Moon
Description
This applet demonstrates the motion of the moon around the ecliptic and its phases from a geocentric perspective. The Moon and Sun travel in their orbits around the Earth from West to East at different speeds. The relative size of the Moon and Sun orbits are not drawn to scale. The Elongation shows the observed angle between the Sun and Moon along the ecliptic. The corresponding phase of the moon is shown in the lower left view.
Usage
The Animate checkbox will set the Moon and Sun in motion around the Earth. The Speed Slider adjusts the Speed of the Moon around its orbit. When Speed = 1, a sidereal month passes every 10s of real time. The Year Length slider adjusts the relative speed of the Sun around its orbit in units of sidereal months. On Earth, a tropical year is 13.4 sidereal months long.
When the Animate checkbox is checked, a description of the moon's phase will appear below the moon shown in the lower left. When it is not checked, the position of the Moon and can be manually adjusted with the Moon Position and Sun Position Sliders.
Things to Try
Measure the Length of a Synodic Month
A sidereal month refers to the time it takes for the moon's zodiac to return to the same position along the ecliptic. A Synodic month refers to the time from one full moon to the next full moon.
Leaving the Speed slider fixed, check the Animate checkbox. When you see the moon appear full, start a stopwatch. When it becomes full again, record a Lap time on your stopwatch. Do this for several synodic months. Average the lap times.
Repeat this exercise for different values of Year Length.
Use spreadsheet software to make a graph of your results.
When the Year Length slider is set to 13.4 months, estimate the length of a synodic month given a sidereal month given is 27.3 days.
Estimate the Astronomical Unit
Around 270 BCE, Aristarchus used the length of the lunar eclipse to reasonably estimate the distance from the Earth to the Moon. By measuring the elongation between the Moon and the Sun at a quarter moon, he attempted to compare this distance to the distance between the Earth and the Sun. His method was sound but the available technology was not sufficient to the task.
Follow his method to compare these two distances in this simulation.
Leave the Animate checkbox unchecked. Adjust the Moon Position slider until a quarter moon is shown. Observe the elongation between the Sun and the Moon. Use the appropriate trigonometric function to estimate the ratio of the distance between the Earth and the Moon to the distance between the Earth and the Sun.