 This is a scale model of the lunar model 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 see the sun shield 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 module's return and docking with the orbiting command module. All Apollo spacecraft, whether the lunar module or the command and 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 x-y 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 positions 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, that equals zero, and the ball appears at the center of the lens. As it rolls along the hemisphere toward the x-y plane, notice that its distance from the center increases until 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 have cluttered the eyepiece, so instead they used an ingenious method to measure the distance being rotated in 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 being needed to merely rotate the spiral until it touches the star Sirius and then enter into the computer the amount of this rotation. The onboard 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 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 a 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 modules 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, warm 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 Havoc, the engineer guy.