Midterm Key

Multiple Choice (1 pt each)

1 B
2 A
3 C
4 C
5 A
6 C
7 B
8 D
9 D
10 A
11 B
12 A
13 C
14 B
15 A or B (depends on B_nu vs. B_lamda)
16 A
17 D
18 D
19 B
20 B
21 D
22 B
23 B
24 C
25 E
26 C
27 D
28 B
29 accept any answer
30 C
31 A
32 C


Q33 (4 pts):
Give all points if they make the point that the orbital plane of the Moon about the Earth and the orbital plane of the Earth about the Sun are not perfectly aligned; partial credit if they get that the Moon doesn't always pass directly in front of the Sun.

Short answer: because the orbit of the Moon and the plane of the ecliptic make a 5 degree angle, and because the shadow of the Moon has finite extent.

Explanation: A solar eclipse happens only when the Moon, the Earth and the Sun are in the same plane, and aligned so that the Moon is between the Sun and the Earth, while the Earth enters Moon's shadow. Moon's orbit does not lie in the plane of the ecliptic; they intersect in two points (the nodes). The Moon completes a full orbit in about a month, and so twice per month, it crosses the plane of the ecliptic. But in order for the Solar eclipse to happen, the Moon needs to be at one of these intersection points while it is 'in front' of the Earth, towards the Sun (new Moon phase), casting shadow on the Earth. Also, for us to observe an eclipse, the shadow of the Moon must swipe right over our observation site. One can calculate that the conditions for a Solar eclipse happen about 2-5 times per year, when the shadow reaches some places on Earth's surface. For any given spot on Earth, these events are much rarer.

Q34 (4 pts):
2 points - colder stars - not enough H atoms in atmosphere excited to n=2 (which is necessary for Balmer absorption lines)
2 points - hotter stars - too many H atoms in atmosphere are ionized

Long explanation:
Spectral lines from the Balmer series are formed due to transitions from/to the second energy level in hydrogen atoms. In order for these transitions to occur with a significant rate (i.e. in order for us to see the spectral lines), the n=2 level in H atoms of a star needs to be populated. That is the first excited state, and it gets populated mostly through collisional excitations, in interaction with other atoms. Thus, the energy of the random motions of atoms/ions, measure of which is the temperature, needs to be high enough for the first excited state to get populated. Thus, there is a lower-limit on the temperature of the star where the Balmer lines appear. On the other hand, if the temperature is too high, the collisions and the photon absorption rather ionizes the atoms, or lifts their electrons to even higher energy levels, depleting the population of n=2. As a consequence, most of the H-atoms in O-type stars are ionized and there is no Balmer emission.


Essay question (10 pts):
Use your judgement to assign points.  Things to look for (they definitely don't need to hit all of these points though):

-addresses multiple wavelengths

-possible comparisons: resolution, atmosphere, detectors, size, cost, space-based vs. ground-based, special techniques (AO, interferometry), noise sources, science targets / things you can see at that wavelength

-additional limitations: computing speed, speed of data transfer from satellites, brightness of sources at different wavelengths, need better clocks & faster electronics for short wavelength interferometry

Long discussion:
-Earth's atmosphere is transparent in optical and most of radio (from near IR, out to ~10m wavelengths), and so these telescopes can be either ground-based, or space-based. For far IR, UV, x and gamma rays, balloon or satellite missions are needed.
-optical, radio, UV and IR telescopes have primary collectors which are reflective surfaces (parabolic mirrors), and the incidence angle of the EM radiation can be arbitrary, and so can the view field; in the case of x and gamma ray telescopes, we need to be more careful in the choice of the reflective material, because the radiation we want to observe is highly penetrating; as a consequence, x and gamma ray telescopes can only collect rays with large incidence angles and have very narrow view fields.
-for each one of the bands, we need to take care of the backgrounds/contamination from the sources we are not observing, in order to extract the desired signal in particular:
optical telescopes: these can be refractors and reflectors; technical difficulties in the case of reflectors are in constructing big single-piece mirror with perfectly paraboloid surface; this problem is overcome with the usage of segmented mirrors; as far as observing limitations go, the biggest problem is seeing; adaptive optics systems are used to compensate for the effects of seeing
radio telescopes: the collectors are paraboloid antennas (dishes); since the resolution of an instrument depends on the ratio of the wavelength observed and the diameter of the collecting surface, and since in radio-astronomy, we are typically dealing with wavelengths on the order of mm/cm/meters, the resolution of single dishes is rather poor, in comparison with the optical telescopes of the same size; this problem is solved using interferometry and aperture synthesis IR telescopes: these instruments observe 'heat' radiation from astronomical sources, and thus need to be cooled and kept at very low temperatures, to reduce the noise levels.