Please read and sign the following honor pledge:
“I pledge on my honor that I have not given or received any unauthorized assistance on this examination.”
Instructions for this examination:
1. Answer all questions in Section A. Answer THREE out of four questions in Section B. Section A is worth 40 points, and Section B is worth 60 points. So you should plan to spend slightly more than have of your time on Section B.
2. No electronic calculators of any kind are to be used
3. This is a closed-book exam: no notes are allowed.
4. Please write your answers directly on this exam paper in the gaps after each question. Do not feel that you have to use all of the available space.
5. If you need more space than provided, write the continuation of your answer on the back of the page. If yet more space is needed, please ask for additional sheets of paper. Be sure to write your name and the question number on every additional sheet you use.
Please circle the letter corresponding to the correct answer.
1. Which aspect of the old “geocentric” model of the solar system did Copernicus preserve when he developed his “heliocentric” model?
a. Planets move in circles
b. Epicycles are needed to produce retrograde motion
c. The Earth is at the center of the solar system
d. The Earth is stationary
2. Suppose that we discover a distant planet orbiting the Sun with a semi-major axis of 100AU. What is the period with which the planet orbits the Sun?
a. 1 year
b. 10 years
c. 100 years
d. 1000 years
3. What is the main reason why a simple projection of the Earth’s lines of Latitude and Longitude onto the sky does not provide a useful coordinate system for the sky?
a. The location of the zero-point of Longitude (i.e., the Meridian) is still a matter of debate.
b. The location of the zero-point of Latitude (i.e., the Equator) is still a matter of debate.
c. Such a coordinate system would move relative to the stars as the Earth rotated.
d. Scientists can’t figure out how to do this projection.
4. When standing in College Park, the Zenith is located
a. Directly above you
b. Close to the Northern Celestial Pole
c. On the horizon
d. At the point where the Celestial equator crosses the ecliptic
5. Why is a sidereal day (i.e., a day defined using the motion of the stars around the sky) slightly shorter than a solar day (i.e., a day defined using the motion of the mean Sun around the sky)?
a. The spin axis of the Earth is undergoing precession, leading to this slight difference in the two definitions of a day.
b. The Earth speeds up and slows down in its orbit due to the elliptical nature of its path around the Sun
c. The Earth moves slightly on its orbit during the course of a day, making the Sun appear to shift slightly relative to the stars.
d. The spin rate of the Earth is gradually slowing down.
6. A star’s radiation (which can be treated as being approximately blackbody in form) peaks at a wavelength of 290nm. From Wien’s law, its surface temperature is
7. The resolution of a (perfectly functioning) human eye is about 0.5 arcminutes. This is determined by
a. The “diffraction limit” which is caused by the wave-like nature of light
b. Motions and turbulence of the air in the Earth’s atmosphere (i.e., seeing)
c. Inevitable and unavoidable “haze” in the Earth’s atmosphere
d. Biological limitations in the quality of the eye’s lens
8. An X-ray telescope on the Earth’s surface would be
a. A powerful tool for studying interesting and violent phenomena in the Universe
b. Worthless because astronomical objects do not emit X-rays
c. Worthless because the X-rays could not possibly get through the Earth’s atmosphere
d. Impossible to make because scientists cannot figure out how to focus X-rays
Answer any THREE out of the following four multi-part questions. If you answer all four questions, your best three scores will be used. Write your answers into the space provided. If you need more space, write on the back of the page.
9. Kepler’s laws and orbits
a. [6 points] State Kepler’s laws of planetary motion.
b. [8 points] State Newton’s laws of motion and gravity. In what sense are these more fundamental than Kepler’s laws.
QUESTION CONTINUES ON NEXT PAGE
c. [6 points] Some scientists believe that, in the future, it may be possible to launch satellites into orbit around the Earth using a large “gun” on the ground. The idea is that the gun accelerates the satellite to the required speed to achieve orbit and then literally shoots it into the sky. Explain why we cannot place a satellite into a long-lived orbit around the Earth using this technique alone. As part of your answer, draw possible paths taken by the satellite on the diagram below [Hint – apply Kepler’s first law of planetary motion to the orbit of the satellite around the Earth.].
10. Spectroscopy and energy levels within atoms
a. [8 points] Carefully describe under what circumstances we would see (i) a black body spectrum, (ii) an emission line spectrum, and (iii) an absorption line spectrum?
b. [4 points] Give one reason why studies of emission and absorption lines from astronomical objects are so important.
c. [8 points] The figure shows the first three emission lines of the Balmer series of Hydrogen (these lines are referred to as Ha, Hb, and Hg, respectively). Draw a labeled energy level diagram of a Hydrogen atom, and label the transitions that give rise to these three emission lines.
11. Tides and tidal forces
a. [8 points] The differential gravitational force that the Moon exerts on different parts of the Earth results in the rise and fall of the Earth’s oceans twice per day. Briefly describe two other (more subtle) phenomena that are associated with the action of tidal forces in the Earth-Moon system.
b. [12 points] In addition to the Earth-Moon system, we have discussed in class several other cases where tidal forces create interesting phenomena. Describe two of these cases, writing about one full paragraph for each.
a. [8 points] Draw a labeled diagram of a reflecting telescope (it is your choice which particular configuration of reflecting telescope you decide to draw).
b. [8 points] The diffraction limit, measured in arc-seconds, is given by , where l is the wavelength of light and D is the diameter of the objecting lens/mirror of the telescope. Suppose we wish to achieve a diffraction limit of 0.1 arcsecond at a wavelength of 1000nm (i.e., just a little bit into the infra-red). How large would the objective mirror of the telescope have to be? Show your working.
c. [4 points] Why would we have problems achieving this resolution if the telescope were on the ground?