> 12C + 4He

Question 15

What does the relative importance of the p-p drain and CNO-cycle depend upon?

Answer 15

The core temperature. If our sun was a little hotter, the CNO-cycle would play a more dominant part before becoming the dominant process at even higher temperatures.

Question 16

Derive the shell model of the sun as an ideal gas.

Answer 16

See slides.

Question 17

Which picture of the energy production does the shell model give us?

Answer 17

That 90% is produced in the core, within a radius of 0.25 R_sun.

Question 18

What is the temperature of the core, according to the shell model? What about the density?

Answer 18

About 15 million K. Density of about 100 g / cm^3, which is about 70 times the average density.

Question 19

How is energy liberated in the core transported through the radiation zone? How far does the radiation zone stretch?

Answer 19

By gamma radiation. It stretches to about 0.7 R_sun.

Question 20

How is the energy transported beyond the radiation zone, and what is this zone called? How far does it stretch?

Answer 20

After 0.7 R_sun, the energy is transported by thermal convection up till the surface. This is called the convection zone.

Question 21

Where does the visible radiation emitted by the sun come from? How does the temperature change in this zone?

Answer 21

The very thin photosphere (about 200 km). It decreases (from 8000K to 4500 K).

Question 22

How is the photosphere structured? Draw a picture, and give typical values of size.

Answer 22

By convection rolls (granules). See slides.

Question 23

Which zone follows the photosphere? How thick is this zone? What does it consist of?

Answer 23

The chromosphere follows the photosphere. It is approximately 10 000 km thick. It consists of hot particles having enough energy to leave the photosphere.

Question 24

What follows outside the chromosphere? What does it consist of? What is the temperature here, and how thick is it?

Answer 24

The corona. Consists of very hot particles. Temperature ofa bout 1 million K and a thickness of 1 million km.

Question 25

What are solar winds?

Answer 25

Solar winds are particles with sufficient energy to leave the gravitational pull of the sun.

Question 26

Name some dynamic activities on the sun.

Answer 26

Eruptions, protuberances, flares, sun spots.

Question 27

What are flares?

Answer 27

Flares are short eruptions that lasts from some minutes to hours. Very energetic.

Question 28

What are sun spots?

Answer 28

(badly explained in notes, check some other source)

Question 29

What is the radius of the earth?

Answer 29

6.4 * 10^6 m.

Question 30

What is the equation for the incident power P from the sun?

Answer 30

P = (1-R) * π * R_earth^2 * SC,

where R is the reflectivity, and SC is the solar constant.

Question 31

What is the albedo, and what does it depend on?

Answer 31

The albedo is the reflectivity of earth. It depends on things such as clouds, water, snow, vegetation, desserts. The values are quite different, for example water at equator (normal incidence) contributes R = 0.05 while in the Northern hemisphere it can be as much as 0.25. Clouds and snow have values that range from 0.2-0.7.

Question 32

If we treat the Earth as a black body with emissivity e = 1, what is the equilibrium temperature of the earth?

Answer 32

(1-R) * π * R_earth^2 * SC = 4πR_earth^2 * sigma * T_E^4

T_E = -19C. This is obviously false, because the green house effect is not accounted for. (average temperature is +15C).

Question 33

How do we measure the integrated absorption due to atmospheric molecules depending on the length of path through the atmosphere?

Answer 33

By air mass, AM. AM0 is outside the atmosphere, AM1 is at the equator, AM1.5 is at Munich etc.

Question 34

How much does the energy flux of the inside of the earth contribute to the temperature?

Answer 34

Almost nothing, ≈ 0.02%.

Question 35

How long is the periodicity of high solar spot activity?

Answer 35

About 11 years.