Download Discovering Kepler`s Law for the Periods of Planets

Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 10082
Discovering Kepler's Law for the Periods of Planets
Students listen to a video that describes Kepler's determination that planetary orbits are elliptical and then will use data for the solar distance and
periods of several of the planets in the solar system, then investigate several hypotheses to determine which is supported by the data.
Subject(s): Science
Grade Level(s): 8
Intended Audience: Educators
Suggested Technology: Computer for Presenter,
Internet Connection, Basic Calculators, Microsoft Office
Instructional Time: 3 Hour(s)
Resource supports reading in content area: Yes
Freely Available: Yes
Keywords: Kepler, Kepler's laws, planets, period, orbits, integration of mathematics and science, cosmology, solar
system
Resource Collection: iCPALMS
ATTACHMENTS
KEPLERLESSONPLAN.docx
worksheetforstudents.docx
KEPLERDATA_forstudents.xlsx
LESSON CONTENT
Lesson Plan Template: Confirmatory or Structured Inquiry
Learning Objectives: What will students know and be able to do as a result of this lesson?
1. Students will discover and explain that the relation between distance and period involves exponents.
2. Students will learn how to use data to create a law and that the law does not constitute a theory since the data fitting does not include an explanation (Newton's
theory).
3. Students will combine their knowledge from algebra and geometry with fundamental ideas in astronomy.
4. Students will explain how our knowledge has evolved through history.
Prior Knowledge: What prior knowledge should students have for this lesson?
1. Students should understand the heliocentric model of the solar system and that the planetary paths are close to circular.
2. Students should understand the meaning of integer exponents.
3. Students should understand the basics of scientific notation.
Guiding Questions: What are the guiding questions for this lesson?
1. How do the period and speed of a planet vary with distance from the sun?
2. How can a hypothesis that is not supported by data contribute to our understanding?
Introduction: How will the teacher introduce the lesson to the students?
1. One of the oldest questions in science is "What is the structure of the solar system?" For many centuries the most common belief was that the earth is the center of
the solar system with the sun, moon, and planets revolving around the earth. In the 1500s, Copernicus suggested that the sun is the center of the solar system with
the planets traveling in circular paths around the sun. Shortly thereafter, Tycho Brahe proposed a hybrid model: the sun and moon revolved around the earth, with
the other planets (Mercury, Venus, Mars, Jupiter, Saturn) revolving around the sun.
page 1 of 3 2. We will see a video that describes what happened next.
Investigate: What question(s) will students be investigating? What process will students follow to collect information that can be
used to answer the question(s)?
1. Do all planets travel at the same speed? Students will be provided the distance from the sun and the orbital period for the six planets known to astronomers in
1600.
2. Is the period proportional to the square of the distance from the sun?
3. Is the square of the period proportional to the square of the distance from the sun?
4. What is the simple law that describes the relationship between the distance from the sun and the orbital periods of the planets?
Analyze: How will students organize and interpret the data collected during the investigation?
Students will be provided the data and will need to calculate quantities related to the data.
Closure: What will the teacher do to bring the lesson to a close? How will the students make sense of the investigation?
The teacher will ask questions such as
1. Does the relationship between solar distance and period that you found provide an explanation?
2. This activity provides an example of how scientists in different countries contributed to our understanding of the structure of the solar system. Moreover, we see
how even an incorrect hypothesis can be valuable in providing the motivation for important discoveries.
Summative Assessment
1. Name two important results of Kepler's investigation.
2. Why is Kepler's wrong idea regarding the distances of the planets important?
3. Suppose you had data regarding the length of a pendulum and its period. What would you do to seek a law that relates the length and the period.
Formative Assessment
1. After the students have finished watching the Kepler video, the students will complete the questions on their worksheet that relate to the video. A short class
discussion will be included.
2. After the students have determined whether or not the planets move at the same speed, the teacher will inquire whether there is any pattern, e.g. do the planets
closer to the sun travel faster or slower than the planets further away.
3. Are there any relationships in mathematics wherein one quantity is proportional to the square of another? Possible answer: area of circles, squares.
4. After some students have "discovered" the law D3 = P2, ask whether we understand why that relationship seems to work. Also, ask whether we have proven that
this law must be valid for other planets, such as Uranus and Nepture.
Feedback to Students
The lesson plan includes many notes to the teacher indicating suggestions for discussions.
When students test a hypothesis and it turns out NOT to be supported by the data, they should be complimented on their attempt and to try another hypothesis. If
there is insufficient time for them to complete the testing, they should be encouraged to indicate some possibilities that could be tested.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
1. Students will work in teams of 2-3.
2. Included are extensions that enable students who work quickly to develop a deeper understanding of the concepts.
Extensions:
Indicate the distance-period relation for the solar system when distances are measured in kilometers.
It has been observed that the period of Uranus is approximately 3.06x104 days. Use Kepler's law to estimate the distance of Uranus from the sun in both AU and
kilometers.
Suggested Technology: Computer for Presenter, Internet Connection, Basic Calculators, Microsoft Office
Special Materials Needed:
Graph paper.
SOURCE AND ACCESS INFORMATION
Contributed by: Steve Blumsack
Name of Author/Source: Steve Blumsack
District/Organization of Contributor(s): Leon
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
SC.8.E.5.7:
Description
Compare and contrast the properties of objects in the Solar System including the Sun, planets, and moons to those of
Earth, such as gravitational force, distance from the Sun, speed, movement, temperature, and atmospheric
page 2 of 3 MAFS.8.EE.1.2:
MAFS.8.EE.1.4:
MAFS.8.EE.2.5:
conditions.
Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is
a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know
that √2 is irrational.
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific
notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very
small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been
generated by technology.
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional
relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to
determine which of two moving objects has greater speed.
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
When students work toward meeting this standard, they build on grades 6–7 work with proportions and position
themselves for grade 8 work with functions and the equation of a line.
MAFS.8.F.2.4:
SC.8.N.1.1:
SC.8.N.1.6:
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial
value of the function from a description of a relationship or from two (x, y) values, including reading these from a table
or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models,
and in terms of its graph or a table of values.
Define a problem from the eighth grade curriculum using appropriate reference materials to support scientific
understanding, plan and carry out scientific investigations of various types, such as systematic observations or
experiments, identify variables, collect and organize data, interpret data in charts, tables, and graphics, analyze
information, make predictions, and defend conclusions.
Understand that scientific investigations involve the collection of relevant empirical evidence, the use of logical
reasoning, and the application of imagination in devising hypotheses, predictions, explanations and models to make
sense of the collected evidence.
Remarks/Examples:
Florida Standards Connections: MAFS.K12.MP.4: Model with mathematics.
Select models useful in relating the results of their own investigations.
SC.8.N.3.1:
Remarks/Examples:
Florida Standards Connections: MAFS.K12.MP.4: Model with mathematics.
Related Access Points
Access Point Number
SC.8.N.1.Su.1:
SC.8.N.1.Su.4:
Access Point Title
Recognize a problem from the eighth grade curriculum, use materials to gather information, conduct a simple
experiment, and record and share results.
Recognize that the basic process used in scientific investigations involves questioning, observing, and recording and
sharing results.
page 3 of 3