Science RWLO Template Title Placeholder



Calculate Solar Planetary Constant

By Reza Mihankhah

Professor of Physics

Henderson Community College

Henderson, KY

Project Overview

Students will use real time data from ten satellites to

(a) Calculate solar system planetary value for each satellite

(b) Calculate the mass of the earth using Kepler’s third law

(c) Obtain the mass of the earth from an internet site

(d) Calculate the percent error between the two values

Student Learning Objectives

After completing this RWLO, the students will be able to:

• Apply Kepler’s Third Law of Planetary Motion

• Collect radius and mass of the earth from a web site

• Collect altitude and period for each satellite from a web site

• Calculate planetary constant for each satellite, the mass of the earth, and percent error

Procedure

Time: Approximately 75 minutes

Materials: Computer, online access, printer, calculator, pencil and paper

Prerequisites: Students should have knowledge of Kepler’s third Law.

Implementation: This RWLO can be used as a laboratory project or as a homework assignment. Students can work individually or in groups of up to two.

1. Prior to class, the instructor should become familiar with the J-Track 3D and Hyper-Physics web sites. Students must be advised to turn off their pop-up blockers when using the J-Track 3D web site.

2. Introduce Kepler’s 3rd law: the square of the orbital period of a planet is directly proportional to the cube of the average distance of the planet from the Sun; that is,[pic].

To simplify the derivation, we will use circular orbit for the planets. The centripetal force Fc necessary to keep the planet of mass Mp in a circular orbit is the gravitational force FG exerted on it by the sun of mass Ms.

Thus,

Fc = FG or [pic] (1)

Where [pic] is the speed of the planet,[pic] and [pic] is the period for one revolution. Substituting for [pic] in equation (1),

[pic]

Solving for[pic]2 gives

[pic] , we will let, [pic] (2)

Where [pic]is the planetary constant. Thus,[pic] which is Kepler’s 3rd law? Let [pic]= mass of any planet at the center of a circular motion, solving for M in equation (2) will yield

[pic] (3)

Students will use this equation to find the mass of the earth using [pic] of each satellite.

Content Material

Student Directions:



1. Go to

2. Click “+J-TRACK 3D” button

3. JTrack-3D window will open, click “satellite”, click “select”

4. Scroll down and locate the first satellite from the data Table II and

click on the name

5. The orbital path of the satellite will be displayed

6. Close the satellite window, you are back to the +JTrack-3D

window, click on view, click on satellite position

7. Enter the values for Altitude in meters and period in seconds in

Table II. Close the satellite position window and repeat steps 3-6

for the remaining nine satellites

8. To complete the project, you will need: the mass of the earth, the radius of

the earth, and the Gravitational Constant. These values can be found from:

and



Record these values in Table I

9. Find the distance each satellite is from the center of the earth and

record it under the Radius column

10. Calculate the [pic] for each satellite and record it in table II

11. Use equation (3) and find Mearth

12. Find and record the percent error between the calculated

value of Mearth and the value from table I

Table I

|R, Equatorial Radius of the Earth (m) |G, Universal Gravitational Constant | Mass of the Earth (kg) |

| |(N.m2/kg2) | |

| | | |

Table II

|Name of satellite |Period |Altitude (m) |R |K of Satellite |MEarth Calculated |MEarth |% Error |

| |(s) | |(m) | | |Table I | |

|AQUA | | | | | | | |

|NOVA I | | | | | | | |

|CANX-1 | | | | | | | |

|ORBCOMM FM 13 | | | | | | | |

|AO-7 | | | | | | | |

|SINAH 1 | | | | | | | |

|KO-25 | | | | | | | |

|SAUDISAT 1B | | | | | | | |

|KOMPSAT | | | | | | | |

|KITSAT-3 | | | | | | | |

Referenced URLs:

You may review Kepler’s Laws of Planetary Motion at the following site:



Assessment

Each student will submit a formal lab report using the following format:

1. Objective (5 pts.) - This section is a brief statement of what you are

investigating with this experiment.

 

2.             Theory (15 pts.) - This section explains the theory you believe explains

your objective (5 points). The theory should be explained both qualitatively (in words, 5 points) and quantitatively (develop, list, and explain all formulas, 5 points).

 

3.             Procedure (30 pts.) - This section is used to explain, in detail, step by

step reconstruction of what you did. This section should be written so

that anyone who reads the report can reconstruct your experiment.

Three-point deduction for each missing step.

 

4.             Data and Analysis (35 pts). - This section is where you present all your experimental results and the results of any calculations (10 points). The values should be labeled as to what they represent and include units (4 points).  You will also perform one sample calculation of every type of calculation you will need to do in the experiment (5 points). Start by listing the formula in algebraic form and then substitute numbers in for the variables (3 points). Show how you solve for the unknown and how the units cancel (5 points). The sample calculations should be written directly below the data (8 points.).

 

5.             Discussion/Conclusion (15 pts.) - This section is used to explain how

accurately the theory explains/predicts the observation (8 points). If you are not 100% accurate, you need to suggest ways in which the experiment or theory might be improved (3 points). You should end this section with a brief summary of what was accomplished (4 points).

 

Links to Course Competencies

This RWLO could be applied in the following courses: College Physics I, Applied Physics I, Astronomy I, and Introduction to Physics I. Specifically, this RWLO meets the following course competencies:

• To understand, analyze, summarize, and interpret a variety of reading material.

• To communicate effectively using standard written English.

• To explain the application of fundamental physical principles to various physical phenomena.

• To elaborate upon knowledge to create thoughts processes that are new to the student.

• To think critically and make connections in learning across the disciplines.

Supplementary Resources

Kepler’s Laws of Planetary Motion:



Science @NASA: this site contains information about satellites:



Minds-On Physics Planetary and satellite Motion:



Tutorials in Kepler’s Laws:





Recommendations

This project is designed for the first semester of a two semester algebra-based physics course. However, it can be used in any introductory and/or calculus-based physics and Astronomy I courses.

Back-up:

If the internet is unavailable, the data provided in the Back-up-Data sheet could be used.

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