(GM/R)
and Vesc = (2)
x Vcirc. (For earth a low circular orbit has
Vcirc = 7 km/s). Note that a rocket in circular orbit needs
about a 41% boost in speed (2
= 1.414) to escape into a parabolic orbit (or hyperbolic if given yet
greater speed).
The Third Exam will cover material presented in the lectures since exam 2. In the text this is from page 50 (Ch 2.5) to page 81 (end of Ch 3) then page 131 to 145 (all Ch 6, but omitting Chs 4 and 5). From my "ASTR 121 Course Outline", the topics go from "Circular velocity, Escape Velocity" though Ch 3 and most of Ch 6, up to "Brief review of origin of solar system" (depending on how far I get in class on Monday).
The Exams for this course are true/false, multiple choice and short answer format. The review questions at the end of the chapters are typical, including the advanced questions. Below I supply a few sample questions so you know what to expect. Note: this sample is not comprehensive, it is approximately representative although it emphasises questions with a bit more math, since these are the kind of questions which most people have the most trouble with.
1. A spaceship is in a circular orbit about Jupiter, with a speed of 1000 m/s. In order to just escape Jupiter's gravitational pull, the rocket engines are burned. How fast should the spaceship be travelling when the engines are turned off ?
2. T/F If an object is moving at its escape velocity it's orbit will be hyperbolic.
3. T/F The Declination Coordiante of the Pole Star (Polaris) is approximately +90 degrees.
4. What is the Declination of the Sun on December 22 ?
5. A star has a Right Ascension of 12 hours. In which month is it impossible to observe the star because it is only above the horizon during the day ?
6. At 25 degrees North latitude, how high is the Sun in the sky above the southern horizon at Noon of the Summer Solstice (answer to the nearest degree) ?
7. In June the sun rises
8. What are the Latitudes of : The Arctic Circle, The Antarctic Circle, the Tropic of Cancer and the Tropic of Capricorn. Observationally, what is significant about each of these regions ?
9. Why is it warmer in the Summer ? <\P>
10. T/F The sidereal day is about 4 minutes shorter than the mean solar day.
11. Paris is about 90 degrees in Longitude to the East of Chicago. If it is 12 Noon in Chicago, about what time is it in Paris?
12. T/F The year 1900 was a leap year.
13.You see a third quarter moon directly overhead. About what time is it?
14. T/F A Synodic month is about 1/12 of a month shorter than a Sidereal month.
15. Why are there two high tides each day, and what causes Spring and Neap tides.
16. T/F : Lunar eclipses occur when the moon is waxing gibbous.
15. Explain why someone is more likely to have seen a total lunar eclipse than a total solar eclipse.
17. What is the difference between a total eclipse of the sun and an annular eclipse of the sun --- both the appearance and the reasons for the difference.
18. Eclipses do not occur at every full or new moon because
19. Underline the correct word from the brackets. Jovian planets are [larger/smaller] have [more/less] satellites and are [nearer/further] from the sun, than terrestrial planets.
20. How old is the earth. How old is the sun. How do we know?
21. The division of planets into inner Terrestrial and outer Jovian results from
Do the 21 questions, write down your choice of answers, then check yourself with these Answers Think about the ones you missed. If you missed several, redouble your study efforts ! Also, dont forget the TA office hours in room 267 of 9am - noon (Tues, Thurs) and 3:30pm - 6:30pm (Mon, Wed, Fri). And my own office hours 2pm to 3pm (Mon, Wed, Fri).
Below are listed the main themes covered in class, some posed as questions.
A. Know about the two simplest orbital velocities : circular
velocity and escape velocity, with Vcirc = (GM/R)
and Vesc = (2)
x Vcirc. (For earth a low circular orbit has
Vcirc = 7 km/s). Note that a rocket in circular orbit needs
about a 41% boost in speed (2
= 1.414) to escape into a parabolic orbit (or hyperbolic if given yet
greater speed).
B. Appreciate that we have only considered simple 2-body orbits; 3 or more objects have more complicated orbits. Discovery of Neptune from Perturbations to orbit of Uranus is good example.
C. What are coordinate systems ? What are Longitude/Latitude, and Right Ascension/Declination; how are they similar and different. Know that the zero for RA is the vernal equinox (equivalent to Greenwich on Earth for Longitude). What are the units for RA. Why do we specify an "epoch" for a given RA, DEC coordinate? Realise that the Sun has RA = 0 hours on March 21, and RA = 12 hours on September 22.
D. Understand how the tilt of the earth's axis leads to the seasons (NOT the ellipticity of the earth's orbit). Be able to visualize, for a typical mid-latitude observer, the daily motion of the sun (rise, transit, set) in each of the seasons. How is this linked to the declination of the Sun, which varies through the year. Know how the rise/set locations, hight of the noon sun, and length of day vary through the year. Understand the terms solstice, equinox. Know why average temperatures vary with the season. Know roughly how seasonal changes vary with latitude. Know the location and meaning of the Arctic and Antarctic circles, as well as the Tropics of Cancer and Capricorn.
E. Understand the difference between Solar and Sidereal days. Which is shorter and by how much. Know that the length of the apparent solar day varies, so we define "mean" solar time. Understand zone times, including GMT and UT. Approximately how many degrees of longitude span one time zone?
F. Know the difference between Sidereal and Tropical years. Realise the basic task of a calendar : to fit whole days into a seasonal year. Know, roughly, the history of our calendar -- why Julius Caesar introduced the leap year, its limitations and modification by Pope Gregory in the 16th century. What are the current rules for leap years?
G. Why does the moon show phases? Know the phase cycle. Be able to relate the phase of the moon and its position in the sky to the time of day or night.
H. Realise there are two months : sidereal and synodic. Which is shorter, by how much, and why ? Does the moon rotate on its axis? What is meant by synchronous rotation and why has it occurred?
I. Know how gravity acting on a body can cause stretching, or Tidal, forces. Know that the Tides pull spheres into a prolate (football) shape whilst planet rotation causes planets to be oblate (bigger equator) spheres. Why do we have two high tides each day. Does the moon or sun provide the stronger tidal force? When do you expect to find spring tides and neap tides. How does the tidal interaction between the earth and moon cause a gradual lengthening of the day and the month ?
J. Understand the zones in a shadow cast by an extended source of light (eg the Sun). What are the Umbra and Penumbra regions. At what phase of the moon can we have a lunar eclipse, and at what phase can we have a solar eclipse? Understand the difference between Total, Partial and Penumbral LUNAR eclipses; and between Total, Annular, and Partial SOLAR eclipses. What do each of these types of eclipse look like from earth.
K. Why do we not get eclipses at every New and Full moon. Realise the plane of the moon's orbit is inclined by about 5 degrees to the ecliptic. What are the "Nodes" of the moon's orbit, and what is the "line of nodes". What are eclipse seasons, and why are they not simply 6 months apart ? What is, roughtly, the interval between consecutive eclipse seasons.
L. Know the overall properties of the solar system. Contents : Sun, planets, moons, asteroids, comets. Know the overall shape and motion : flat, nearly coplanar circular orbits with highly dominant sun's mass. Know the two basic types of planets : Terrestrial and Jovian, and how their properties differ (size, mass, density, position in the solar system). Understand that their compositions represent high and low boiling point substances which reflects the location in the protoplanetary disk where they formed.
M. Know, roughly, the methods which have been used to establish the age of objects in the solar system. What IS the age of the solar system and the earth. Know, roughly, the modern nebular hypothesis for the formation of the solar system from a collapsing, rotating, interstellar gas cloud. Disk formation, with temperature gradient, and planets forming in the disk, with terrestrial planets forming in the inner hotter regions and the Jovians forming in the outer cooler regions.
N. What is "differentiation" ? How do planets come to have structures with dense cores and less dense outer regions. Why were young planets hot and liquid, allowing differentiation to occur ?