PHYS 106 Fall 2151 Homework 3 Due: Thursday, 8 Oct 2015 When you do a calculation, show all your steps. Do not just give an answer. You may work with others, but the work you submit should be your own. I expect numeric answers to have a reasonable number of significant figures and correct units. First Question. Go to the Circular Motion Vignette at <http://ivv.rit.edu/cm/1192/>. Circle the letter of your choice or write it on the line provided. (a) Which way did you predict that the bowling ball would need to be hit? A. Mainly along the path. B. At some angle to the path, about halfway between along the path and perpendicular to the path. C. Mainly perpendicular to the path, toward the center of the circle. (b) What did you predict the ball would do when the professor stopped hitting it? A. It continues in its circular path. B. The path stays curved but deviates from the circle. C. It goes straight and abandons its curved course. D. The path curves away from the circle. E. It goes in some other direction. (c) What did you find most helpful in understanding that gravity (which always pulls inward) is required to hold planets and moons in their circular (or elliptical) orbits? A. the class activity B. the video vignette C. both D. neither you knew this from some other class already Please explain your choice briefly. HW3 2151 Page 1/5
Second Question. Use the NAAP Planetary Orbit Simulator at http://astro.unl.edu/naap/pos/pos.html to answer the following questions adapted from the Planetary Orbit Simulator Student Guide (pdf). The study guide and background material are all linked near the bottom of the page at: http://astro.unl.edu/naap/pos/pos.html ----------------------- Answer the following questions after reviewing the Kepler's Laws and Planetary Motion and Newton and Planetary Motion background pages or looking in the text or your class notes. Question 1: Draw a line connecting each law on the left with a description of it on the right. Kepler s 1 st Law Kepler s 2 nd Law Kepler s 3 rd Law Newton s 1 st Law planets move faster when close to the sun planets with large orbits take a long time to complete an orbit only a force acting on an object can change its motion planets orbit the sun in elliptical paths Question 2: When written as P 2 = a 3 Kepler's 3rd Law (with P in years and a in AU) is applicable to (Circle one.) any object orbiting our sun. any object orbiting any star. any object orbiting any other object. Question 4: For a planet in an elliptical orbit to sweep out equal areas in equal amounts of time it must (Circle one.) move slowest when near the sun. move fastest when near the sun. move at the same speed at all times. have a perfectly circular orbit. HW3 2151 Page 2/5
Question 5: If a planet is twice as far from the sun at aphelion than at perihelion, then the strength of the gravitational force at aphelion will be as it is at perihelion. four times as much twice as much the same one quarter as much one half as much Kepler s 2nd Law Use the clear optional features button to remove the 1st Law features. Open the Kepler's 2nd Law tab. Press the start sweeping button. Adjust the semimajor axis and animation rate so that the planet moves at a reasonable speed. Adjust the size of the sweep using the adjust size slider. Click and drag the sweep segment around. Note how the shape of the sweep segment changes, but the area does not. Add more sweeps. Erase all sweeps with the erase sweeps button. The sweep continuously check box will cause sweeps to be created continuously when sweeping. Test this option. Question 12: Erase all sweeps and create an ellipse with a = 1 AU and e = 0. Set the fractional sweep size to one-twelfth of the period. Drag the sweep segment around. Does its size or shape change? Question 13: Leave the semi-major axis at a = 1 AU and change the eccentricity to e = 0.5. Drag the sweep segment around and note that its size and shape change. Where is the sweep segment the skinniest? Where is it the fattest? Where is the planet when it is sweeping out each of these segments? (What names do astronomers use for these positions?) Question 14: What eccentricity in the simulator gives the greatest variation of sweep segment shape? Newtonian Features Important: Use the clear optional features button to remove other features. Open the Newtonian features tab. Click both show vector boxes (on the graph) to show both the velocity and the acceleration of the planet. Observe the direction and length of the arrows. The length is proportional to the values of the vector in the plot. HW3 2151 Page 3/5
Begin with the Earth, but set the eccentricity to be 0. Question 19: (a) The acceleration vector is always pointing towards what object in the simulator? (b) The direction of the velocity is along the: (Circle one.) radius of the orbit tangent to the orbit between the radius and the tangent (c) The angle between the velocity and acceleration is always equal to what value? (d) Describe the value of the velocity as the zero eccentricity Earth orbits the Sun. Question 20: Create an orbit for Planet X with a = 5 AU and e = 0.5. For each marked location on the plot on the back of the page indicate (a) whether the velocity is increasing or decreasing at the point in the orbit (by circling the appropriate arrow) and (b) the angle! between the velocity and acceleration vectors. Note that one (at the top) is completed for you. Question 21: (a) The acceleration vector is always pointing towards what object in the simulator? (b) Where do the maximum and minimum values of velocity occur in the orbit? max? min? (c) What is the angle between the velocity and the acceleration when the velocity is: max? min? Question 22: What can you say about the angle between the velocity and acceleration vectors when the planet is (a) speeding up? (b) slowing down? HW3 2151 Page 4/5
61º 6161 Astronomers refer to planets in their orbits as forever falling into the sun. There is an attractive gravitational force between the sun and a planet. By Newton s 3 rd law it is equal in magnitude for both objects. However, because the planet is so much less massive than the sun, the resulting acceleration of the planet (from Newton s 2 nd law) is much larger. While Kepler s laws are largely descriptive of what planet s do, Newton s laws allow us to describe the nature of an orbit in fundamental physical laws! HW3 2151 Page 5/5