Astronomy And Cosmology A Level Questions

[Cecelia Seiner]

Im looking for a modern astrophysics text. I've had Barbara Ryden's book Foundations of Astrophysics recommended to me and it sounds okay, but the only review of it I've seen slagged off the problem sets as "more complex than they would initially seem, and often don't actually derive from the chapter."

I have an okay grasp of calculus and I'm currently teaching myself introductory mechanics, so I'm not a complete novice (close, but not quite). I'm definitely looking for a college text, not popsci. I'm looking for an introductory astronomy text that assumes 2 semesters of calculus and 2 semesters of introductory physics - basic mechanics and basic electricity and magnetism, essentially. So nothing too high-powered, but also not too watered down.

What about Astronomical Algorithms by Jean Meeus. It's a mathematical discussion of the formulae behind astronomical events such as solar eclipses, occultations and transits. I have read it. It is a wonderful book. The only aspect that might not be satisfactory is the modern aspect. It's somewhat old.

I used Foundations of Astrophysics by Ryden and Peterson in my first college astronomy course, which focused on stars, the ISM, and galaxies. The textbook itself goes far beyond those topics, delving into cosmology, planetary science, and more, and we actually use it for another intro-level course for majors covering those topics. I think it could be used well as the text for any such course.

I do think Ryden and Peterson satisfies the other requirements quite well; it doesn't use more than single-variable calculus (and even that only sparingly, I think), and it actually doesn't require much mechanics or electricity and magnetism, so in turns of prerequisites, you should be fine. One thing to note is that Ryden and Peterson doesn't include example problems done out in the same way many physics textbooks do - I don't know if that's a turn-off for you.

I should add a disclaimer that my opinion might be slightly skewed because of the textbook used in my seminar this past semester, LeBlanc's An Introduction to Stellar Astrophysics. LeBlanc is comparatively drier, denser, and more specialized (on, of course, stellar astrophysics). I found it substantially less accessible, even though I had much more experience in the subject at that point. This, then, may have affected my hindsight view of Ryden and Peterson. Ironically, we did use Carroll & Ostlie as supplementary reading (as well as Ryden and Peterson) on certain sections, which was much more helpful, and I daresay a refreshing change of pace.

The evidence for the Big Bang comes from many pieces of observational datathat are consistent with the Big Bang. None of these prove theBig Bang, since scientific theories are not proven. Many of these factsare consistent with the Big Bang and some other cosmological models,but taken together these observations show that the Big Bang is thebest current model for the Universe. These observations include:The darkness of the night sky -Olbers' paradox.The Hubble Law - the linear distance vs redshift law.The data are now very good.Homogeneity - fair data showing that our location in the Universe is not special.Isotropy - very strong data showing that the sky looks the same in all directions to 1 part in 100,000.Time dilation in supernova light curves.The observations listed above are consistent with the Big Bang or with theSteady State model, but many observations support the Big Bang over theSteady State:Radio source and quasar counts vs. flux. These show that the Universehas evolved.Existence of the blackbody CMB. This shows that the Universe hasevolved from a dense, isothermal state.Variation of TCMB with redshift.This is a direct observation of the evolution of the Universe.Deuterium, 3He, 4He, and 7Liabundances. These light isotopes are all well fit by predicted reactions occurring in the First Three Minutes.Finally, the angular power spectrum of the CMB anisotropy that does existat the several parts per million level is consistent with a dark matterdominated Big Bang model that went through the inflationary scenario.

The evidence for an accelerating expansion comes from observations of the brightness of distant supernovae.We observe the redshift of a supernovawhich tells us by what the factor the Universe has expanded since thesupernova exploded. This factor is (1+z), where z is the redshift.But in order to determine the expected brightnessof the supernova, we need to know its distance now.If the expansion of the Universe is acceleratingdue to a cosmological constant,then the expansion was slower in the past,and thus the time required to expand by a given factoris longer, and the distance NOW is larger.But if the expansion is decelerating, it was faster in the pastand the distance NOW is smaller. Thus for an accelerating expansion thesupernovae at high redshifts will appear to be fainter than they wouldfor a decelerating expansion because theircurrent distances are larger.Note that these distances are all proportional to the age of theUniverse [or 1/Ho],but this dependence cancels out when the brightness of a nearby supernova atz close to 0.1 is compared to a distant supernova with zclose to 1.

Quintessence, or the fifth essence, is a fifth element beyond the standardearth, air, fire and water of ancient chemistry.Steinhardt and colleagues have adopted quintessence as the name for a particular model for the vacuum energy which causes the acceleratingexpansion of the Universe.A search of astro-ph on the LANL preprint serverarXiv for "quintessence" in the abstracthits over 600 articles of which theoldest dates from1998.

This question makes some hidden assumptions about space and time whichare not consistent with all definitions of distance and time. One assumes that all the galaxies left from a single point at the BigBang, and the most distant one traveled away from us for half the age ofthe Universe at almost the speed of light, and then emitted light whichcame back to us at the speed of light. By assuming constant velocities,we must ignore gravity, so this would only happen in a nearly emptyUniverse. In the empty Universe, one of the many possible definitionsof distance does agree with the assumptions in this question: theangular size distance, and it does reach a maximum value ofthe speed of light times one half the age of the Universe.See Part 2 of the cosmology tutorial for a discussion of the other kindsof distances which go to infinity in the empty Universe model sincethis gives an unbounded Universe.

When talking about the distance of a moving object, wemean the spatial separation NOW, with the positions ofboth objects specified at the current time. In anexpanding Universe this distance NOW is larger than thespeed of light times the light travel time due to theincrease of separations between objects as the Universeexpands. This is not due to any change in the units ofspace and time, but just caused by things being fartherapart now than they used to be.

What is the distance NOW to the most distant thing we cansee? Let's take the age of the Universe to be 14 billionyears. In that time light travels 14 billion lightyears, and some people stop here. But the distance hasgrown since the light traveled. The average time whenthe light was traveling was 7 billion years ago. For thecritical density case,the scale factor for the Universe goes likethe 2/3 power of the time since the Big Bang, so theUniverse has grown by a factor of 22/3 = 1.59 sincethe midpoint of the light's trip. But the size of theUniverse changes continuously, so we should divide thelight's trip into short intervals. First take twointervals: 7 billion years at an average time 10.5 billionyears after the Big Bang, which gives 7 billion lightyears that have grown by a factor of 1/(0.75)2/3 =1.21, plus another 7 billion light years at an averagetime 3.5 billion years after the Big Bang, which has grownby a factor of 42/3 = 2.52. Thus with 1 interval wegot 1.59*14 = 22.3 billion light years, while with twointervals we get 7*(1.21+2.52) = 26.1 billion lightyears. With 8192 intervals we get 41 billion lightyears. In the limit of very many time intervals we get42 billion light years. With calculus this whole paragraphreduces to this.

If the Universe does not have the critical density thenthe distance is different, and for the low densities thatare more likely the distance NOW to the most distantobject we can see is bigger than 3 times the speed oflight times the age of the Universe.The current best fit model which has an accelerating expansiongives a maximum distance we can see of 47 billion light years.

We have observations that say that the radius of curvature of the Universeis bigger than 70 billion light years. But the observations allowfor either a positive or negative curvature, and this range includes theflat Universe with infinite radius of curvature. The negatively curvedspace is also infinite in volume even though it is curved.So we know empirically that the volume of the Universe is more than 20 times bigger than volume of the observable Universe.Since we can only look at small piece of an object that has a large radiusof curvature, it looks flat. The simplest mathematical model for computingthe observed properties of the Universe is then flat Euclidean space.This model is infinite, but what we know about the Universe is that itis really big.

Of course the Universe has to be older than the oldest stars in it. So thisquestion basically asks: which estimate is wrong -The age of the UniverseThe age of the oldest starsBothThe age of the Universe is determined from its expansion rate: theHubble constant, which is the ratio of the radial velocity of adistant galaxy to its distance. The radialvelocity is easy to measure, but the distances are not. Thus there is currently a11% uncertainty in the value of the Hubble constant measured directly by the Hubble Space Telescope. John Huchra gives a good discussionof the historical uncertainties in the Hubble constant since even beforeHubble's work.There is now a more precise but more indirectdetermination from WMAPobservations of the CMB anisotropy, and a more accurate direct measurement fromRiess etal..

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