# Final Exam Concepts

### Contents of the Exam

The Exam will cover material presented in the lectures and covered in the on-line lecture notes (Topics 1-6). Much of the material is also to be found in the lab manual : Sections 1.4, 1.5, 1.6, 2.2; Appendices A, B, and C.

Here is a list of the major themes we have discussed in class, presented partly in question form. This should give you some idea of the range and scope of the topics.

A. What were some of the historical motivations for interest in astronomy? What kind of objects does one see in the night sky.

B. Know how to use angles on the sky --- both large ones (eg 90 degrees separates the zenith from the horizon; the sun and full moon are 180 degrees apart) as well as small ones (e.g. the size of the moon is 30 arcmins; the separation of a double star is 10 arcsec). Know the "handy angles".

C. Know the magnitude system used by astronomers to indicate the brightness of stars. Know that a magnitude difference of 5 corresponds to a factor of 100 in brightness, with the smaller (more negative) magnitude for the brighter object. An alternative expression for the link between difference in magnitudes and ratio of brightness is that 1 magnitude corresponds to a factor 2.51 in brightness. Know that the magnitude of the star Vega is defined to be zero.

D. Constellations : physical vs cultural significance. What arguments help us identify the cultural origin for the "ancient" constellations. How are modern constellation boundaries defined. Destinguish between constellation and asterism. Over what period of time do constellations change due to stellar motions ? Know the various ways stars are named.

E. Know the basic properties of light : its speed, its wave-like electromagnetic nature. Be able to put in sequence the various wavelength bands of electromagnetic radiation (gamma, X-, ultra-violet, optical, infra-red, microwave, radio) as well as the colors of optical light. Know that the approximate wavelength of light is 400nm (blue) to 700nm (red). Which electromagnetic wavebands can be observed from the ground and which must be observed from space ?

F. Understand the common scientific abbreviations : milli- micro- nano- kilo- mega- giga- .

G. Understand how an image is formed by both a lens and a concave mirror. Understand the meaning of the terms : focal length; focal ratio; primary; secondary; eyepiece; field of view; magnification; angular resolution.

H. Know how to calculate the magifying power of a telescope from the focal length of the primary (or objective) and the focal length of the eyepiece.

I. Know how the light gathering power of a telescope depends on the diameter of the primary.

J. What determines the sharpness of a telescopic image? How does the atmosphere play a role in this, and how much does the telescope limit the sharpness and why?

K. Know how binoculars are labelled --- i.e. that, for example, 7x50 says their magnification is 7 and the diameter of each objective lens is 50mm.

L. Know the basic designs of refracting, reflecting and Schmidt telescopes. Know the advantages and disadvantages of each type. Why does the Schmidt telescope need the correcting element at the front?

M. Know the various focus positions that are commonly in use in reflecting telescopes: e.g. prime, newtonian, cassegrain.

N. Know the two basic types of telescope mounting systems: the Alt-Az mount and the Equatorial mount. Know the advantages and disadvantages of each. How are the mirrors for the largest telescopes made today?

O. What factors affect the viewing conditions on a given night? What are the various sources of light that interfere with seeing faint objects?

P. How does your eye work, and how is it similar or different from a CCD camera? Why can cameras attached to telescopes see objects that are so much fainter than your eye?

Q. Understand the concept of the Celestial Sphere. Know the meaning of the celestial poles and the celestial equator.

R. Understand diurnal motion --- which direction does the earth rotate; how do the stars appear to move in the sky during a 24 hour period ?

S. Know the observer's view of the sky : the horizon (tangent plane to the earth); the cardinal directions (N,S,E,W); the zenith; nadir; meridian. Know where to find the celestial poles and equator on the night sky. Know that the altitude of the celestial pole is equal to the latitude of the observer. Know what the circumpolar zones are.

T. Know how to label directions at any part of the sky : north takes you to the NCP; West is the direction the diurnal motion takes you.

U. Know what the ecliptic is and why it is inclined relative to the celestial equator by 23.5 degrees. Know that the constellations through which the ecliptic passes are the "zodiac" constellations. Know how the position of the sun on the ecliptic gives rise to the seasons. Understand how, at different times of the year, the suns daily arc across the sky is different, as is the length of the day and night. Understand the terms : equinox and solstice. Know how to calculate the noon altitude of the sun at different times of the year. Understand the terms Arctic and Antarctic circle and Tropics of Capricorn and Cancer. What is special about these latitudes on the earth.

V. Understand the Declination coordinate of a star -- how it is identical to the concept of latitude on the earth, with positive values 0 - 90 from the celestial equator northwards, and negative values 0 to -90 going south. Be able to find the altitude of a star as it transits given its declination.

W. Understand the two sets of coordinates: Right Ascension and Declination as applied to the celestial sphere; and Azimuth and Altitude as applied to the visible sky for an observer. (You should already know the coordinate system for the earth: Longitude and Latitude.) Know the units that these coordinate systems are measured in and where their zero points are.

X. Understand Hour Angle and Siderial time. Hour angle tells you the time until/since an object crosses the meridian, while siderial time tells you what RA is currently on the meridian. Understand the relation between these three quantities : HA = ST - RA. Be able to estimate the Siderial time given the time of day and day of year. Know that 24h of siderial time (ie a siderial day) is 23h 56m of normal (solar) time (i.e. a normal solar day). Know why these two days have different lengths and why the siderial day is 4 mins shorter than the solar day.

Y. Be able to convert, roughly, from RA, Dec and ST to Alt, Az and visa versa -- ie to be able to estimate where in the sky an object of a given RA and Dec will be at a give time of day and year. Conversely, be able to estimate the RA and Dec if you know where and object is in the sky at a given time of day on a given day of the year. Specifically, know that at transit, the altitude of an object is 90-Lat+Dec degrees, and that the hour angle is ST-RA.

Z. Understand and know the names of the phases of the moon. Know how the phase of the moon relates to the angular separation between the moon and sun in the sky. From this know how to estimate where the moon is in the sky from its phase and the time of day.

A2. Know the difference between the synodic month and the siderial month and why they are different by about 2.6 days. Know that the orbit of the moon is approximately in the plane of the ecliptic.

B2. Understand how the pull of the moon and the sun on the bulge of the earth causes precession --- a 26000 year motion of the earths rotation axis. Know that this causes the NCP to gradually move in a circle of radius 23.5 degrees around the pole of the ecliptic. Thus, the NCP has only recently (last 1000 years) been close to the star Polaris in the sky. Understand that this same motion causes the location of the vernal equinox to move around the ecliptic with the same long period. Realise that this causes the RA and Dec coordinates of a star to change slowly with time, and hence astronomers usually quote the RA and Dec of a star at a reference epoch (usually 1950 or 2000).

C2. Eclipses! Two types, each ocurring at a particular lunar phase. Recall the structure of shadows cast by extended objects (such as the sun). Know the terms 'umbra' and 'penumbra', and the phenomenon of the 'umbral cone' cast by a spherical object.

D2. Know about the THREE types of lunar eclipse. Which one do you hardly notice ? Why is a totally eclipsed moon still visible to us ? Who gets to see a lunar eclipse --- many people or just a few (ie, from where on the earth is a lunar eclipse visible)? How did the Greeks use lunar eclipses to figure out that the earth was spherical?

E2. Know about the THREE types of solar eclipse. For which one can you see the sun's corona ? Know that because the moon and sun appear the same size in the sky, this means the earth is just about at the tip of the moon's umbral cone. What circumstances lead to an annular eclipse as opposed to a total eclipse ? Approximately what fraction of the earth's surface witnesses a total eclipse/a partial eclipse/no eclipse.

F2. Know the moon's orbit is inclined by 5 degrees to the ecliptic plane. What are the 'nodes' of the orbit and why do eclipses only occur when both the moon and the sun are on the 'line of nodes'. Understand why eclipses tend to occur only in "eclipse seasons" approximately twice yearly. Understand the subtlety of the "regression of the line of nodes" which leads to an interval between eclipse seasons of about 5.6 months. Why do the nodes regress?

G2. Understand why the planets are always found near the ecliptic plane. This places them always in zodiac constellations, hence the importance of these constellations for astrology (which, in case I forgot to mention, is rubbish!).

H2. Know the various terms: inferior planet, superior planet, conjunction, opposition, quadrature, elongation, greatest elongation. Know how to estimate the distance of an inferior planet to the sun using its greatest elongation. Know the difference between sidereal and synodic periods of planets. In general, are synodic periods longer or shorter than sidereal periods? Know how the phases and brightnesses of planets change during their synodic cycle. Can superior planets show crescent phases ? Why do, for example, Mars and Venus show such large changes in brightness as the months go by?

I2. Understand why planets basically move eastwards with briefer periods of westward (retrograde) motion. Understand why the retrograde motion occurs when the planet is at opposition (for superior planets). How does the length of time spent in retrograde motion depend on how far away the planet is (eg compare the motions of Saturn with Mars) ?

J2. What is Albedo and how does it effect a planets brightness. Explain the phenomenon of "The old moon in the new moon's arms". Understand why the Earth, as seen from the moon, is so much brighter than the moon seen from the earth.

K2. Know some of the most noticable characteristics of viewing the planets through a small telescope. Venus' phases, high brightness, white color with no features (cloud covered). Mars' reddish (rusty!) color. Why are Jupiter and Saturn not spherical planets? Why are their moons and rings all orbiting in the equatorial planes? What is Cassini's division in Saturn's rings and why does it occur?

L2. Large asteroid collisions with earth happen every few hundred million years. Some of these collisions may be responsible for significant extinctions of species (eg the demise of the dinosaurs, 65 million years ago.

M2. Know that Comet nuclei are similar in size to asteroids but are made of dirty ice. During perihelion passage, ice is evaporated to generate the comet tail. Since a few meters of ice are evaporated with each passage of the sun, the comet disappears in a few hundred orbits or a few hundred thousand years.

N2. Particles left behind by the comet follow in its orbit and if the earth happens to pass through this orbit path, we witness a meteor shower.

O2. The properties of stars: Understand the difference between apparent magnitude and absolute magnitude. Why is absolute magnitude a measure of a star's luminosity? How are stellar surface temperatures measured? How do we measure the mass of stars? Know the Mass-Luminosity relation, namely that more massive stars are very much more luminous. Understand that this also means more massive stars die sooner.

P2. Know the basic form of the Hertzsprung Russell diagram -- star luminosity (y) plotted against star color (x). Know the three important locations: Main sequence; red giants; white dwarfs.

Q2. Know the basic structure of stars and their nuclear reactions. The furnace at the core, surrounded by an intert envelope, ending in the surface which radiates the energy into space. The basic fuel is hydrogen which converts to helium. Why does one need higher temperatures for helium to burn to carbon? Understand how heavier elements up to iron are made by a sequence of nuclear reactions at ever higher temperatures. The overall efficiency of these nuclear reactions is 0.7% compared to full conversion of mass to energy. Know that while hydrogen is burning, the star is on the main sequence, and after that it is a red giant.

R2. Understand the two types of stellar death: Low mass stars gently eject their outer envelopes and appear as planetary nebulae. High mass stars explode in supernovae. Either way, the newly made heavy elements are ejected into interstellar space and find their way into new generations of stars. Ultimately, all the matter on earth, and in you, was made inside former generations of stars.