This is a scale model of the lunar module that landed on the moon in six of the Apollo
missions.
I’ll share with you one tiny aspect of the module’s design that highlights the ingenuity
of the Apollo engineers; it exemplifies the hundreds of thousands of decisions made in
designing the Apollo spacecrafts.
The part I’m talking about is the alignment optical telescope.
It would stick out right here — near the module’s radar and docking station.
In this photo you can see the sunshield of the telescope.
It descends like a periscope into the module.
Through it the astronauts sighted on stars and used that information to align the gyroscopes
of their inertial measurement unit — the device that kept track of the module’s position
when it traveled through space — which was essential in navigating the modules return
and docking with the orbiting command module.
All Apollo spacecraft, whether the lunar module or the command service module, were navigated
by reference to what NASA called the “Basic Reference Coordinate System,” where the
location of stars and other celestial objects were defined relative to the Earth or the
Moon.
The key was to align the coordinate system assigned to each spacecraft to this Basic
Reference Coordinate System.
This was done by star sightings which revealed two angles: an angle phi in the xy-plane of
the spacecraft’s coordinate system, and an angle theta — the angle measured from
the spacecraft’s z-axis.
To measure these two angles the Lunar Module used an Alignment Optical Telescope.
The telescope, which had a 60 degree field of view, rotated to one of six fixed position,
chosen based on the star field the crew needed to examine.
As an example, consider the Apollo 12 mission.
Moments after Pete Conrad and Al Bean landed on the moon, Bean peered through the telescope.
He sighted on the star Sirius to obtain the two angles used to align the lunar module’s
guidance system.
He would need this information when he powered back up the lunar module in preparation for
departure.
To determine the two angles Bean used a cursor inscribed on a rotatable eyepiece.
He first measured what the Apollo engineers called the “orientation angle,” which
revealed phi directly.
And then to get theta he measured the distance of Sirius from the center of the eyepiece.
The Apollo engineers noticed that the projection of the angle theta onto the lens of the telescope
is proportional to the distance from the center.
To see this watch what happens as this blue ball moves along the surface of the hemisphere.
If it’s on the z-axis, theta equals zero, and the ball appears at the center of the
lens.
As it rolls along the hemisphere toward the xy-plane, notice that its distance from the
center increases until at theta equals 60 it reaches the perimeter of the lens.
To aid the astronauts in measuring the distance from the center, the Apollo engineers could
have marked the eyepiece with a dense set of concentric circles, but this would cluttered
the eyepiece, so instead they used an ingenious method: To measure the distance Bean rotated
an Archimedes spiral superimposed on the eyepiece.
This spiral has a very useful property: notice that it touches each concentric circle on
one and only one point.
So, Bean needed to merely rotate the spiral until it touched the star Sirius and then
enter into the computer the amount of this rotation.
The on-board Apollo Guidance Computer used the amount of rotation to calculate the distance
from the center of the eyepiece, and thus the angle theta.
Once they’d made this measurement Bean and Conrad could partly power down the lunar module,
and then walk across the moon — this assured that when they returned, the lunar module
was ready to fly to the orbiting Command module.
To me the spiral used on the telescope exemplifies the clever engineering used throughout the
Apollo project.
The spiral came about because the engineers had to create a lunar module as lightweight
as possible: every extra gram chewed up fuel better used for emergencies.
Weight was so important that the module’s designers considered substituting the ladder
under the hatch with a knotted rope!
They also wanted five legs, but that would be too heavy, so they settled for four.
These weight restrictions prohibited a standard telescope and sextant — an instrument that
could pinpoint stars within a 10 arc second error.
To get this precision motion it used motors, worm gears, and rigid tracks — all too heavy
for the lunar module and so replaced by the simple twist of an Archimedes spiral!
I’m Bill Hammack, the engineer guy.