RocketSTEM Issue #12 - July 2015 | Page 38

S.T.E.M. for the Classroom

The thrill(e)
on the Rille
Vocabulary
• Depth: ​ ow deep the rille is.
H
• Distance: How far from the edge
of the rille to its center.
• Rille:​A collapsed lava tube that resembles a small canyon.
• Rope Length: The amount of rope needed to descend Hadley Rille.
• Rope Weight: The mass of the rope
per standard length.
• Slope: The angle the rille wall makes to the horizontal.

Narrative
Apollo 15 landed near Hadley Rille in the Apennine
Mountains of the Moon back in 1971. It has been heralded as the most scientifically robust of all the Apollo
expeditions. Its Commander, Dave Scott, and Lunar Module Pilot, Jim Irwin, were indeed true explorers. They had
even wanted to take a sample of rocks from the bottom
of the rille. The idea was to tie a rope to Scott with Irwin
acting as an anchor. Scott would shimmy down the slope
of the rille while Irwin would play out the line. It was considered a dangerous plan with a high scientific return.
It was not approved.
But what if NASA had said yes? How much rope would
Scott have needed? How much would the rope have
weighed? And what was the slope of the rille that the
Commander would have had to traverse?

Analysis
NASA studied the Moon prodigiously before going
there, and took great pains to select each precious
landing site. Thus, Hadley Rille was fairly well known geographically.
To solve this hypothetical problem, we use basic trigonometry. The hypotenuse of the triangle is the length of
rope needed for the traverse, the adjacent side is the
Distance, and the opposite side is the Depth. The slope
is the angle between the hypotenuse and the adjacent

For a more in-depth treatment of this high
school project by Joe Maness & Rich Holtzin
visit www.stemfortheclassroom.org.

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Fig. 3. Cross section of the rille at Apollo 15 site (at station 10). Vertical ruling is mare basalt; triangles
are talus deposits. Scale in meters. Topography by R. M. Batson, in Swann et al., 1972.
© Lunar and Planetary Institute • Provided by the NASA Astrophysics Data System

side. Dashed lines are provided to help with the measurements.
The length of the rope can be found using the Pythagorean Theorem:

A one­ half-­nch diameter nylon rope weighs in at 100
i
grams per meter, or 0.1 kg/m. Therefore,

The Slope can be found using one of the trigonometric
identities. Since we are given the opposite (Depth) and
the adjacent (Distance) sides, we can use the tangent
ratio.

We