Galileo's Moon Mountain
General Description
This program illustrates the method used by Galileo to measure the
height of a mountain on the Moon. Using his improved telescope
design, Galileo was able to see spots of light in the otherwise dark
potion of the Moon. He interpreted these spots as mountain peaks
which caught the rays of the sun even though the sun did not
illuminate the Moon's surface at the base of the mountain. He
measured the distance of the bright spot from the terminator (the line
separating the lit and unlit portions of the Moon) as a fraction of
the Moon's radius. Then he was able to use a geometrical argument to
determine the height of the mountain as a fraction of the Moon's
radius. Galileo knew that the Moon's radius was approximately 1600
km (he didn't use those units, of course), which allowed him to
determine the absolute height of the mountain. (Note that the modern
value for the Moon's radius is about 1740 km.)
One window shows the view from above the North pole of the Moon. The
mountain appears near the bottom of this window. A ray of sunlight
which just grazes the Moon's surface at the terminator is shown.
Controls allow the user to adjust the angle of sunlight (thus altering
the Moon's phase) and the height of the mountain.
The other window
shows the view from Earth. When sunlight strikes the top of the
mountain a bright spot becomes visible in the dark area of the Moon.
Likewise, when the mountain is in the bright region it casts a
shadow. The distance across the Moon's face from terminator to
mountain in shown.
View From Above North Lunar Pole
- Display Options Menu
- Show Geometry: removes the Moon and mountain and displays
lines illustrating the geometry of the situation.
- Show Angle Value: shows the numerical value of the angle of
sunlight (in degrees).
- Show Height Value: shows the numerical value of the mountain's
height as a fraction of the Moon's radius.
- Visual Elements
- Light Gray / Black Disk: the Moon (lit and unlit sides).
- Light Gray Triangle: the mountain.
- Red arrow: shows direction to Earth.
- Yellow arrow: ray of sunlight that grazes the terminator.
- White line: from center of Moon to surface along
terminator.
- Cyan line: from center of Moon to top of mountain.
- Green line: perpendicular to cyan line, shows distance
from terminator to mountain along face of Moon.
- Controls
- Angle: angle of sunlight (in degrees), controls phase of Moon.
- Height of Mountain: height of mountain above lunar
surface, as a fraction of Moon's radius.
View From Earth
- Display Options Menu
- Show Distance from Mountain to Terminator: displays the
distance from mountain to terminator, measured along the face
of the Moon, as a fraction of the Moon's radius.
- Visual Elements
- Background: image of the full moon as seen from Earth.
Dark portion is covered.
- Bright spot: illuminated peak of the mountain.
- Black triangle: shadow cast by mountain.
Todd K. Timberlake (ttimberlake@berry.edu)