The video Apollo Program Guidance and Navigation System 79974 explains that the spacecraft's sextant could be used together with the navigation computer to determine a position fix while in Earth orbit, and an attitude fix when en-route to the Moon.

This paper states on page 14:

The sextant articulating star line of sight makes the precision measurement of star direction for the IMU alignment. For the entire Apollo 8 mission the IMU was scheduled to remain operating continuously. Periodic realignment was performed 30 times with the sextant each time using the automatic star pointing acquisition of program P52.

Question: This describes attitude determination using two stars. But was the sextant ever used or even demonstrated to help make position determinations using a point on the Earth in combination with a star?

Screen shots from video, open in new window for full size.

Apollo Sextant 4 Apollo Sextant 1

Apollo Sextant 2 Apollo Sextant 3

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    $\begingroup$ I think the Apollo sextant was too slow for position determiniation while in Earth orbit. A classical sextant on a marine ship was used while the Earth did a full rotation in 24 hours. But the Apollo CM in Earth orbit had a period of only 90 minutes, that is 16 times faster. Earth rotation needs 4 seconds per arcminute, but the Apollo orbit needs 15 seconds for one degree or 0.25 seconds for an arcminute. $\endgroup$ – Uwe Jan 25 '18 at 21:07
  • $\begingroup$ @Uwe it's a good point. Both the star and the point on the Earth will be moving at a rate determined by the spacecraft pitch rate (which will probably nearly follow the orbital rate) and the point on the Earth will have an additional motion component due to geometry, since it is close, rather than on the celestial sphere. It would be hard to get a highly accurate fix on to points moving differently, at the same time. However, if this is an emergency backup capability, anything would be better than nothing, even if less than optimally accurate. $\endgroup$ – uhoh Jan 25 '18 at 21:55
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    $\begingroup$ It was a problem to get an accurate fix of the Earth horizon. If you want to measure both a star and a landmark on Earth, you need goot lighting conditions to see both the star and the point on Earth. Not too much sunlight and not too few. When sextants were used on marine ships, measuring a star's height above the horizon was difficult. You need to see both the star and the horizon. It was possible only in a short period with nautical twilight, but not during the day or in the night. $\endgroup$ – Uwe Jan 26 '18 at 11:24
  • $\begingroup$ @Uwe if "It was a problem..." refers to an experience by Apollo astronauts, is there a source for this information? (I'm guessing you were not there personally, but do I assume too much?) If this is known, please consider posting an answer and sharing the source! This sounds very interesting! $\endgroup$ – uhoh Jan 26 '18 at 12:41
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    $\begingroup$ The problem with the Earth horizon is described in the paper you cited on page 24 and 25 under the title Earth Horizon Navigation Reference. $\endgroup$ – Uwe Jan 26 '18 at 13:59

IMU realignments using the sextant were done regularly, by all Apollo missions. Using the sextant for a position update was also done by most missions, or at least it was practiced for the case of loss-of-communication with the ground. Then the sextant and onboard computer were needed to for navigation to get the astronauts home.

There were two separate programs in the Command Module Computer for this type of position update. Program 22 (Orbital Navigation) and Program 23 (Cislunar Navigation). P22 in low lunar and Earth orbit did not involve any of the navigation stars. Instead you would point the sextant at a predetermined landmark with known latitude and longitude and take five marks on it at short time intervals. This was practiced successfully during the Earth orbital missions Apollo 7 (see the Mission Report page 5-95) and Apollo 9. The same method could be used in lunar orbit, either for updating the position of the spacecraft in the computer or to calculate the coordinates of a landmark on the lunar surface. This second method was used for the lunar landing missions to get more accurate coordinates of the landing site, before and after the actual landing.

The other Program, P23, is the one that uses the position update method you were describing, pointing the sextant at a star and a position on Earth. This program actually had a few different modes: Earth horizon, Earth landmark, Lunar horizon, Lunar landmark. So you could give the computer coordinates of a known landmark on Earth or Moon or you could also use the horizon closest to the navigation star. This last method is the one that was used the most, usually a few hours after TLI, while still close to the Earth. For example, Apollo 11 Flight Plan, page 3-7.

Program 23 best works during the mission phase a few hours after TLI or TEI and a few hours before LOI or reentry. And that's when Apollo 8 practiced these procedures. Later missions like Apollo 11 only tested P23s in the hours after TLI.

Now, Program 23 was also attempted in Earth orbit by Apollo 7. But it didn't work very well. Here the quote from the Mission Report, page 5-98:

Midcourse navigation/star horizon/landmark.- A number of star/earth horizon measurements were scheduled, but all attempts to perform these sightings were unsuccessful. This failure resulted partially from the difficulty of the control task at the relatively high earth-orbital rates, but primarily from the crew's inability to define a horizon locator, which was the primary purpose of these tests. The dichroic filter in the sextant landmark line-of-sight did not aid in land/sea definition and actually smoothed out the horizon such that it was impossible at earth orbital ranges to define a locator for repeatable sightings. The crew stated that at longer ranges, the sightings should be accomplished with ease. The capability for performing star/lunar landmark sighting was demonstrated using the star Alphard and lunar landmark 5 (crater Diophantus).

  • $\begingroup$ A sextant needs two points to measure an angle between them. On Earth for instance the angle between the horizon and a star or the Sun. " P22 in low lunar and Earth orbit did not involve any of the navigation stars. Instead you would point the sextant at a predetermined landmark with known latitude and longitude and take five marks on it at short time intervals." If a landmark was measured but no star, was the horizon used to measure the angle between landmark and one or both horizons seen from the Eart orbit? $\endgroup$ – Uwe Jan 26 '18 at 14:53
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    $\begingroup$ Well, in P22 they didn't actually use the sextant in the classical way, so the split line-of-sight wasn't required. In this case, and during an IMU realignment, the sextant would basically be used as a telescope. The sextant had a field of view of 2°, so that allows for precise measurements. P22 instead works mostly with the computer, and it needs at least 3 measurements on the landmark, but nothing else. The computer used something like the Gauss' method. $\endgroup$ – indy91 Jan 26 '18 at 15:01
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    $\begingroup$ @indy91 this is fantastic, thank you for digging into this and explaining the different procedures so clearly! It's late here, I'll give it a thorough read in the morning. $\endgroup$ – uhoh Jan 26 '18 at 15:04
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    $\begingroup$ When the astronauts had the landmark aligned in the sextant they would press a "mark" button. This sent a signal to the computer, which then stored the current sextant angles (shaft and trunnion) and IMU attitude (pitch, yaw and roll) for this specific mark. With a bunch of conversions the computer could calculate the direction of the landmark from the CSM in the inertial coordinate system from these angles. So no, a small rotation didn't hurt the measurements. $\endgroup$ – indy91 Jan 26 '18 at 15:52
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    $\begingroup$ @indy91 I've been reading more about the automatic target selection and automatic optics positioning, as well as automatic tracking of the target on the next revolution that is performed by the guidance computer. It never ceases to amaze me how much automation could done with such a tiny amount of memory for program storage and for execution! $\endgroup$ – uhoh Jan 28 '18 at 4:05

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