Astro 001.101 Summer 2002 Exam 2

ASTRO 001.101 SUMMER 2002 EXAM 2

NAME (print): ______ID# ______

Sun’s diameter = 93,000,000 miles = 150,000,000 km Sun mass = 333,000 Earth masses Earth’s diameter = 7900 miles = 12,800 km = 0.0092 Solar diameters

c GM M GmM 1 P 2  a 3 e  F  ma F  1 2 W  E  f E  a d 2 R 2  a 3 Energy emitted per sq meter  T 4 M  m  P 2

I. Multiple-Choice. In each case, please chose the one best response. [2 pts each]

Consider the mysterious planet Xenon. Here’s a scale drawing of Xenon and Earth:

Xenon Earth

Xenon are Earth are equal in mass. Xenon and Earth both orbit the Sun. Earth orbits at a mean distance from the Sun of 1.0 AU (of course!). Xenon orbits at a mean distance of 3.0 AU from the Sun. Please refer to this information and the included sketch when responding to Questions 1 - 11.

1. If you weigh 135 lbs on Earth, how much will you weigh on the surface of Xenon?

a) More than 135 lbs. b) Less than 135 lbs. c) Exactly 135 lbs. d) Can’t tell, based on the information provided.

2. On Earth, you drop a wrench, and it accelerates toward the ground at a rate of 9.8 m/s/s. The rate of acceleration on Xenon would be ______.

a) Greater than 9.8 m/s/s. b) less than 9.8 m/s/s. Exsu02_2

c) exactly 9.8 m/s/s. d) Can’t tell, base on the information provided. 3. Which of these planets is subject to the greater gravitational force exerted by the Sun, and by what factor?

a) The Sun exerts 3 times as much force on Earth. b) The Sun exerts 3 times as much force on Xenon. c) The Sun exerts 9 times as much force on Earth. d) The sun exerts 9 times as much force on Xenon. e) Can’t tell, based on the information provided.

Xenon 1 2

Y 4. Above is a sketch of Xenon’s orbit ellipse (Sun is on the right; Xenon is the white disk on the left). The dashed lines cross at the center of the orbit. X, Y and Z are some points around the orbit. Which of the labeled dimension (1, 2 and 3) is equal to 3.0 AU?

a) 1 b) 2 c) 3 d) None of these dimensions is equal to 3.0 AU.

5. At which point would Xenon experience minimum acceleration?

a) X b) Y c) Z d) Xenon’s acceleration is always the same, so there is no “minimum.”

6. Placing the Sun farther from the center of Xenon’s orbit (without changing Xenon’s average distance from the Sun) would have what effect on the eccentricity of the orbit?

a) The eccentricity would increase. b) The eccentricity would decrease. Exsu02_2

c) The eccentricity would not change. 7. Suppose Xenon’s orbit were a perfect circle, with the average distance from the Sun still 3.0 AU. How would Xenon’s orbit period change?

a) The orbit period for the circle would be longer. b) The orbit period for the orbit as shown above (ellipse) would be longer. c) The orbit period would not be altered. d) Can’t tell, based on the information provided

8. Doubling the Sun’s mass (without changing anything else) would have what effect on Xenon’s orbit period?

a) The orbit period would decrease. b) The orbit period would increase. c) The orbit period would not change. d) Can’t tell, based on the information provided.

9. Doubling the Sun’s mass (without changing anything else) would have what effect on the gravitational force the Sun exerts on Xenon?

a) The force would double. b) The force increase by four times. c) The force would be one-half. d) The force would be one-fourth. e) The force would not change.

10. Suppose Xenon’s average distance from the Sun were doubled. Its new orbit period would be closest to which of the following?

a) 1.6 times its present value. b) Twice its present value. c) 2.8 times its present value. d) 4 times its present value. e) 8 times its present value. Exsu02_2

OK, now let’s change the situation. Take the Sun out of the picture entirely, and have Earth orbit Xenon at a constant distance of 100,000 miles (measured center-to-center). [Dr. Martell is not goofing on you. This sort of thing does occur, but typically with stars, not planets.] Anyhow, here’s what we have:

Xenon Earth

100,000 miles

11. Ah, er, I’m not sure that this stuff about “Earth orbiting Xenon” is quite right. Which of the following gives a better description of what’s going on if we should find Earth orbiting near Xenon?

a) Xenon and Earth both orbit a point midway between Xenon and Earth. b) Xenon and Earth both orbit a point, but that point is closer to Xenon than to Earth. c) Xenon and Earth both orbit a point, but that point is closer to Earth than to Xenon. d) It’s Xenon alone that does the orbiting, and it orbits the center of a stationary Earth. e) Well, actually we had it right the first time – Earth orbits the center of a stationary Xenon. Yikes!

12. What does temperature measure?

a) the average mass of atoms in a substance b) the average size of atoms in a substance c) the average kinetic energy of atoms in a substance d) the total kinetic energy of atoms in a substance e) the total number of atoms in a substance

13. Kepler’s 2nd law (“law of areas”) could be used to determine ______.

a) how fast Mars goes in its orbit compared to Jupiter b) the masses of planets c) how fast Earth rotates on its axis d) how Earth’s orbit speed changes during a year Exsu02_2

Earth 4 2

Here’s a picture of the orbits of Earth and Venus, about the Sun. Numbers 1, 2, 3 and 4 indicate some possible positions of Venus on its orbit. Please refer to this diagram and description when responding to Questions 14 - 15.

14. For which of the locations 1, 3 and 5 could Venus be viewed (from Earth, as shown here) shortly after sunset?

a) 1 only b) 1 and 3 only c) 5 only d) 1, 3 and 5 e) None of these locations correspond to an “after sunset” view of Venus. Exsu02_2

15. Of the positions shown, Venus will appear farthest from the Sun in the sky (as viewed from Earth, as shown here) when at position ______.

a) 1 b) 2 c) 3 d) 4 e) 5

16. While Copernicus was correct in constructing a model of the solar system that placed the Sun (instead of Earth) at its center, he erred in ______.

a) insisting that planets move on elliptical orbits b) insisting that planets move on circular orbits c) insisting that the Sun is much less massive than any planet d) persisting in the ancient Greek belief that Earth cannot rotate e) removing all epicycles from his model

17. If an object is accelerated, what must change?

a) Its speed must increase. b) It speed, which could either increase or decrease. c) Its direction of motion. d) Either its speed, or direction of motion, or both.

18. In what way do electromagnetic (em) waves differ from other kinds of waves (e.g., sound waves)?

a) em waves have only one wavelength b) em waves have only one frequency c) em waves have zero amplitude d) em waves can travel in a vacuum

19. The sun radiates approximately like a blackbody. Suppose the sun’s temperature were half its present value (i.e., 2900 K instead of 5800 K). How would the total amount of energy radiated per second by the sun change?

a) It would be equal to its present value. b) It would be less than half its present value. c) It would be exactly half its present value. d) It would be twice its present value. e) It would be more than twice its present value. Exsu02_2

Here’s a picture that depicts the orbit of a planet in the model of Ptolemy. Point 1 lies on the larger (dashed) circle; points 2 and 3 lie on the smaller circle. The gray disk lies at the center of the larger (dashed) circle. Please refer to this diagram when responding to Questions 20 – 21.

20. As viewed from Earth, a planet such as Mars would be observed to be in retrograde motion when at what position?

a) 1 b) 2 c) 3 d) None of the other answers is correct.

21. The gray disk near the center of the larger circle most probably represents what?

a) Earth b) The Sun. c) Any planet other than Earth. d) The Moon. e) Either Venus or Mercury.

22. Which of the following statements correctly states the significance of Galileo’s observation that Jupiter is orbited by moons? Exsu02_2

a) It showed that Jupiter must be four times the size of Earth as Jupiter has four moons, whereas Earth has only one. b) It showed that Jupiter must orbit the sun, not Earth. c) It showed that celestial objects can orbit bodies other than Earth. d) It was interesting, but had no particular importance.

23. Mars’ surface appears reddish in color because ______.

a) its temperature is unusually low b) its temperature is unusually high c) it reflects blue and violet light better than red and orange light d) it reflects red and orange light better than blue and violet light e) its thick atmosphere prevents sunlight from reaching its surface

24. According to Newton’s 3rd Law, if a force is acting on an object, then ______.

a) the object must move along a circular path b) there must be some other force also acting on the object, with the same strength, but in the opposite direction c) the object must accelerate d) there must be some other force acting on a different object, with the same strength, but in the opposite direction

25. What is the relationship between color and wavelength for light?

a) Wavelength decreases from violet to red. b) Color depends only on brightness, and is independent of wavelength. c) Wavelength increases from violet to red. d) Wavelength increases from violet to green, then decreases to red.

26. Which of the following is the correct sequence of electromagnetic radiation, in order of increasing energy of the photons?

a) Visible light, microwaves, radio waves, infrared rays b) Gamma rays, radio waves, x-rays, infrared rays c) Visible light, UV radiation, x-rays, gamma rays [BOTH c) AND d) d) Radio waves, infrared rays, visible light, x-rays ARE CORRECT]

27. A glass prism is able to split white light into its constituent colors because ______. Exsu02_2

a) the speed of light in the glass depends on wavelength b) the speed of light in the glass depends on amplitude c) the glass blocks some colors from passing through it d) the speed of light in the glass depends on temperature e) the direction of motion of photons of light is changed when the photons collide with atoms in the glass

28. Atoms of deuterium and tritium differ from atoms of “ordinary” hydrogen in ______.

a) the number of electrons b) the number of neutrons in the nucleus c) the number of protons in the nucleus d) the number of neutrons in the electron cloud e) the number of photons in the nucleus

29. Galileo invented the telescope.

a) True b) False

30. Atoms in a thin, hot gas emit light ______.

a) at specific wavelengths (or colors), the pattern depending on the composition of the gas b) at all wavelengths, the brightness at each wavelength (color) depending on the temperature of the gas c) only at one, specific wavelength d) only at visible wavelengths

31. The astronomer who made the very accurate naked-eye observations of Mars (and other planets) that led to our present picture of planetary orbits was ______.

a) Galileo b) Kepler c) Newton d) Copernicus e) Brahe

32. Earth’s gravity does not extend beyond a few miles above its surface.

a) True b) False

13.6 eV

12.8 eV Exsu02_2

12.1 eV 4 5 10.2 eV

Here’s the energy level diagram for the hydrogen atom. Several possible transitions of electrons between energy levels are indicated by numbered arrows (1 – 5). Please refer to this diagram when responding to Questions 33 - 34.

33. Which transition, as shown, is not possible?

a) 1 b) 2 c) 3 d) 4 e) 5

34. Which transitions involve photons in the visible part of the electromagnetic spectrum?

a) 4 and 5 b) 1, 2 and 4 c) 1, 2, 4 and 5 d) 1 and 2 e) None of these transitions involve visible-light photons.

35. Which of the following statements about an asteroid orbiting the Sun on a perfect circle is not true?

a) It is moving at a constant speed. [ALL RESPONSES GRADED b) It is accelerating. CORRECT.] Exsu02_2

c) It is moving on a plane. d) It is moving with constant velocity. e) Two of the statements a), b), c) and d) are untrue.

36. In his approach to solving the problem of the shape of Mars’ orbit, Kepler ______.

a) attempted to find the closed curve that best fit observations made by others b) used the inverse-square law of gravity to predict where Mars should be found c) personally observed Mars in the night sky dozens of times d) assumed that planets move under the influence of magnetism e) assumed that Earth is stationary at the center of the solar system

37. Compared with the waves emitted by a source at rest, waves emitted by a source moving away from an observer will be seen by that observer to have ______.

a) longer wavelength b) higher frequency c) shorter wavelength d) higher speed e) lower speed

1 2 3 4

38. In the configuration shown above, where 1 = hot source of continuous light; 2 = cooler, thin gas; 3 = prism; 4 = observer; the observer will see ______.

a) a continuous spectrum b) an emission line spectrum c) an absorption line spectrum d) a magnified image of the continuous source (1) e) a Doppler-shifted spectrum

39. A force applied to a brick results in an acceleration of 4.0 m/s/s. If the same force is applied to half a brick, what acceleration results?

a) 8.0 m/s/s b) 4.0 m/s/s c) 2.0 m/s/s Exsu02_2

d) 0 m/s/s

40. Astronauts orbiting Earth in the Space Shuttle find themselves in a condition commonly called “weightlessness;” i.e., they float freely within the cabin of their spaceship. This condition arises because, at the altitude at which the Shuttle orbits, Earth exerts no gravitational force on the astronauts.

a) True b) False

41. If we measure the wavelengths of emission and absorption lines from the same gas (e.g., hydrogen), we find that (ignoring any Doppler shifts) ______.

a) the patterns of lines are completely different b) the patterns of lines are identical c) the emission lines are all shifted to longer wavelengths d) the emission lines are all shifted to shorter wavelengths

42. A substance said to be in the plasma state would be characterized by which of the following conditions?

a) Nearly all atoms would be ionized. b) Nearly all atoms would be neutral. c) The substance must be at very low temperature. d) The atoms would be very close together. e) The substance would have to be of very high density.

II. Essay/Short Answer. Please respond to each of the following in the space provided. Thank you.

43. [6 Pts] Kepler formulated his 3rd Law in the following way:

a 3 1  (a in AU; P in years) P 2 Exsu02_2

Yet Newton re-formulated the 3rd Law as follows:

a 3 m  M  (m and M in units where the Sun’s mass = 1) P 2

Explain how these two formulations of Kepler’s 3rd Law can be reconciled.

a 3 m  M  P 2 a 3 m  1  P 2 m  1 (Planets are much less massive than the Sun.) Consequently, m  1  1, so a 3 1  , which gives us Kepler's 3rd Law, the way Kepler wrote it. P 2

44. [10 pts] Choose ONE of the following (either a) or b)):

a) Discuss the general appearance of the planets in the night sky: how they appear to the naked eye; where they are located; how they move on the celestial sphere. Relate (as best you can) apparent location/motion on the celestial sphere to actual location/motion in the solar system (i.e., as seen by an observer located outside the solar system). Discuss both Exsu02_2

planets that orbit nearer the Sun than Earth, and those that lie beyond Earth’s orbit. Be sure to account for the strange phenomenon of retrograde motion.

b) The Greeks and their predecessors (and indeed most of their descendents to the time of Copernicus) were largely convinced that Earth must be stationary. Discuss some rational arguments marshaled in favor of this point of view. a) Planets appear star-like to the naked eye, but betray their identity as they drift across the celestial sphere, relative to the stars. The drift results from watching planets orbiting the Sun from a platform (Earth) which itself moves (orbits). The resulting motion can be rather complicated. However, planets are always found within the Zodiac, very close to the Sun’s apparent path on the celestial sphere, the ecliptic. This circumstance arises because most planets’ orbits lie in planes near the plane of Earth’s orbit (ecliptic plane). So, as the motion of the Sun around the sky is simply a reflection of Earth’s orbit motion about the Sun, we find planets always near the Sun’s path on the sky. Planets that orbit closer to the Sun than Earth (Mercury & Venus) will always be found relatively close to the Sun in the sky:

Earth Angle є is no larger than 28o for Mercury, and 47o for Venus.

Planets orbiting outside Earth’s orbit obviously can be found up to 180o from the Sun in the sky. Retrograde motion occurs (for a planet orbiting outside Earth’s orbit) when that planet is overtaken by Earth (Earth’s orbit speed exceeds the orbit speeds of the outer planets). Retrograde motion is thus is misperception due to relative motion – much like passing a slower car on the highway: As you overtake the slower can, from your point of view it appears that the car is moving backwards. Thus it is for the slower planets that Earth overtakes from time to time. b) Arguments raised by the Greeks included: Exsu02_2

1) Dropping an object, without giving it any obvious sideways motion, results in that object falling straight down. Now, if the Earth rotates, shouldn’t that object fall to the side, as the Earth must have moved some distance in its rotation during the time it took the object to fall? The Greeks misunderstood that the object, while it’s still in your hand, partakes of the motion of Earth, at your location. And that this sideways motion persists while the object is in flight (due to Newton’s First Law of motion). Thus, while it falls, it “keeps up” with Earth.

2) If Earth orbits the Sun, shouldn’t we see stars shift their location in the sky through the year? Here’s a diagram:

As Earth (the blue disk) circles the Sun, we might expect to see a nearby star shift its position relative to more distant stars (an example of the “parallax effect”) This effect is not observed (using only the naked eye); consequently the Greeks concluded that Earth does not orbit the Sun. However, the Greeks failed to realize that stars lie at very great distances. For the nearest star to the Sun, the angle  is only ~ 1/1800o. The smallest angular separation the human eye can perceive is about 1/60o; consequently, it’s not hard to understand how the Greeks could have misinterpreted their inability to observe the apparent shifting of stars.

Other arguments were based on a mistaken physics, wherein the Greeks proceeded from the assumption that heavy objects (like rocks) find their “natural place” near Earth’s surface; thus, Earth, as the biggest of all rocks, should be located at the center of the universe. In addition, some cultures invoked the religious notion that human beings, as the most important of all creatures, obviously belong at the center of the universe. The last argument is, of course, supremely irrational.