Satellite Motion - Complete Toolkit

Objectives

1. State and explain the meaning of Kepler’s three laws of planetary motion.
2. Explain the reason that a satellite can be thought of as a projectile that falls around the Earth instead of into it; and to compare and contrast a circular orbit with an elliptical orbit in terms of the force, acceleration and velocity vectors.
3. Use equations to calculate the orbital speed, orbital acceleration and orbital period for a satellite that orbits a central body of known mass a known distance away.
4. Discuss the meaning and the cause of weightlessness and to explain why an orbiting astronaut would experience weightless sensations.
5. Use an energy analysis to explain both the changes in speed and the constant speed of a satellite in an elliptical and a circular orbit.

 

Readings from The Physics Classroom Tutorial

1. The Physics Classroom Tutorial, Circular and Satellite Motion Chapter, Lesson 4

 

Interactive Simulations

1. Orbital Motion
   
   The Orbital Motion Interactive simulates the elliptical motion of a satellite around a central body. The eccentricity of the orbit can be altered. Velocity and force vectors are shown as the satellite orbits. The Physics Classroom has prepared a classroom-ready activity for use by teachers with their classes.
   
   
   
   
   
    
2. Open Source Physics:  Kepler System Model
   
   This robust model will let your students visualize all three of Kepler's Laws. The First and Second Law are especially well-modeled for the beginner, mostly because of the array of tools for viewing. You can show the planet's orbital plane, view the elliptical plane, trace orbits of both Earth and one other chosen planet, show a line-of-sight vector. To explore the Third Law, you can set your own parameters for a user-defined planet. All the computational data was taken from the National Space Science Data Center's fact sheets. The model provides two windows -- one simulates the Sun with Earth and one other planet orbiting; the second shows the view of Sun and Planet against the background stars as see from Earth.
   
   
   
   
    
3. Open Source Physics:  Newton’s Mountain Model
   
   As Newton pondered, what would happen if you launched a projectile from a VERY tall mountain on Earth? This HTML sim lets you explore the idea of Newton's Mountain. The model is based on the diagram taken from Newton's "A Treatise on the System of the World", found in the Principia. Newton concluded that a projectile launched horizontally with sufficient speed would orbit Earth, rather than crashing back to the surface. You can set initial speed and launch angle, allow the projectile to pass through Earth, or designate Earth as a point mass.
   
   
   
   
    
4. The Physics Interactives: Elevator Ride
   
   The Elevator Ride Interactive is a simulation depicting the forces acting upon an elevator rider while ascending and descending. The emphasis on the Interactive is on communicating the sensations of weightlessness and weightiness experienced by a rider. The Physics Classroom has prepared a classroom-ready activity for use by teachers with their students.

 

Background Information on Space Flight

Videos

Animations

 

Labs and Investigations

Video Analysis Exercise

Elsewhere on the Web

 

Minds On Physics Internet Modules:

The Minds On Physics Internet Modules are a collection of interactive questioning modules that target a student’s conceptual understanding. Each question is accompanied by detailed help that addresses the various components of the question.

1. Circular Motion and Gravitation, Ass’t CG8 -  Satellite Motion
2. Circular Motion and Gravitation, Ass’t CG9 -  Weightlessness
3. Circular Motion and Gravitation, Ass’t CG10 -  Kepler's Laws of Planetary Motion

 
 
 

Concept Building Exercises:

1. The Curriculum Corner, Circular Motion and Gravitation, Satellite Motion
2. The Curriculum Corner, Circular Motion and Gravitation, Weightlessness
3. The Curriculum Corner, Circular Motion and Gravitation, Kepler's Laws of Planetary Motion

 


 

Problem-Solving Exercises:

1. The Calculator Pad, ChapterGoesHere, Problems #19 - #27
   
   Link: http://www.physicsclassroom.com/calcpad/circgrav/problems

 

 

Science Reasoning Activities:

1. Kepler's Law of Harmonies
   
   Link: http://www.physicsclassroom.com/reasoning/circularmotion

 

Common Misconception:

1. Satellites as Projectiles
   
   Students at first find it difficult to believe that artificial satellites are projectiles. They figure that there must be a force other than gravity acting upon them. While such satellites may on occasion use thrust to fine-tune their orbits, they are essentially projectiles that fall towards the Earth relative to their inertial path without ever getting any closer to the earth. When provided the logic behind this concept, they tend to buy in to the essential nature of satellite motion.
    
   
    
2. Causes of Weightlessness
   
   Ask a student why astronauts feel weightless and you will undoubtedly hear the response that there is no gravity acting upon them. A good deal of poor word choice for numerous years has likely contributed to this misconception. References to "microgravity" and "zero-gravity" may not be the best choice of terms to describe the gravitational conditions of orbiting astronauts as students assign different meaning to these terms as was intended by those who use them. The result is often some very strong conceptions about what is meant by weightlessness. It is important to explain to students that weightlessness does not result when there is no gravity force but rather results when the only force present is the gravity force.

 


 


 

Standards:

A. Next Generation Science Standards (NGSS)
 

• Forces and Motion HS-PS2-4:  Use mathematical representations of Newton’s Law of Gravitation to describe and predict the gravitational forces between objects.
• Forces and Motion  HS-PS2-2:  Use mathematical representations to support the claim that the total momentum of a system of objects is conserved when there is no net force on the system.
• Energy  HS-PS3-1:  Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known.

• Forces and Motion-Types of Interactions    HS-PS2.B.i     Newton’s Law of Universal Gravitation and Coulomb’s Law provide the mathematical models to describe and predict the effects of gravitational and electrostatic forces between objects.  
• Forces and Motion-Types of Interactions     HS-PS2.B.ii   Forces at a distance are explained by fields (gravitational, electric, and magnetic) permeating space that can transfer energy through space. Magnets or electric currents cause magnetic fields; electric charges or changing magnetic fields cause electric fields.
• Forces and Motion    HS-PS2.A.ii    Momentum is defined for a particular frame of reference; it is the mass times the velocity of the object.
• Forces and Motion    HS-PS2.A.iii    If a system interacts with objects outside itself, the total momentum of the system can change; however, any such change is balanced by the changes in the momentum of objects outside the system.
• Conservation of Energy    HS-PS3.B.i    Conservation of energy means that the total change of energy in any system is always equal to the total energy transferred into or out of the system.
• Conservation of Energy    HS-PS3.B.ii    Mathematical expressions, which quantify how the stored energy in a system depends on its configuration and how kinetic energy depends on mass and speed, allow the concept of conservation of energy to be used to predict and describe system behavior.
• Relationship Between Energy and Forces    HS-PS3.C.i   When two objects interacting through a field change relative position, the energy stored in the field is changed.

• High School-ETS1.A.i      When evaluating solutions it is important to take into account a range of constraints including cost, safety, reliability, and aesthetics and to consider social, cultural, and environmental impacts.
• High School-ETS1.A.ii   Both physical models and computers can be used in various ways to aid in the engineering design process. Computers are useful for a variety of purposes, such as running simulations to test different ways of solving a problem or to see which one is most efficient or economical; and in making a persuasive presentation to a client about how a given design will meet his or her needs. 

• High School:  The significance of a phenomenon is dependent on the scale, proportion, and quantity at which it occurs.

• High School: When investigating or describing a system, the boundaries and initial conditions of the system need to be defined and their inputs and outputs analyzed and described using models.
• High School:  Models can be used to predict the behavior of a system, but these predictions have limited precision and reliability due to the assumptions and approximations inherent in models. 

• High School:  Scientific knowledge is based on the assumption that natural laws operate today as they did in the past and they will continue to do so in the future.
• High School:  Science assumes the universe is a vast single system in which basic laws are consistent.
• High School:  Science assumes that objects and events in natural systems occur in consistent patterns that are understandable through measurement and observation.

• High School:  Analyze data using tools, technologies, and/or models (e.g., computational, mathematical) in order to make valid and reliable scientific claims

• High School:  Develop and use a model based on evidence to illustrate the relationships between systems or between components of a system.  (Strong alignment)
• High School:  Use a model to provide mechanistic accounts of phenomena.  (Strong alignment)

• High School:  Plan and conduct an investigation individually and collaboratively to produce data to serve as the basis for evidence.
   

• High School:  Construct an explanation based on valid and reliable evidence obtained from a variety of sources (including students’ own investigations, models, theories, simulations) and the assumption that theories and laws that describe the natural world operate today as they did in the past and will continue to do so in the future.

• High School:  Create or revise a computational model or simulation of a phenomenon, process, or system. (Strong alignment)
• High School:  Use mathematical representations of phenomena or design solutions to describe and/or support claims and/or explanations. (Strong alignment)

   
B. Common Core Standards for Mathematics – Grades 9-12

• Reason abstractly and quantitatively
• Model with mathematics
• Make sense of problems and persevere in solving them

• High School N-Q.1: Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

 

• High School A-SSE.1.     Interpret parts of an expression, such as terms, factors, and coefficients.
• High School A-SSE.2      Use the structure of an expression to identify ways to rewrite it.
• High School A-CED.2      Create equations in two or more variables to represent relationships between quantities
• High School A-CED.4      Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. 

 

• High School F-IF.4     For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
• High School F-IF.6     Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

 

• High School F-LE.1.b     Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
• High School F-LE.5     Interpret the parameters in a linear or exponential function in terms of a context.

 

• High School G-C.5     Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality.  
• High School G-GPE.3    Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. 

 
C. Common Core Standards for English/Language Arts (ELA) – Grades 9-12

• High School RST11-12.3      Follow precisely a complex multistep procedure when taking measurements or performing technical tasks; analyze the specific results based on explanations in the text.
• High School RST.11-12.2     Determine the central ideas or conclusions of a text; summarize complex concepts, processes, or information presented in a text by paraphrasing them in simpler but still accurate terms.

 

• High School RST.11-12.7      Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem. 
• High School RST.11-12.9      Synthesize information from a range of sources (e.g. texts, experiments, simulations) into a coherent understanding of a process, phenomenon, or concept.

• High School RST.11-12.10      By the end of Grade 10, read and comprehend science/technical texts in the Grade 9-10 text complexity band independently and proficiently.