Comments on Homework 3

A1.	See Seeds, Fig. 6-2 where he orders the spectrum left to the right in order of increasing wavelength. Recall that c=f and, therefore, increasing frequency corresponds to decreasing wavelength.
A2.	b. E= hf but c = f and, therefore, E = hc/. Energy of photon is directly proportional to frequency, but inversely proportional to wavelength.
A3.	100 times more energy -- see A2.
A4.	Violet (or blue).
A5.	Diffraction causes a point-like object (a star) to be imaged as a fuzzy bright patch surrounded by alternate bright and dark rings with the ring brightness decreasing for larger and larger rings (see Seeds, Figure 6-13). The angular size of the fuzzy central bright patch is proportional to /D where l is the wavelength of the light and D is the diameter ( aperture) of the telescope. The smaller the fuzzy patch, the greater the ability to separate (resolve) two close objects (see Figure 6-13). Seeds defines the resolving power as the size of the patch; the smaller its size the higher the resolving power. I prefer to think of resolving power as a quantity for which 'bigger is better'. In this case, RP is proportional to D/. In light of this potential confusion between my interpretation and Seeds', I accept a or b as correct answers. The answer to A6. is not affected by this confusion
A6.	b. You can arrive at this answer either by working out D/ (or /D) for each of the four examples, or by a process of elimination.
A7.	b.
A8.	e. L = R2T4. Doubling the radius R increases L by 2x2=4 times. Doubling the temperature T increases L by 24=2x2x2x2=16 times. The two effects in combination increase L by 4x16=64 times.
A9.	a.
A10.	A binary star is made up of two stars at the same (effectively) distance from us. The blue star is hotter than the red star (BB Wien's law). We are told that they emit the same amount of energy: Lblue=Lred. Now, L=R2T4. Since Tblue > Tred, we must then have Rblue < Rred to achieve Lblue=Lred.
A11.	d.
A12.	b.
A13.	a.
A14.	d.
A15.	AO (A-zero).
A16.	a. Energy is conserved. A photon has energy. If the photon is absorbed (consumed) by an atom, the atom must assume the photon's energy.
A17.	TiO molecules -all molecules- are fragile; most are more easily split apart into atoms than most atoms will shed an electron or two. For this reason, TiO molecules form and survive in reasonable numbers only in cool stellar atmospheres.
A18.	A neutral atom of a given element has an electron cloud containing electrons equal in number to the number of protons in its central nucleus. Recall that it is the number of protons that defines the element in question. A positive ion of the same element is an atom with one or more fewer electrons than protons.
A19.	Recall that BL/d2. X is half the distance of Y. Therefore, it appears 4 times brighter.
A20.	'Identical' means the stars A and B have the same L. B is 10,000 times fainter than A. Therefore, B is more distant than A. Recalling BL/d2, we need to increase B's distance such that (dB/dA)2=10000 or dB/dA=100, or dB=100dA=35,000 LY.

Part B

NOTE: Points were deducted for answers crammed into margins and spaces between questions. I remind you that Part B questions generally require a few coherent well written sentences as answers. Such prose cannot be written in the margins and, more importantly, cannot be easily read.

B1.	a.	This calls for a description/definition of the Doppler effect.
	b.	This calls for an explanation! See Seeds Fig 7-17 but especially the left-hand column of page 140 immediately below the figure. It does not suffice to write "when the source moves toward you, the waves are bunched up and so the frequency is higher." That is not an explanation, but rather is a restatement of the effect. Why are the waves "bunched up"?
	c.	We observe a star from a moving platform, the Earth. As the Earth orbits the Sun, the relative line of sight velocity between a star and the Earth changes continuously over the course of a year. (The star may also be intrinsically variable ­ a spectroscopic binary, for example.) (A star at the pole of the ecliptic will not show an effect due to the Earth's motion ­ why?)
		In this particular example, the Earth is moving across the sightline to the star in January and July, a 6-month interval. The diagram shows how from Jan. to July it is moving away from the star (equivalent to a positive radial velocity) and from July to Dec. toward the star (equivalent to a negative radial velocity).
B2.	a.	Seeds
	b.	Note that X and Y have the same radius. - X being hotter emits more energy than Y. - X at 50,000K will appear blue. - Y at 3000K will appear red. - X emits more blue light - X also emits more red light. That is, the BLUE-looking blackbody will emit more RED light than the red-looking one. This is not a trick question nor is it a contradiction. As I explained in class, we use red and blue in two different ways.
	c.	The color-temperature connection or Wien's Law applies to blackbodies. Recall the definition of a blackbody: an object that absorbs all of the electromagentic radiation (light) incident upon it. Planets such as Mars do not satisfy this definition. Therefore, the color-temperature is inapplicable to Mars. The red regions on Mars reflect red sunlight well and other wavelengths poorly. The blue regions reflect best the blue sunlight.
B3.	a.	Seeds. Luminosity and brightness can be specified for particular wavelengths. In general, I mean both to refer to energy at all wavelengths.
	b.	Seeds ­ note PROOF was called for. A statement or explication of the law is NOT a proof. A proof in your own words is necessary to show that you understand the problem. See Classnotes 6.
	c.	See Seeds pp.379-380. However, his 'argument' (basically in the caption to Figure 19-1 is terse in the extreme). Consider a homogeneous, static, and infinte universe. Now consider the contribution from stars (galaxies) at a distance d. For simplicity assume all stars have the same luminosity L. A single star contributes B=L/d2, which will get smaller and smaller as we consider greater and greater distances. So why bother about very distant stars? A moment's reflection will show that there are more stars at diastance D than at d, where D>d. The surface area of the shell at D is greater than that at d. Now area of the spherical surface scales as distance-squared. The total brightness contribution from the shell at D is the product of the contribution from an individual star times the number of stars at that distance D, which, if the Universe is uniform etc., is proportional to the surface area of the shell. Then, for all d. In other words, whatever the distance, we get the same contribution from stars to the brightness at Earth. To get the total brightness, we have to add up an infinite number of small contributions from nearby stars to those at infinite distance, i.e., the brightness is infinite (day and night).
B4.	a.	Seeds, Table 7-1, Figure 7-9 and associated text.
	b.	Seeds, Figure 7-10 and associated text.
B5.	a.	See Seeds
	b.	1) The electrons may spontaneously jump to inner orbits. The planets do not jump into orbits closer to the Sun. 2) All the planets orbit the sun in almost the same plane -- viewed edge-on the solar system looks like a frisbee, CD disc, etc. The electrons orbit in roughly spherical clouds. 3) The planets are well-defined entities. The electrons in an atom are better considered as fuzzy indistinct objects.
B6.	a.	See A17.
	b.	Classnotes 10.
	c.	i) T=20,000K ii) 4500K

Hardy said that if you can prove two contradictory theorems then you can prove anything. He was then challenged to prove, given that 2 + 2 = 5, that McTaggart is the Pope. "We also know that 2 + 2 = 4, so that 5 = 4. Subtracting 3 we get 2 = 1. McTaggart and the Pope are two, hence McTaggart and the Pope are one.
E.H. Hardy (1877 ­ 1947), Cambridge mathematician

The world is round. Only one third of its people are asleep at any one time. The other two thirds are awake and causing mischief somewhere.
Dean Rusk (1909 - ?), Former Secretary of State

Most people tire of a lecture in ten minutes; clever people can do it in five. Sensible people never go to lectures at all.
Stephen Leacock (1869 ­ 1944)