My Solar System Name Period Introductien: Every physics student has had a lot of experience with the force of gravity. Unfortunately, their experience is limited to the interaction between a very large object, the Earth, and much smaller objects that are very close to it. This represents a small range of the possibilities. Software simulations of gravitational force allow physics students to explore a variety of other gravitational interactions between objects. These activities are designed to be used with the My Solar System simulation that can be found on the Physics Education Technology (PRET) website at the University of Colorado at Boulder. Directions: Go to the My Solar System simulation on the PRET website. Select the Lab option. Carefully follow the instructiens for each activity below. Answer the questiens, record your results, and use the simulation to check your work before going on to the next activity, The simulatien can be found at the URL below or search "phef my selar https://phet.colorado.edu/sims/html fmy-solar-system/latest/my-solar-system_en.html| Activity 1: Look over the start screen. The simulation controls and settings are on the right. Check the Path and Grid boxes. The simulation inputs are at the bottom left. Check the More Data box. Click Play (*) and write down at least 2 cbservations about this simulation below. Mass (10% kg) Position (AU) Velocity (km/s) v, Activity 2: Click Reset (wl )in the upper right. Itwill x Y VMY save you work and frustration if you always click QO [3000 00] [00] 0] o] Reset before changing inputs. Configure the Mass, [ ] 300 20][00] [oo][ o] Position, and Velocity of Body 1 (yellow) and Body 2 (magenta) as shown at right. Write down your prediction for the motion of each body BEFORE clicking Play. Body 1 (Yellow) motion: Body 2 (Magenta) motion: Q1: Were your predictions correct? Explain, Q2: Click Reset (). Change Body 2's mass to 0.1 kg x 102, Click Play (). What is different about the motion? Why do you think this is? Q3: In what direction (x or y) should Body 2's initial velecity be so that it doesn't hit Bedy 17 Q4: Zoom out by clicking E upper left twice. Click Reset (#!). From now on you need to remember to click Reset on your own. Give Body 2 an initial v velocity of 10 km/s. What happens when you click Play ()7 Increase Body 2's y velocity in increments of 0.5 km/s until it doesn't touch Bedy 1. At what velocity does this first happen? What is the shape of the resulting orbit? (5: Continue to increase Body 2's velocity until the orbit has a circular shape. Use the grid to decide if it is a circle, your eyes can be deceived! When it is close, adjust it by increments of 0.1 km/s until it is as close to a perfect circle as you can get. Check the Values box and observe the displayed speed. If the orbit is circular, speed will be constant. There might be small variations because of the accuracy of the simulation. What velocity resulted in a circle? Q6: Assuming a perfectly circular orbit. would the velocity of Body 2 be constant? Explain. Activity 3: Draw a free-bedy diagram of Bedy 2 (m) in its circular orbit about Body 1 (M) below. Using Newton's Second Law, the Law of Gravity, and the equation for centripetal acceleration, derive an expression for the Universal Gravitational Constant, G. Using the values from Body 2's orbit, solve for the value of G used in the simulation. Show ALL your work below. Record your resultin the units of the simulation: AU, km, s, and kg 1025, G= Q7: In metric units, G = 6.67 % 101! m3/kgs Given that 1 AU = 1.496 x 101! m, convert your G wvalue to the units of m?#/kgs?. It should be close to 6.67 x 10-1! m#/kgs. Show all your work. (8: Rearrange your equation for G to solve for the speed of an object in a circular orbit. Using this equation, solve for the speed required for Body 2 to be in a circular orbit about Body 1 witha 4 AU radius. Use G = 4.46 AUkm?/skgx 102 for the rest of the lab. Show all your work below. Activity 4: Zoom out all the way by clicking &, Change Moss (0% kg) Position{AU) Velocity ) the number of bodies to 3 by clicking Bodies arrow in o 2 L L L 300.0 ] oo oo 0.0 0.0 lower left. Input the values shown at right. usingyour 5 s01] z0] [00] 00 7 wvalues for Y from Q5 and Q8. Using your equation from o [=o1 (08, the fact that speed is the distance over time, and the equation for the circumference of a circle, derive an equation for the period of an objectin a circular orbit in terms of G, M, and r. Simplify your equation and show all your work below. 40] [on 0.0 T Q9: Using your equation for period from above, predict the ratio of Body 3's (cyan) period to Eody 2's (magenta) period. Use the simulation to verify your result. Show all your work below. It is easier to measure the period if you click Pause just as a body completes an orbit. Activity 5: Add velocity to Body 2 (magenta) in increments of 2 km/s until it reaches a maximum radius of about 8 AU on the left side of its orbit. You can select the Fast option to make this go quicker. Change the velocity in increments of 0.1 km/s until it is as close to 8 AU as you can get. 'Write the velocity that achieved a max radius of 8 AU below. Q10: Click Reset (ml] then Play () and observe Body 2 (magenta) carefully during the first half of its orbit. What happens to its distance from Body 1 (yellow) as it travels this part of the orbit? 'What happens to its speed? Q11: Observe Body 2 (magenta) carefully during the last half of its orbit. What happens to its distance from Body 1 (vellow) as it travels this part of the orbit? What happens to its speed? Q12: For an elliptical orbit like that travelled by Body 2. the point closest to the central body (Bedy 1) is known as the periapsis, the farthest is the apoapsis. Write down periapsis, apoapsis, or same for the location of each quantity listed below for body 2 in an elliptical orbit. Max Velocity Max Kinetic Energy. Max Potential Energy Max Force. Max Angular Momentum Max Mechanical Energy. w Q13: Use censervation of angular momentum and the equation for the angular momentum of a particle to predict the speed of Body 2 at apoapsis. Show all your work below. Use the simulation to find the speed of Bedy 2 at apoapsis and compare it te vour prediction. Find the % error. Activity 6: Select the "Sun and Planet\" preset from the drop-down menuin - ~ the upper right. Click Start and observe the motion of Body 1. In this ' system, the mass of the small bedy is not insignificant relative to the larger I' body. Both bodies orbit their center of mass. In this activity you will create . anew 2-body system where each body erbits in a circle about the center v - of mass as shown in the figure at right. The radius of each orbit is equal to '\\ l S the distance between the center of the body and the center of mass. Body Moo -t 1 has a mass of 300 kg x 10 (m1). Body 2 has a mass of 75 kg x 1028 T (m2). Their centers are separated by 4 AU Calculate the distance m1 is from the center of mass, This distance will be the radius of the smaller circular orbit. What is the radius of mz's larger orbit? Show all your work below., Q14: Each body will have the same circular orbit period. Knowing this, which body will have the greatest speed? Which body will have the greatest angular speed? Explain. Draw a free-body diagram of m below. Using Newton's Second Law, the Law of Gravity, and the equation for centripetal acceleration, derive an expression for the speed of my. Use this equation to calculate the speed of mi, Show all your work below. Hint: The quantity r used in the gravitation equation is the distance between the centers of 2 objects. The quantity r in the centripetal acceleration equation is the radius of the circle. Unlike in Q8, these two quantities are NOT the same because the mass of body 2 is significant. Derive an equation for the speed of mz using the same method used for my. Using this equation, calculate mz's speed. Show all your work below. Set up this 2-body simulation using your center of mass and velocity calculations. Refer to the figure at the top of the previcus page to help set the Positions. Both mjand mz should trace the path shown by the dotted lines. AL't:iviI_:g. 7: Input the values shown at right. This. puts Mass (10%kg) P ': - L:u' v:.'?ew\"'"::] Body 2 just above the surface of Body 1 and moving o 3000 a0] [20 00 away at a large speed. Write down your prediction for the ? =01 a7 [20 900 o0 motion of Body 2 below before you click Play. I Q15: Was your prediction correct? Increase Body 2's x velocity in increments of 1 km/s. At what velocity does Body 2 leave the screen? Setting the simulation to Fast makes this go quicker. There is a minimum velocity that will result in Body 2 never returning. This is called escape velocity. Using the fact that an object on an escape trajectory has zero total energy. use conservation of energy to derive an equation for escape velocity for an initially stationary object. Use your equation to determine its x velocity so that Body 2 escapes Body 1. The result should be a little larger than the value you found in Q15. Show your work below. One More Activity on Back 5 Activity 8: Conservation of energy can be used to predict Mass (107 kg) Position (AU} Velocity v'll X 1 'y the maximum separation of 2 objects moving apart with o [0 0] [28] 346] [ 60 an initial velocity. Input the values shown at right. Use e (o] (z0] [240] [ o0) conservation of energy to predict their greatest separation Draw a sketch below showing their initial and final pesitions. Verify your prediction by clicking Play. Click Pause when Body 1 and Body 2 are at their greatest separation. This is easier if the simulation is in Normal or Slow mode. Meazure the distance between their centers using the Measuring Tape. Find the percent error. Show all your work below. Congratulations! You have completed your tasks. Try some of the other presets in the drop-down menu favorite? Mine is the Four Star Ballet