### Lunar orbit

**Purpose: **Students will practice analyzing and graphing data about the moon’s orbit. The activity will help students understand the Earth-moon system and the nature of elliptical orbits.

**Procedural overview: **After reading the *Science News* articles “Apollo astronauts left trash, mementos and experiments on the moon,” students will graph lunar orbital data, analyze how the moon’s orbit changes over time and consider the implications of those changes.

**Approximate class time: **1 class period to complete the activity questions, calculations and graphing.

**Supplies:**

Lunar Orbit student activity guide

Calculators

Graph paper or computers with graphing software

Online access to research additional information as needed

A projector for introducing the activity (optional)

**Directions for teachers: **

Before engaging in this activity, frame the general concepts behind the data being analyzed by having students read the *Science News* articles “Apollo astronauts left trash, mementos and experiments on the moon.” If students have time and need an extra challenge, there is a set of bonus questions about how the moon’s orbit and phases can explain certain lunar phenomena.

If a projector is available, show students the data on perigee and apogee in Table 1 on the screen. If a projector is not available, explain to students where to find the data table in their activity guide.

Discuss the following questions and answers with your students before allowing them to engage with the data on their own.

Based on the *Science News* article “Apollo astronauts left trash, mementos and experiments on the moon,” why is it important to understand how the distance between the moon and Earth changes?

*The positions of the Earth and moon are determined by the laws of motion and gravity. Understanding how those positions change over time can offer a test of Einstein’s theory of general relativity.*

What are some implications of the moon moving closer to and/or farther from Earth?

*Answers may include how tides are affected (higher tides when the moon is closer and lower tides when the moon is farther) or how the timing of a day may be affected by tidal friction.*

The moon orbits Earth in an elliptical path. What does this path mean for the distance between the moon and Earth?

*In a single orbit of the moon (a lunar month, about 29 days), the moon reaches both its farthest distance (apogee) and closest distance (perigee).*

What do the data in Table 1 show?

*The data in Table 1 show every perigee and apogee in 2019 and the distance between Earth and the moon at each occurrence.*

**Note to teacher: **The Teacher Answer Key provides answers for student questions.

**Directions for students:**

After a class discussion covering the general information about the moon’s orbit, look at Table 1 and answer the questions that follow. When needed, use additional resources to find background information.

**Table 1**

Apogee – 2019 | Perigee – 2019 |

Date | Distance (km) | Date | Distance (km) |

January 8 | 406,117 | January 21 | 357, 342 |

February 5 | 406, 555 | February 19 | 356, 761 |

March 4 | 406, 391 | March 19 | 359, 377 |

March 31 | 405, 577 | April 16 | 364, 205 |

April 28 | 404, 582 | May 13 | 3569, 009 |

May 26 | 404, 138 | June 7 | 368, 504 |

June 23 | 404, 548 | July 4 | 363, 726 |

July 20 | 405, 481 | August 2 | 359, 398 |

August 17 | 406, 377 | August 30 | 357, 176 |

September 13 | 406, 377 | September 27 | 357, 802 |

October 10 | 405, 899 | October 26 | 361, 311 |

November 7 | 405, 058 | November 22 | 366, 716 |

December 4 | 404, 446 | December 18 | 370, 265 |

*Source*: https://www.timeanddate.com/astronomy/moon/distance.html?year=2019&n=59

**Background questions**

1. The moon’s orbit around Earth is elliptical. Explain what this means.

2. The equation that follows describes the eccentricity of the moon’s orbit — how much the orbit varies from being a perfect circle. In this equation for eccentricity (*e*), *a* is apogee distance and *p* is perigee distance.

When *a* and *p* are approximately equal, what is the rough value of *e*? What happens to *e* as *a* becomes much larger than *p*?How does the value of *e* affect the shape of the ellipse?

3. In which month is the moon’s closest approach (perigee)? In which month is its farthest approach (apogee)? What do you notice? Describe your observations.

4. In which month is the farthest perigee? In which month is the closest apogee? How does this compare with the closest perigee and farthest apogee?

5. What is the average distance for perigee? What is the average distance for apogee?

6. If the moon continues moving away from Earth at the rate indicated in the article, 3.8 centimeters per year, how long will it take the moon to move one kilometer away?

7. If the radius of the moon’s orbit did increase by one kilometer but the moon still traveled along its path at the same speed, how would the length of the lunar month change?

Use the base distance of 398,304 km and the equation:

In this equation, *a* is the average distance of the moon in meters, *P* is measured in Earth seconds and *M*_{1} and *M*_{2} are measured in solar masses.

8. How far would the moon have to move away from Earth to change the moon’s orbit by one day?

**Data analysis and graphing**

9. Use graph paper, a computer or a calculator to graph the data for both perigee and apogee on the same set of axes to trace the path of the moon’s orbit. What type of graph might you use?

10. What does the shape of the graph tell you about the moon’s orbit around Earth?

11. Where on the graph is the difference between perigee and apogee distance the greatest? During what month is the difference least? Calculate the rough eccentricity for these months.

12. How did your calculations of the two eccentricities compare? What does that tell you about the shape of the moon’s orbit?

13. If the eccentricity of the moon’s orbit were to double, how would the ratio *a* to *p* be affected?

14. What causes variations in the moon’s eccentricity?

15. How do the variations in the moon’s eccentricity affect Earth?

16. With the moon slowly moving away from Earth, how might the eccentricity of the moon’s orbit be affected?

**Bonus questions**

17. Humans have known since ancient times that we can only see one side of the moon from Earth. Why do we only see one side of the moon?

18. The phases of the moon are caused by the orientations of Earth, the moon and the sun. Sketch and label what phases of the moon will occur at the various positions on the moon’s orbit around Earth.

19*. *If a solar eclipse occurs when the moon comes between the sun and Earth, why don’t eclipses occur every month? What is the difference between a total and partial eclipse?

20. Using your knowledge of the moon’s orbit, can you explain what a “super moon” is?

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