Lab #2

Lab assisgnment

https://cunysps.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=d590505e-e9ac-431d-92fe-ae6e0162ccd4

https://stellarium-web.org/

Instructions

This lab has three objectives. The first is to observe the period of revolution of the planets. The second is to measure the distance to each planet from the point of view of the Sun. The third and final objective is to use Kepler’s 3rd law and prove or disprove the existence of a constant resultant.

AST 101: Introductory astronomy: THE SOLAR SYSTEM LABORATORY ASSIGNMENT #2

Kepler and the Laws of Motion of the Planets

ALL WRITING IN RED MUST BE FOLLOWED BY YOU, THE STUDENT, IN YOUR OWN LAB REPORT)

Hypothesis

Keplers assertion that all planets and celestial objects observed to move, do so in elliptical orbits.

Question Asked: How can we empirically prove Keplers 3rd Law?

Introduction

Johannes Kepler was mathematical wizard who worked with Tycho Brahe. Using Tychos detailed observations of the celestial objects, Kepler was able to come up with empirical solutions to how the planets move and discovered that their motion was elliptical. A fact, which rescued the Copernican Heliocentric model from its many inaccuracies.

Summarized as the three laws:

INSERT THE THREE LAWS HERE AND A SUMMERY EXPLAINING THEIR MEANING. USE ILLUSTRATIONS IN ADDITION TO YOUR WRITTEN EXPLANATION, MAKING SURE TO REFERENCE YOUR IMAGE BOTH AS A FOOTNOTE AND IN YOUR RESOURCES SECTION AT THE END OF THE LAB

Objectives

This lab has three objectives. The first is to observe the period of revolution of the planets. The second is to measure the distance to each planet from the point of view of the Sun. The third and final objective is to use Keplers 3rd law, and prove or disprove the existence of a constant resultant.

Procedure

USING THE STEP BY STEP GUIDE IN APPENDIX A, WRITE UP A PROCEDURE EXPLAINING HOW YOU CONDUCTED THIS LAB. USE THE SAME FORMAT AND STYLE AS WAS PRESENTED TO YOU IN LAB #1.

AS PART OF YOUR PROCEDURE YOU WILL FILL OUT THE FOLLOWING TWO TABLES:

TABLE 1

Planet

Start Date(MM/DD/YR)

End Date(MM/DD/YR)

Orbital Period , p(days)

Orbital Period , P (years) p/365.25

Mercury

Venus

Earth

Mars

Jupiter

Saturn

Uranus

Neptune

TABLE 2

Planet

Orbital Radius (a) (AU)

Orbital Period (P) (years) from table 1

a3 (AU3)

P2 (years2)

P2/ a3

Mercury

Venus

Earth

Mars

Jupiter

Saturn

Uranus

Neptune

Discussion

IN THE DISCUSSION SECTION (FOR THIS LAB), YOU WILL WRITE A DISCUSSION OF YOUR EXPERIENCE, AND YOUR TAKE ON THE FOLLOWING QUESTION Discuss the importance of this lab assignment. How well did the your calculations fit with Keplers laws?

Conclusion

IN THIS SECTION YOU WILL ANSWER THE HYPOTHESIS, AND PRESENT A CONCLUDING STATEMENT ABOUT KEPLERS LAWS AND THEIR ROLE IN HELPING US UNDERSTAND THE NATURE OF CELESTIAL MECHANICS

References

INSERT YOUR OWN HERE

Chaisson, Eric and McMillan, Steve

Astronomy Today Volume I : The Solar System, 8th Edition, 2013

APPENDIX A STEP BY STEP INSTRUCTIONS

Instructions:

• Begin by launching Stellarium
• Set the default location by opening the Location window (You can find the Location icon at the left-hand side of the screen, or by pressing the F6 key). Enter New York City, in the search bar, and then click on New York City, United States of America.
• Make sure to check the box titled use current location as default and then close this window.
• We will be journeying to a viewpoint outside of the Earth. To do this we must make sure to turn off the atmosphere (A key), fog (F key) and ground (G key).

The function allowing us to view the solar system from above is called Solar System Observer.

• Use the search function (CTRL-F or F3) and enter Solar System Observer. Press Enter.
• To actually have the view point of any solar system object that youve selected enter CTRL-G (think GO).
• You should now be looking from a point high, high above the solar system. You can use the mouse to locate the Sun, or, once again use the CTRL-F or F3 to find the Sun and center it on the screen.
• We will adjust some the of the settings, so that we can view the planets in their orbits.
• Press F4 to call up the sky and viewing options screen.
• Go to the in the Sky tab
• Disable Dynamic eye adaptation and stars (uncheck the boxes)
• Go to the SSO Tab and make sure that the show orbits box is checked and the only orbits of the major planets box is the only one checked.
• Make sure that the Show planetary nomenclature is also checked.
• Change the tab to Markings and make sure to uncheck the Celestial Sphere box.
• When done, you can close this options window.
• Turn on the orbital lines, try pressing the letter O (which will look red), and begin zooming in and out to see the orbits of the planets (You can use your mouse wheel or the page up/down keys on your keyboard).
• As you zoom in and out, you can also start playing with time! Press the L key to move time forward, do this several times until you see the planets moving.

Tips:

• If you find that you are going too fast, press the K key to stop all motion and return you to normal time.
• You can always press the number 8 to return you to the present day.
• To go backwards in time, press the J key.
• What can you observe of the planets motion?

What is the relationship between the distance from the Sun and the speed at which the planets seem to move? OPTIONAL TO ANSWER

• Of the three laws, which law best describes this relationship? How? OPTIONAL TO ANSWER
• In the next part, we will be observing each planets orbital period (P) and Semi-major axis (a) and using this information, we will be proving that the ratio in Keplers 3rd Law is indeed 1.
• Image 1- Mercurys orbit

Image 1- Mercurys orbit

• We will start the exercise by zooming in on the planet Mercurys orbit. Make sure it fills the screen, but you are still able to see the entire orbit itself.
• Place a finger, or a piece of paper with tape to mark the position of Mercury on your screen. Note the start date on the table below.
• Press the L key to move time forward. No more than 7 presses should do it.
• When Mercury returns to its original starting point not the end date in the table below.
• Enter the amount of days it took for Mercury to complete one orbit. Convert this number into the equivalent amount of Earth years by dividing your finding by 365.25 days.
• Repeat this measurement for each of the planets in order. (We will not be measuring Pluto!)
• TABLE 1 FILL THIS OUT IN THE PROCEDURE SECTION

Planet

Start Date(MM/DD/YR)

End Date(MM/DD/YR)

Orbital Period , p(days)

Orbital Period , P (years) p/365.25

Mercury

Venus

Earth

Mars

Jupiter

Saturn

Uranus

Neptune

• To find the distances that the planets are from the Sun, we must first go to the Sun!
• Use the CTRL-F or F3 keys to find the Sun. Then travel to the Sun by pressing CTRL-G
• Now, all you have to do is search each planets name in turn (again CTRL-F or F3) and obtain their distance information in au from the informational chart on the upper left hand of your screen.
• Fill in the information in the table below, and perform the necessary math indicated in each row. (round to the nearest hundredth -> two decimal points, ex: 8.9341=8.93)

Planet

Orbital Radius (a) (AU)

Orbital Period (P) (years) from table 1

a3 (AU3)

P2 (years2)

P2/ a3

Mercury

Venus

Earth

Mars

Jupiter

Saturn

Uranus

Neptune

• TABLE 2 FILL THIS OUT IN THE PROCEDURE SECTION