Physics Independent Project ... 2020/06/08  · Mars, it is critical to take into account...

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Transcript of Physics Independent Project ... 2020/06/08  · Mars, it is critical to take into account...

  • Student Name: _______________________ School Name:_____________________ Teacher Name:_____________ 

    Physics Independent Project   Hello Students,    This resource packet includes a project that you can work on independently at home. You should  also have project packets for some of the other courses you are enrolled in. These projects are  standards-aligned and designed to meet the Remote Learning instructional minutes guidelines by  grade band.    

    High School Physics: What is the best Earth and Mars orientation to  launch a spaceship to get to Mars?  Estimated Time  ~225 minutes 

    Grade Level  Standard(s) 

    HS PS2-4​ Use mathematical representations of Newton’s Law of Gravitation  and Coulomb’s Law to describe and predict the gravitational and  electrostatic forces between objects.    HS ESS1-4​ Use mathematical or computational representations to predict the  motion of orbiting objects in the solar system 

    Caregiver Support  Option 

    Caregivers can support by providing push pins, string, cardboard, and a  ruler. They can also assist with drawing of circles and with the mathematical  calculations. 

    Materials Needed  Paper and Pencil, Calculator, ~30 cm Length of String, Push Pins, Cardboard, Ruler 

    Question to Explore  What is the best Earth and Mars orientation to launch a spaceship to get to Mars? 

    Student Directions  Directions are given throughout the packet. Please record your responses on a separate sheet of paper unless otherwise indicated.    Introduction Reading Adapted From: ​The Mars 2020 rover has a new name: Perseverance  Devin [email protected], March 5, 2020    Investigation 1 Introduction Adapted From: ​Kepler's Laws and Newton's Laws​, Mount Holyoke  College, AST 223/23 Planetary Science Course Page, by Darby Dyar.    Investigation 2 Activity Adapted From:   Let's Go to Mars! Calculating Launch Windows   Education.com - Orbital Eccentricity | Science Project  Science Friday: Scale Solar System Orbits—And Satellites!       

    https://www.nextgenscience.org/sites/default/files/evidence_statement/black_white/HS-PS2-4%20Evidence%20Statements%20June%202015%20asterisks.pdf https://www.nextgenscience.org/sites/default/files/evidence_statement/black_white/HS-ESS1-4%20Evidence%20Statements%20June%202015%20asterisks.pdf https://techcrunch.com/2020/03/05/the-mars-2020-rover-has-a-new-name-perseverance/ https://www.mtholyoke.edu/courses/mdyar/ast223/orbits/orb_lect.html https://www.jpl.nasa.gov/edu/teach/activity/lets-go-to-mars-calculating-launch-windows/ https://www.education.com/science-fair/article/orbital-eccentricity/ https://www.sciencefriday.com/educational-resources/scale-solar-system-orbits-and-satellites/

  • Student Name: _______________________ School Name:_____________________ Teacher Name:_____________  Introduction    The next NASA rover to go to Mars has shed its code name  and assumed a new one, sourced from the ingenuous  youth of our nation. Keeping with the tradition of using  virtues as names, the Mars 2020 rover will henceforth be  known as “Perseverance.”    This particular virtue was suggested by Alexander Mather, a  middle-schooler in Virginia. He and some 28,000 other kids  proposed names in an essay contest last year. The final  nine contenders were: Endurance, Tenacity, Promise, Vision, Clarity, Ingenuity, Fortitude, Courage  and, of course the winner, Perseverance.    “Like every exploration mission before, our rover is going to face challenges, and it’s going to make  amazing discoveries. It’s already surmounted many obstacles to get us to the point where we are  today,” said Thomas Zurbuchen, NASA’s associate administrator of the Science Mission Directorate, in  a news release. “Alex and his classmates are the Artemis Generation, and they’re going to be taking  the next steps into space that lead to Mars. That inspiring work will always require perseverance.” 

      NASA scientists working on this mission have not only had to design and  name the rover, but they have also needed to figure out the exact  date in the near future that will be best to launch the spacecraft that  will carry the Perseverance rover to Mars. When planning a launch to  Mars, it is critical to take into account the relative positions of Earth  (inner planet) and Mars (outer planet) at the time of launch. In  addition, sending a mission to Mars is an incredibly expensive task that  requires enormous amounts of fuel, so NASA pays close attention to  choosing the best route to conserve fuel cost. As a result, to help the 

    NASA scientists, your task in this packet is to figure out the answer to the driving question, ​“What is the  best Earth and Mars orientation to launch a spaceship to get to Mars?”   

    1. The five diagrams below show five different orientations of Earth and Mars that the NASA team  is debating on as the best time point to launch a spacecraft to Mars. Here is some key  information about the system: 

    ● Earth’s orbital radius is smaller than Mars’s, which means in the diagrams below, Earth is  on the inner orbit and Mars is on the outer orbit. 

    ● Earth and Mars orbit the Sun counterclockwise (in this diagram), as indicated by the  arrows on each planet. 

  • Student Name: _______________________ School Name:_____________________ Teacher Name:_____________ 

    Option A  Option B  Option C  Option D Option E

         

      2. On each of the five diagrams above, draw the path that you think a spaceship would take to 

    travel from Earth to Mars. Be sure to indicate where you think Mars would be when the rocket  arrives there. Record your response on a seperate sheet of paper. 

      3. Which of the five options do you think would be the best orientation of Earth and Mars to 

    launch the spaceship? Why? Record your response on a seperate sheet of paper.    Investigation 1: What role does gravity play in picking the best launch orientation?    To help us figure out the best orientation of Earth and Mars to  launch a spaceship to Mars, it will first help us to figure out the  different ways that Earth and Mars orbit the Sun.    The Earth and Mars have been orbiting the Sun since the  beginning of the solar system about 4.5 billion years ago. But  why do they stay in these defined orbits and why don’t they  just fly off into space? The reasons are complicated but the  first good explanation was provided by one of the greatest  scientists ever, Isaac Newton, who lived in England about 300  years ago. Newton realized that the reason the planets orbit  the Sun is related to why objects fall to Earth when we drop  them. The Sun's gravity pulls on the planets, just as Earth's  gravity pulls down anything that is not held up by some other  force and keeps you and me on the ground. Newton’s discovery that the force of gravity that acts  on an object on Earth as well as the planets orbiting the Sun led to him to formulate the Universal Law  of Gravitation, which is usually stated as an equation:   

    F g = G r2 M M1 2  

      where F​g​ is the attractive gravitational force between two objects of mass M​1​ and M​2​ separated by a  distance r. The constant G in the equation is called the Universal Constant of Gravitation. The value of  G is 6.67 X 10​-11​ meters​3​ kilograms​-1​ seconds​-2​.   

  • Student Name: _______________________ School Name:_____________________ Teacher Name:_____________  Interestingly, Newton’s Law of Gravitation can also be used to figure  out the velocity of a planet in its orbit around the Sun, if you assume  the orbit of a planet is circular. When you combine Newton's Law of  Gravitation and circular acceleration, you can derive the relationship  between velocity of a planet, its mass, and the radius of its orbit. You  get the equation shown below:   

    v = √ rGm1    

    4. To help us figure out the relative motion of the Earth and Mars, complete the table below to  find the force of gravitational attraction between the Sun and each planet as well as the  orbital velocity of each planet. Complete your work on a seperate sheet of paper. 

     

    Planet  Planet Mass  (kg) 

    Mass of the  Sun   (kg) 

    Orbit Radius   (m) 

    F​g​ (N)    F g = G r2 M M1 2  

    Orbital Velocity  (m/s) 

    v = √ rGm1   Venus  4.87 x 10​24  1.989 × 10​30  1.082 x 10​11  5.522 × 10​22  3.5×10​4  

    Earth  5.97 x 10​24  1.989 × 10​30  1.496 x 10​11     

    Mars  0.642 x 10​24  1.989 × 10​30  2.279 x 10​11     

    Jupiter  1898 x 10​24  1.989 × 10​30  7.786 x 10​11     

    Saturn  586 x 10​24  1.989 × 10​30  14.34 x 10​11     

      5. What patterns or relationships do you see in the data? Consider discussing: 

    a. How the orbital velocity relates to the orbital radius.  b. How the gravitational force relates to the orbital radius. 

    6. Using the data above, predict the approximate relative positions of Earth and Mars after 3  months (¼ of an Earth orbit) and 6 months (½ of an Earth orbit). 

    Hypothetical Starting  Orientations 

    Orientation at 3 Months  Orientation at 6 Months 

     

       

     

  • Student Name: _______________________ School Name:_____________________ Teacher Name:_____________  7. Explain your two predictions on a separate sheet of paper. Cite evidence from the data table 

    in Question 4 to support your predict