Download ASTRONOMY 120

Astronomy 120
HOMEWORK - Chapter 12
Our Sun: Local Star
Use a calculator whenever necessary.
For full credit, always show your work and explain how you got your answer.
Be careful about units!
Please CIRCLE or put a box around your final answer if it is numerical.
1. Zeilik Study Exercise 12.2
Which measurements must be made to find out the sun’s luminosity? Which of these is least
accurate?
2. Zeilik Study Exercise 12.7
Describe how to estimate the sun’s surface temperature from its continuous spectrum.
3. Zeilik Study Exercise 12.8
Use the concept of opacity to explain why it takes photons hundreds of thousands of years to
walk out of the sun’s core to the surface.
4. Zeilik Study Exercise 12.4
Explain the appearance of the sun’s spectrum by simple atomic processes.
5. Zeilik Study Exercise 12.5
Why do you not see helium absorption lines in the sun’s visible spectrum, even though
helium is the sun’s second most abundant element?
6. Zeilik Study Exercise 12.11
We can see spectral lines of helium from the sun’s chromosphere but not the photosphere.
Why?
7. Zeilik Study Exercise 12.6
Should the chemical composition of the sun’s core differ from that of its photosphere? Why
or why not?
8. Zeilik Study Exercise 12.9
In one sentence, describe the source of the sun’s energy. (not how it produces energy)
9. Zeilik Study Exercise 12.13
In what sense do neutrinos allow us to “see” the sun’s core directly? What have been the
results of the solar neutrino experiments to date?
10. Zeilik Study Exercise 12.12
How do we know that the photosphere marks the top of the sun’s convective zone?
11. Zeilik Study Exercise 12.15
Consider an ideal gas. Suppose you double its density and triple its temperature. By how
much will its pressure change?
12. Thanks to Copernicus, we know how to find the distances to the planets in terms of the
Earth-Sun distance (1 A.U.). Venus is 0.723 A.U. from the Sun. If we aim radar signals at
Venus and allow them to bounce off its surface and return to Earth, we receive those signals
278.12 seconds later. If light (radar) travels at 2.98  108 m s , how far away is the Sun from
the Earth in meters? How many kilometers? How many miles is that if 1 mile = 1609
.
km?
You will need to make use of the relation: d  vt , where d is distance, v is velocity and t is
time.
0.723 A.U.
Sun
Venus
Earth
1 A.U.
13. The Sun's angular diameter is 32 arc minutes, and it lies 1 A.U. away from the Earth. If we
convert arc minutes to degrees, and A.U.'s to kilometers, we can figure out the Sun's diameter
in terms of kilometers. If there are 1.496 x 108 km per A.U., what is the Sun's real diameter
in kilometers? in miles?
1 A.U.
Sun
Earth
32’
tan  
opposite
adjacent
14. Newton's second law of motion is:
F  ma
where F is the force exerted on an object which has mass m and therefore is accelerated by an
amount a.
Newton's Universal Law of Gravitation is:
F
GMm
r2
where F is the gravitational force between two masses; one large (M) and the other smaller
(m), and r is the distance between their two centers of mass.
if a is the acceleration due to gravity, then ....
F
GMm
 ma
r2
(*)
By setting these two equations equal, we can figure out the centripetal acceleration of the
Earth about the Sun, or conversely, if we know the Earth's acceleration, we can figure out
the Sun's mass.
Centripetal acceleration is a 
v2
, where v is the linear velocity
r
of an object in motion a distance r from the center.
Finally, the Earth's velocity can be found from d  vt . where d is equal to the Earth's
circumference about the Sun, and t is the period (1 year). The formula for circumference is
C  2r . So....
v
d 2r
, then

t
t
v 2 4 2 r 2 4 2 r
a

 2
r
rt 2
t
Thus, if we substitute this value of the acceleration into the above starred (*) equation for F,
we can solve for the Sun's mass (M).
a) Solve for the Sun's mass
b) Density   
mass
;
volume
4 3
r , where r is the radius of the sphere. Use your
3
value for the Sun's mass from above and the value for the Sun's radius from problem
#13, to figure out the Sun's average density.
and the volume of a sphere is V 
15. Wien's law is:
 max
2.9  10 3

meters
T
where max is the wavelength at which the most energy is emitted by an object of
temperature T in Kelvin.
a) If the Sun's surface temperature is about 5800 K, at what wavelength does it emit most of
its light?
b) what is the frequency of this light? c  f  
c) what type of light is this? (look at p. 101, Zeilik – the electromagnetic spectrum).