What Equations Calculate Solar Constant and Galactic Escape Velocity?

[nobunaga84]

1)Flux from the sun that measured in the upper level of Earth atmosphere is 1370W/m^2.%This quantitiy is named the solar constant S and is equal to pai*f(sun).Calculate the pai*F(surface of the sun) with the angular radius of the sun that measured from earth.

I really don't which equation should ued to slove this question!

2)Calculate the most possible escaping velocity from our galaxy in the solar neighbourhood if the circular orbiting velocity of the sun around the galactic center is 220km/s.

I know an equation that possibly relate to this question but the problem is that equation is to determine the mass of our galaxy(the Milky Way) with
the known escaping velocity of the sun from the galaxy,the distance of sun from the center of the galaxy(8.5kpc) ,the mass of sun (m) and lastly the universal gravitational constant (G).By the way,I don't quiet understand the question.What does it mean of the escap[ing velocity from our galaxy in the solar neighbourhood?
Can anyone explain it to me?

This two question is from my tutorial work,although I had hand it to my tutor but still I don't know what is its solution.Anyway I still want to know how to solve it ,so please help me to find the solution or you can just guide me how to slove this two question.

 

[dextercioby]

1.What is "pai"??I haven't seen that acronym before.
Can u compute the Solar radius measured from Earth??Or is it the "normal" radius,the one tabulated and is about 696000Km??

2.If u have the formula,please post it and see whether u can identify & compute what the problem is asking you.
That is a misfortunate use of words.It has no logics.

Daniel.

 

[Astronuc]

I believe "pai" = pi = \pi as in the area of a circle = \pi r^2.

In question 1, it would appear that one is to calculate the solar flux at the surface of the sun.

Then one simply looks at the ratios of the areas.

The total energy emitted is the product of flux at some distance * area at that distance.

Let S = total energy emitted from Sun. The flux f(S) at sun surface = S/4 \pi {r_S}^2.

At the Earth this flux is f(E) = S/4 \pi {r_e}^2, were r_e = 1 AU or 149,597,870.691 km, or mean distance between sun and earth.

The solid angle looking from the center of a sphere is 4\pi steradians. The solid angle of some object of area, A, at distance r from the center of a sphere then just 4\pi * A / 4\pi r^2, or 4\pi * ratio of areas. From Earth the solid angle represented by the sun is 4\pi * \pi{r_S}^2 / 4\pi{r_e}^2, where r_S is radius of sun, and r_e is as above.

 

[nobunaga84]

Yes,you're right."pai" is pi.I'm not really often type all this word,that's why I made mistake.I'm sorry for that.
Thanks to astronuc , you help me a lot for solving the first question.