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PHY 150 - Astronomy
Homework Assignment #3
October 9, 2007
1)
Explain some of the advantages of reflecting telescopes over refracting telescopes.
Refracting telescopes have a number of serious difficulties. 1) Chromatic aberration of light
through an objective lens places the image of an object at different distances from the objective
lens for different colors. 2) The objective lens actually absorbs some of the light (completely for
some frequencies), thus restricting the light gathering power of the telescope. 3) Defects in the
objective lens serve to scatter light and blur the image. 4) Large apertures require large objective
lens which, because of their weight, sag and distort the image.
Reflecting telescopes do not have the problems mentioned above, in particular, they can be made
with very large diameters. But they do have problems of their own. 1) To reduce spherical
aberration and produce a sharp focus, the reflecting mirror must be ground to a parabolic shape.
This type of mirror only accepts parallel rays, thus, the field of view is limited. 2) Images off
axis suffer a defect called coma which affects the image off the central axis of the telescope.
2)
Why are radio telescopes so large?
All telescopes have diffraction-limited angular resolutions where the minimum resolution is
given by
θ = 2.5 × 105
λ
D
where λ is the wavelength and D is the diameter of the entrance aperture of the telescope
objective. Radio waves have much longer wavelengths than optical light; therefore, much larger
aperture are needed to minimize angular resolution.
3)
What would be the diffraction-limited resolution of a telescope with a 50-meter objective
mirror be for yellow light with a wavelength of 500 nm?
According to the formula given above, this resolution would be
−8
500 × 10−9 m
5 50 × 10
θ = 2.5 × 10
= 2.5 × 10
= 2.5 × 10−3 radians
50m
50
5
4)
If hydrogen and helium account for 98% of the mass of all the material in the universe, why
aren’t the Earth and Moon composed primarily of these two gases?
Hydrogen and helium were present when the Earth and Moon formed but were in the form of vapor.
As the temperature of the nebular surrounding the newly formed sun decreased the heavier,
refractive elements condensed out first. The gaseous hydrogen and helium in the early atmosphere
escaped with time.
What techniques are used to detect planets orbiting other stars? Why are these techniques unable
to detect planets like Earth?
There are essentially two techniques for detecting planets about other stars: 1) visual wobble of the
star, and 2) spectroscopic Doppler shift of radiation from the star. Both of these techniques work
if the planet is big enough to cause measurable wobble of the star. The Earth is relatively small
compared to the sun and causes little wobble.
5)
The inner core of the Earth is at a higher temperature than the outer core. Why, then, is the
inner core solid and the outer core molten instead of the other way around?
Seismographic data give us an indication of the chemical composition of the Earth's interior as a
function of depth. From this data we are able to calculate the density of the Earth as a function of
depth and thus the pressure as a function of depth. These data also allow us to infer the temperature
as a function of depth. The core is separated into two parts, an inner solid iron core and a molten
outer iron core. The inner core is solid because the pressures found at the center of the Earth do not
allow the iron to melt, even at the relatively high core temperatures.
6)
What techniques are used to detect planets orbiting other stars? Why are these techniques
not very effective in detecting planets like the Earth?
Planets revolving around far away stars cannot be resolved from the star by any telescope.
However, their existence can be inferred from several techniques, among them: 1) If the star is close
enough to Earth then it might be observed to optically wobble in its orbit over time,. This would
indicate a planetary companion, and 2) iIf the light from the star is observed to exhibit a timedependent Doppler shifted this too would also indicated a planetary companion.
7)
Describe the process of plate tectonics. Give specific examples of geographic features
created by plate tectonics.
Plate tectonics is the movement of large portions of the crust. These plates ride on the semi-molten
asthenosphere. The movement is caused by magma squeezing out along mid-oceanic ridges pushing
the plates apart in a process called sea-floor spreading. Where these plates collide they can cause
appreciable deformation of the plate edges. Some geographical features created by plate tectonics
are mountain ranges, submarine trenches, and volcanoes.
8)
Draw a cross-sectional picture of the Earth. Describe the different regions of the Earth and
their differences. What process led to these distinct regions?
The inner core is composed
of a solid iron-nickel
mixture. The outer coil has
much the same composition
but is a molten slush.
Outside of the core is the
mantle which is composed
of high density rock. This is
surrounded by a lowerdensity rock mantle. Near
the outer limit of the outer
mantle is a thin layer of
semi-molten rock called the
asthenosphere. On top of
this layer riders several large
crustal pieces called tectonic
plates.
9)
Africa and South America are separating at a rate of about 3 centimeters per year, as explained
in the text. Assuming that this rate has been constant, calculate when these two continents must
have been in contact. Today the two continents are 6600 km apart.
We can calculate:
1 year 100 cm 1000 meter
x
x
x 6600 km = 2.2 x10 8 years
3 cm meter kilometer
This is comparable to the value of 2 x 108 years deduced by Wegener in 1924.
10) Starry Night exercise 7-44.
Mercury - At this magnification you can clearly see craters and fault lines. I jumped ahead a few
days to get a clear picture.
Venus - You only see yellow clouds with some bands in them. The surface cannot be seen.
Earth - You can clearly see continents and water even with a partial cloud cover.
Mars - I could see the polar ice cap, some craters, but no sharp features.
Ceres - I had to work a little to find Ceres. When I did I zoomed in and was clearly able to see
craters. Of course, there is no atmosphere on this asteroid.