Download Chapters 5,12

Homework Chapters 5 & 12
Due: January 13, 2014
1.
ASTRON 311 Introduction to Astronomy
Prof. Menningen
p. 1/2
Name: __________________________________
Explain some of the advantages that reflecting telescopes have in comparison to refracting telescopes.
Advantages of reflecting telescopes include the fact that the light does not have to pass through
any glass, there is no chromatic abberation, they can be made larger, and their weight is easier
to support.
2.
What are the optical window and the radio window? Why isn't there an X-ray window or an ultraviolet window?
The optical window and the radio window are wavelength regions in which our atmosphere is
transparent.
There are no X-ray or ultraviolet windows because our atmosphere is not transparent in these
wavelength regions.
3.
Compare the light-gathering power of an Earth-based, 8.3 m telescope with that of the Hubble Space Telescope (HST),
which has a 2.4 m objective mirror.. What advantages does the HST have over the Earth-based telescope?
Light-gathering power is proportional to the area of the mirror or lens that collects the light.
The diameter of the Earth-based telescope mirror is 8.3 m (similar to the Subaru telescope),
which is 3.5 times larger than the HST mirror. The light-gathering power of the Earth-based
telescope, which is proportional to the square of its diameter, is 3.52 = 12 times greater than
that of the HST. The HST advantage is due to its location in space; it is not affected by the
blurring of the atmosphere nor any atmospheric absorption, and it is unaffected by light
pollution.
4.
Suppose your Newtonian reflector has an objective mirror 20 cm (8 in.) in diameter with a focal length of 2.0 m. What
magnification do you get with eyepieces whose focal lengths are (a) 9 mm, (b) 20 mm, and (c) 55 mm? What is the
telescope's diffraction-limited angular resolution when used with orange light of wavelength 600 nm?
Magnifying power equals the focal length of the mirror divided by the focal length of the
eyepiece. The telescope’s focal length is 2000 mm.
(a) A 9-mm eyepiece gives a magnification of 2000 mm/9 mm = 222.
(b) A 20-mm eyepiece gives a magnification of 2000 mm/20 mm = 100.
(c) A 55-mm eyepiece gives a magnification of 2000 mm/55 mm = 36.
The angular resolution is given by:
2.5 105  6.0 10 –7 m 

5 
, or  = 0.75 arcsec.
  2.5 10

D
 0.20 m 
5.
The mission of the Submillimeter Wave Astronomy Satellite (SWAS), launched in 1998, is to investigate interstellar
clouds within which stars form. One of the frequencies at which it observes these clouds is 557 GHz
(1 GHz = 1 gigahertz = 109 Hz), characteristic of the emission from interstellar water molecules.
(a) What is the wavelength (in meters) of this emission? In what part of the electromagnetic spectrum is this? (b) Why is
it necessary to use a satellite for these observations? (c) Suppose SWAS has an angular resolution of 4 arcminutes.
What is the diameter of its primary mirror?
(a) For a frequency of 557  109 Hz, the wavelength is
c 3.00 108 m/s
λ 
 5.39 10–4 m  0.539 mm .
v 5.57 1011 /s
This radiation is in the far infrared near the microwave region.
Homework Chapters 5 & 12
ASTRON 311 Introduction to Astronomy
Prof. Menningen
p. 2/2
5.
(continued next page)
cont’d
(b) Because this radiation is strongly absorbed by the atmosphere, a satellite is necessary
for these observations.
λ
λ
(c) From   2.5 105 , we have D  2.5 105 , where  = 4 arcmin = 240 arcsec.
D

–4
5.4 10 m
Therefore D  2.5 105
 0.56 m .
240 arcsec
6.
At the present time, the dominant energy source that powers the Sun is
a. release of gravitational energy as the Sun slowly contracts.
b. thermonuclear fusion of helium into heavier elements in the core.
c. release of energy trapped in strong magnetic fields.
d. thermonuclear fusion of hydrogen into helium in the core.
7.
How does the Sun's overall magnetic field behave?
a. The northern and southern hemispheres have opposite magnetic polarity, and this polarity reverses
every 11 years.
b. Magnetic polarity is randomly distributed over the Sun, while the strength of the magnetic field increases
and decreases with an 11-year cycle.
c. The northern and southern hemispheres have the same magnetic polarity, and this polarity reverses
every 11 years.
d. The poles of the Sun have the opposite magnetic polarity from the equator, and this polarity reverses
every 11 years.
8.
If thermonuclear fusion in the Sun were suddenly to stop, what would eventually happen to the overall radius of the
Sun? Justify your answer using ideas associated with hydrostatic equilibrium and thermal equilibrium.
The Sun would decrease in radius because gravity would no longer be balanced by internal
pressure. The cooling of the Sun caused by radiation would cause the internal pressure to drop.
9.
Describe the three regions of the Sun's interior (below the photosphere). Include references to the main physical
processes that occur in each region.
Core - temperature greater than 10 million K, density extremely high, hydrogen fusion
occurring producing energy.
Radiative zone - temperature less than 10 million K, density lower than in the core, matter is
ionized, photons transporting energy in short hops.
Convective zone - temperature less than in the radiative zone, density is low, matter is partially
neutral, warm material rising, cool matter sinking..
10. How much energy (in Joules) would be released if each of the following masses were converted entirely into their
equivalent energy: (a) a carbon atom with a mass of 2.0×10–26 kg, (b) 6.0 kilograms (about 13 lb), and (c) a planet as
massive as the Earth (6×1024 kg)?
The problem involves the straightforward use of Einstein’s equation E = mc2.
(a) E  mc2   2.0 10–26 kg  3 108 m/s   1.8 10–9 J
2
(b) E  mc 2   6.0 kg   3  108 m/s   5.4  1017 J
2
(c) E  mc 2   6 1024 kg  3 108 m/s   5.4 1041 J
2