Visualizing the Tilt of the Lunar Orbital Plane

Demonstration of the GeoGebra 3D Visualization of the Tilt of the Moon's Orbit in the Celestial Plane

https://drive.google.com/file/d/1c6OYWdOdEUrIxQPsio6QQKLgx_IFl0oJ/view?usp=sharing

Menelaus' Early Observations for Geography and Astronomy

https://drive.google.com/file/d/1SWyVzLJimJzRyrOQpPEVWqr4HkOAWrFi/view?usp=sharing

Instructions:

Please recreate the GeoGebra applet and review the gathered information about Menelaus' early observations in geography and astronomy.

Lunar Nodes

1. What is the line of lunar nodes?

A) The intersection of the Moon's orbit and the Sun's path across the sky. B) The intersection of the ecliptic plane and the celestial plane of the Moon's orbit. D) The orbit of the Earth around the Sun C) The path the Moon follows during a solar eclipse.

Solar Eclipse

2. When does a lunar or solar eclipse occur?

B) When the Moon crosses the line of nodes, the intersection between the ecliptic plane and the celestial plane, during a full or new moon. C) When the Moon is at its farthest point from Earth in its orbit. D) When the Earth's axis is tilted at 23.5 degrees. A) When the Earth’s orbit aligns with the Moon’s orbit at the equinoxes.

Tilt of the Moon's orbital plane

3. What is the tilt of the Moon's orbital plane relative to the ecliptic plane?

A) 45° D) 90° C) 5° B) 23.5°

GeoGebra 3D Visualization

4. How does GeoGebra help in visualizing the intersection of the ecliptic and celestial planes?

A) By showing the distance between the Earth and Moon in real-time. C) By plotting the coordinates of the Sun's path across the sky. D) By illustrating the tilt of the Earth's axis during the solstices. B) By allowing the user to adjust the Earth's orbital position and the Moon's position relative to the Earth.

Moon’s position around the Earth

5. In the GeoGebra activity, how is the Moon’s position around the Earth controlled?

D) By a slider that changes the position of the Sun. C) By a slider that rotates the Moon's orbital plane. A) By a slider that adjusts the Moon's position based on its orbital tilt. B) By a slider that controls the Earth's position in its orbit.

Source of Inspiration: Celestial Sphere

Source of Inspiration: Three Great Circles

Source of Inspiration: Lunar Nodes

Textbook Reference and Source of Inspiration:

Bondoc, J. M. F., Villa, J. C. S., & Pawilen, G. T. (Eds.). (2024). [i]History of mathematics[/i]. Rex Marketing Publisher.