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ON LINE LAB 04 Nebraska Astronomy Applet Project Student Guide to the Planetary Orbit Simulator Background Material Answer the following questions after reviewing the “Kepler's Laws and Planetary Motion” and “Newton and Planetary Motion” background pages. Draw a line connecting each law on the left with a description of it on the right. Kepler’s 27¢ Law Kepler’s 3r Law ‘Question 1: When written as P? = a® Kepler's 3rd Law (with P in years and a in AU) is applicable to ... only a forceacting on an object can change its matio. planets move faster when close to the sun planets orbit the sun in dliptical paths planets with large orbits take 2 ong time to complete an orbi a) any object orbiting our sun. Lab 4 NAAP — Planetary Orbit Simulator 1/8 b) any object orbiting any star. @any object orbiting any other object. L — Scanned with CamScanner

Question 2: The ellipse to the right has an eccentricity of about ... Question 3: For a planet in an elliptical orbit to “sweep out equal areas in equal amounts of time” it must ... a) move slowest when near the sun. @move fastest when near the sun. d) have a perfectly circular orbit. Question 4: 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. a) four times as much b) twice as much c) the same d) one halfas much @onc quarter as much Kepler's 1st Law If you have not already done so, launch the NAAP Planetary Orbit Simulator. e Open the Kepler’s 1 Law tab if it is not already (it’s open Tip: You can change by default). the valuc of a nlidcf by o Enable all 5 check boxes. clicking on the slider bar or by entering a o The white dot is the “simulated planet”. One can click on | number in the value box. it and drag it around. e Change the size of the orbit with the semimajor axis slider. Note how the background grid indicates change in scale while the displayed orbit size remains the same. o Change the cccentricity and note how it affects the shape of the orbit. Lah d NAAP - Planetary (Whit Simulatar 2/8 Scanned with CamScanner

Be aware that the ranges of several parameters are limited by practical issues that occur when creating a simulator rather than any true physical limitations. We have limited the semi-major axis to 50 AU since that covers most of the objects in which we are interested in our solar system and have limited eccentricity to 0.7 since the ellipses would be hard to fit on the screen for larger values. Note that the semi-major axis is aligned horizontally for all elliptical orbits created in this simulator, where they are randomly aligned in our solar system. o Animate the simulated planet. You may need to increase the animation rate for very large orbits or decrease it for small ones. o The planetary presets set the simulated planet’s parameters to those like our solar system’s planets. Explore these options. Question 5: For what eccentricity is the secondary focus (which is usually empty) located at the sun? What is the shape of this orbit? The shape is a circle E=0 Question 6: Create an orbit with a =20 AU and ¢ = 0. Drag the planet first to the far left of the ellipse and lhmto the far right. What are the values of r; and r at these locations? n (AU)—L r2(AU) 20 20 Far Left o Question 7: Create an orbit witha=20 AU and e =0.5. Drag the planet first to the far left of the ellipse and then to the far right. What are the values of r) and 2 at these locations? N LN N s [5—[—] Question 8: For the ellipse with a =20 AU and e = 0.5, can you find a point in the orbit where rj and r; are equal? Sketch the ellipse, the location of this point, and ry and r2 in the At this points rl and 12 are equal Lab 4 NAAP — Planetary Orbit Simulator 3/8 space below. Scanned with CamScanner

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Question 9: What is the value of the sum of ry and r> and how does it relate to the ellipse properties? Is this true for all ellipses? R1+R2=20AU+20AU=40AU=2A and is true for all ellipses. Question 10: It is easy to create an ellipse using a [ loop of string and two thumbtacks. The string is first stretched over the thumbtacks which act as foci. The string is then pulled tight using the pencil which can then trace out the ellipse. Assume that you wish to draw an ellipse with a semi-major axis of a =20 cm and ¢ = 0.5. Using what you have learned earlier in this lab, what would be the appropriate distances for a) the separation of the thumbtacks and b) the length of the string? Please fully explain how you determine these values. C=ae gp you multiply c by 2 to get 2e=2ae= 2*20*.5=20cm The length of string is r1+r2+2c so 20+20+20=60 cm Kepler's 2nd Law o Use the “clear optional features” button to remove the Ist Law features. e Open the Kepler's 2nd Law tab. o Press the “start sweeping” button. Adjust the semimajor axis and animation rate so that the planet moves at a reasonable speed. o Adjust the size of the sweep using the “adjust size” slider. o Click and drag the sweep segment around. Note how the shape of the sweep segment changes, but the area does not. e Add more sweeps. Erase all sweeps with the “erase sweeps” button. e The “sweep continuously” check box will cause sweeps to be created continuously when sweeping. Test this option. Fale ANAAD Dlcstoens Abiis Cimmeilte 410 Scanned with CamScanner

Question 11: 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? No, the size and shape stay the same throughout Question 12: 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?) when it’s farthest from the sun is skinniest, aphelion. Fattest at perihelion when it’s closest to the sun. Question 13: What eccentricity in the simulator gives the greatest variation of sweep segment shape? E=17 Question 14: Halley’s comet has a semimajor axis of about 18.5 AU, a period of 76 years, and an eccentricity of about 0.97 (so Halley’s orbit cannot be shown in this simulator.) The orbit of Halley’s Comet, the Earth’s Orbit, and the Sun are shown in the diagram below (not exactly to scale). Based upon what you know about Kepler’s 2* Law, explain why we can only see the comet for about 6 months every orbit (76 years)? @ > The comet is visible to us for approximately six months during each orbit, which spans a period of 76 years. This visibility coincides with the comet being in its closest proximity to the sun. Additionally, when the comet is closest to the sun, it travels at its highest speed. Scanned with CamScanner

Kepler's 3 Law o Use the “clear optional features” button to remove the 2nd Law features. o Open the Kepler's 3rd Law tab. Question 15: Use the simulator to complete the table below. 1 1.00 I 017 1 1 1.88 1.52 | 093 ijﬂuo 354 4.62 2.77 | 0.08 213 213 50.7 13.7 | 0.38 2570 2570 Question 16: As the size of a planet’s orbit increases, what happens to its period?_ As the size of the orbit increases the period goes up 3square root p(2) Question 17: Start with the Earth’s orbit and change the eccentricity to 0.6. Does changing the eccentricity change the period of the planet? Eccentricity doesn’t change the period of the planet. Newtonian Features o Important: Use the “clear optional features” button to remove other features. o Open the Newtonian features tab. « Click both show vector boxes 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. Question 18: The acceleration vector is always pointing towards what object in the simulator? Toward the sun Question 19: Create an ellipse witha=5 AU and e = 0.5. For each marked location on the plot below indicate a) whether the velocity is increasing or decreasing at the point in the Lab 4 NAAP — Planetary Orbit Simulator 6/8 Scanned with CamScanner

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orbit (by circling the appropriate arrow) and b) the angle 0 between the velocity and acceleration vectors. Note that one is completed for you. Lle=61° . ;) 0=63° 1 |o=s0°, i : 0=80°, 100° )g) 0=100° _/ 9 115° T@ 0=118° Question 20: Where do the maximum and minimum values of velocity occur in the orbit? Maximum velocity 90 degrees left Minimum velocity 90 right Question 21: Can you describe a general rule which identifies where in the orbit velocity is increasing and where it is decreasing? What is the angle between the velocity and acceleration vectors at these times? _When the distance is increasing it is speeding up, when decreasing it is slowing down. n the planet near the stars it speeds up to 90 and then slows down aﬂcr_l_l_passcs 90. Scanned with CamScanner