PTYS 206-2 Spring 2008 Practice Exam 1 SOLUTIONS Potentially Useful Data Gravitational Constant, G = 6.67x10-11 m3/(kg s2) 1 Astronomical Unit (AU) = 1.496x1011 m Mass of the Sun = 2.0x1030 kg Mass of Earth = 6.0x1024 kg 1 meter = 1.09 yards 1 kilogram weighs 2.2 pounds (if measured on Earth) 1 yard = 3 feet Escape Velocity of Earth: 11.2 km/s Period of Miranda = 1.413 days Semi-major Axis of Miranda’s Orbit = 129, 390 kmSection 1: Multiple-Choice Questions (Correct options are underlined) 1. The moon always presents the same face to the Earth because a. its rotation period and orbital period are the same. b. the moon was once part of Earth. c. only one side of the moon is illuminated. d. only the side of the moon facing the Earth is illuminated. 2. The mass of an object a. is in no way related to its weight. b. is smaller on the moon. c. determines how fast it will fall. d. is a measure of the amount of matter in the object. 3. Aristotle used which of these observations to support a spherical Earth theory a. The sun rises in the east and sets in the west b. The shadow of the Earth on the moon is round c. The moon has phases. d. The sun is round in the sky. 4. Eratosthenes made what contribution to planetary science? a. An early estimate of the size of the Earth. b. The observation of craters on the moon. c. The discovery of Pluto. d. A determination of the size of the solar system. 5. Which of the following planets was not known to ancient astronomers? a. Earth b. Mars c. Neptune d. Mercury 6. According to Kepler a. planets orbit in circles. b. planets orbit in ellipses. c. the force of gravity is related to the mass of an object. d. the Earth is the center of the solar system 7. P2 = ka3 is a law of planetary motion. Who discovered it? a. Newton b. Copernicus c. Kepler d. Galileo8. Which of the following is not one of Newton’s laws? a. All bodies with mass exert a gravitational force on each other. b. An object tends at rest tends to stay at rest unless acted on by an outside force. c. Each action has an equal and opposite reaction. d. The line joining a planet to the Sun sweeps out equal areas in equal intervals of time. 9. The area of a football field is 5300 yards2. What is the area in cm2 (to two significant figures)? a. 4.9 x 103 cm2 b. 4.9 x 105 cm2 c. 4.5 x 103 cm2 d. 4.5 x 107 cm2 10. Two planets (Jack and Jill) are orbiting the same star. Jack’s radius is twice Jill’s radius, but Jack is only 1/3 as massive as Jill. Which planet has a larger escape velocity? a. Jack b. Jill c. Neither (the velocity is the same) d. Not enough information given We know the formula for escape velocity (call it Vesc) from a planet with a given mass (call it M) and a given radius (call it R): Vesc = √(2GM/R). This formula tell us that planets with larger masses (larger M) have larger escape velocities (larger Vesc). This makes sense because planets with bigger masses have stronger gravity. This formula also tells us that planets with larger radii (larger R) have small escape velocities (smaller Vesc). This also makes sense because a planet's gravity pulls you toward the center of the planet, so the farther you are from the center of a planet (that is, the bigger the R), the less gravity you feel. If you're standing on the surface of a planet, R is just the planet's radius. Jill has a larger mass and a smaller radius. Therefore its escape velocity is greater than Jack's.Section 2: Short Answer Questions. 1. Define escape velocity. Escape velocity is the speed an object must travel to escape from the gravitational pull of another body. 2. Discuss 2 observations by Tycho Brahe that proved the heavens were not unchanging. Be sure to describe the quantitative measurements he used to support his argument. a. Tycho Brahe observed a new star. Since he observed no parallax for the star, he reasoned that the star was part of the celestial sphere and thus the heavens were not unchanging. b. He designed and tested instruments, compiling the most comprehensive planetary observations ever, with a precision of 1°, about 5 times more precise than any previous observations. 3. What is acceleration? What are the SI units? Give the formula for acceleration due to gravity. Acceleration is a measure of the rate at which velocity changes. The SI units for acceleration are m/s2. The formula for acceleration due to gravity is: a = GM/r2 where G is the gravitational constant, M is the mass of the gravitating body and r is the distance from the gravitating body. 4. What was Anaxagoras’ theory about the heavens? Why was this revolutionary? Anaxagoras proposed that the moon shined by reflecting sunlight and that the Sun was bright because it was hot. This was counter to the widely held belief that the celestial bodies were perfect and not made of terrestrial things such as fire.5. Explain why lunar eclipses occur and why we don’t have them every month. Lunar eclipses occur because the moon passes through Earth's shadow as it orbits. Lunar eclipses only occur during a full moon, when the Earth is between the moon and the Sun. Lunar Eclipses do not occur every month because the moon’s orbit is inclined by 5o to the Earth's orbit. Because its orbit is so inclined to the Earth's orbit, the moon does not pass through the Earth's shadow every month. Section 3. Longer-Answer Questions 1. Describe Newton's three laws of motion with an example for each. An object at rest (or moving at constant velocity) will stay at rest (or at constant velocity) unless acted on by an outside force. Example: A ball rolling along a table. Without outside intervention, it will just continue rolling at the same speed. Force equals mass times acceleration (F = ma). Example: The force of gravity on a 60-kg person standing on Earth can be calculated by taking the acceleration of gravity on Earth (9.8 m/s2) and multiplying by the person’s mass (60 kg): F = (60kg)*(9.8m/s2) = 588 kg m/s2 = 588 Newtons Each action has an equal and opposite reaction. Example: When the Earth exerts a gravitational pull on me, I exert the same gravitational pull on the Earth (but, due to the 2nd law, the acceleration felt by the Earth is much smaller than the acceleration I feel). 2. Calculate the escape velocity of a planet with your mass and a diameter equal to your height. Compare this to the value for Earth. Show your work.
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