In this activity, we will make use of the \"my solar system\" simulator locateed
ID: 803646 • Letter: I
Question
In this activity, we will make use of the "my solar system" simulator locateed online at
http://phet.colorado.edu/sims/my-solar-system/my-solar-system_en.html
1. When the simulator is first brought up, you will see a large yellow object in the middle, and smaller pink object off to the right with a large arrow labled V. Further to the rigth, you will see a pull-down menu wwith different preset scenarios as well as a control box below the pull-down menu. at the bottom of the simulator, there are radio buttons to manually choose the number of objects for your simulation, and boxes to enter initial conditions. take a few minutes to familiarize yourself with how the simulator works and does the calculations.
2. for the remainder of this activity, make sure that the following options in the control box are checked: system centered, show traces, show grid.
3. As described in the help, the units employed by the simulator are arbitrary. to avoid entering in enormous numbers into the boxes, we will employ non-SI units. For mass, we will use the millisun, which happens to be exactly equal to one-thousadth of the mass of the sun. For distances, we will use the centiau, which happens to be exactly equal to one-haundredth of the distance between the sun and earth. For time, we will use the sixmonth, which happens to be exactly equal to half of teh earth's orbital period. For reference, convert the masses of the sun, earth, and mars, the sun-earth distance, the mars-sun distance, the orbital periods for earth and mars, as well as the velocities of earth and mars (your answers from number 6 of the previous activity) into this new strange system:
4. in the simulator, choose the radio button at the bottom indicating three bodies. Manually enter in the numbers from your table above as the initial conditions. For distances and velocities, the simulator requires integers - round appropriately. The simulator uses a standard Cartesian coordinate system, with the origin at the big yellow Sun, positive x to the right, and positive y straight up. Enter the distances as the starting x position , and 0 for teh y position. ( In that case, how should you enter the velocities?) Start the simulation and verify that you get circular orbits.
5. Now we will add another body to repersent a satellite that NASA wishes to send to Mars. Choose the radio button for four bodies, and then re-enter the information for the Sun, Earth, and Mars. For the mass of the satellite, enter in a tenth of the mass of mars . this is about the mass of the moon. (we didn't say which satellite we were sending!) enter in the same x position as the earth, but enter 2 for the y position. (the simulator will complain if we try to put two objects in the same place.) experiment with x and y componentsof the initial velocity to send the satellite from the orbit of earth to the orbit of mars. (Note: this will not be a circular orbit.) Try to use the smallest velocity possible relative to earth (i.e., save fuel!). If you have overshot Mars' orbit, try to change either the magnitude or direction of your velocity vector. When you have finished , enter your starting values here
V(x)= ___________ centiau/sixmonth V(y)=_________________centiau/sixmonth
6. What is the magnitude of the satellite's starting velocity in normal, healthy SI units?
V=___________ m/s
7. Chamces are, when your satellite got to the orbit of Mars, Mars wasn't actually there to welcome it. to six this, change the starting position of Mars as well as the x and y components of the velocity. remember, the distance between the Sun and Mars and the magnitude of Mars' orbital velocity should still be what you entered in the table above. Hence, you should only need to experiment with the x component of the position. All other parameters ( y component of position, x and y components of the velocity) will be determined by the geometry of having a circular orbit! use the picture you drew in activity 2 to help determine how those three parameters are related to the x position and the numbers from your table. (write the correct expression that is a function of x-position.)
Y=
V(x)=
V(y)=
8. What are the optimal initial setting for Mars?
X=________centiau Y=_________centiau
V(x)=___________centiau/sixmonth V(y)=__________centiau/sixmonth
Explanation / Answer
Mass of earth=5.972*10^24kg
Velocity of earth= distance/ orbital period
Distance=100 centiau
orbital period=2/per six month
Velocity=100/2=50centiau/per six month
Mass of mars=6.39*10^23 kg
Distance from sun=227.9 million km
Since 1 half of the distance ( centiau) between earth and sun=150/2=75 million km
therefore 227.9/75= 3.03 centiau
orbital period= 687 days=3.81/ per six month
orbital velocity of mars=3.03/3.81
=0.79 centiau/per six month