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NASA used sextants for star observations in both the Gemini and Apollo
programs. During Gemini 10, Mike Collins used a handheld sextant in a
celestial navigation experiment described in his book "Carrying the
Fire". Results were indifferent, mainly due to the indistinct horizon
seen from space. I'm not sure if any other Gemini missions repeated the 
experiment. Sextants were built into the Apollo spacecraft, though.

Recently I bought "Digital Apollo: Human and Machine in Spaceflight," by
MIT historian David Mindell (The MIT Press, 2008). In 1961 MIT got the 
first large contract of the Apollo program: to design the guidance and 
navigation system. Naturally, the book has a lot to say on that subject.

MIT's initial idea was to have a periscopic sextant covered by a door.
But North American Aviation, the spacecraft prime contractor, didn't 
like that. It would necessitate pressure seals around moving parts, and 
if the optics failed to retract or the door failed to close, thermal 
protection would be compromised during re-entry. Eventually NASA had to 
step into the dispute and decree a fixed window, flush with the skin.

Component location was challenging. Flexure could not be tolerated
between the sextant and the inertial navigation platform. The two
subsystems were mounted together in a beryllium frame. But there
was no space for a long optical train to bring the sextant image to an
eyepiece on the instrument panel. So the navigation station had its own
control panel in the lower equipment bay, below and forward of the 
couches. When standing at the nav station your body was parallel to the 
axis of the conical spacecraft, your head toward the apex.

The sextant line of sight could rotate in "azimuth" (called "shaft
angle") and "elevation" (called "trunnion angle"). Trunnion angle was
limited no more than 50°. That is, the optics viewed a conical area
within 50° of the shaft axis (which was perpendicular to the skin).
Often the spacecraft had to be steered to a different orientation to
bring an object into view.

A common task was correcting the inertial platform orientation with two 
star observations. The computer could help. You gave it a star number (I 
think there were 35 different stars) and it would point the sextant to 
where the star ought to be. Assuming a fairly good platform alignment, 
the star would be in sight. All you had to do was refine the crosshair 
placement.

The computer was clever enough to check for blunders. Regardless of any 
error in platform orientation, the separation angle between any two 
stars was predictable. This value was compared to the angle calculated 
from the astronaut's shaft and trunnion angles, and the difference 
displayed, with an option to reject the observation.

To measure the position of the spacecraft (vs. orientation) you shot a
lunar distance. Or, in the early part of the mission, you shot an "earth
distance" because a lunar is relatively insensitive to position unless
close to the Moon.

Of course this required viewing two bodies simultaneously. The astronaut
had to orient the entire spacecraft to point the shaft axis at the 
substellar point on the limb. A reticle indicated this axis. Then, by 
rotating the shaft and adjusting the trunnion angle he superimposed the 
star on that point and took a "mark". To accomplish this there were 
separate joysticks at the nav station to steer the spacecraft and the 
sextant line of sight. It helped that the computer fired thrusters to 
hold the spacecraft rock steady in any desired orientation. Also, 
coordinate system magic inside the computer caused both objects to 
respond to the joysticks in an intuitive manner as seen in the eyepiece.

Actually, there were two eyepieces and two optical systems. The
"scanning telescope" gave no magnification but a wide field of view. The
sextant magnified 28x.

Apollo 8, the one that orbited the Moon on Christmas Eve 1968, gave this 
system its most thorough checkout. Audio transcripts of the entire 
mission are online at NASA's Apollo 8 Flight Journal site:

http://history.nasa.gov/ap08fj/

Jim Lovell was in charge of navigation. His observations throughout the 
mission involved a great deal of dialog, preserved in the transcripts. 
The separation angle measurements utilizing the lunar or Earth limb 
numbered more than 200. Although guidance was actually based on Mission 
Control's navigation solutions uplinked to the spacecraft, Lovell's 
results were excellent. Later simulations proved Apollo 8 would have 
easily hit its reentry target with onboard observations alone. No 
subsequent mission so thoroughly tested Apollo's capacity for self 
contained navigation.

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