NavList:

Bill wrote:

"You touched on a few of the things that puzzled me.  I know nothing
firsthand about aircraft sextant use, so wondered if a bubble sextant would
be usable with some corrections"

 

A bubble sextant won't work in space (in freefall). A bubble is really just a sophisticated plumb bob. Since there's no local gravitational acceleration, there's no readily measurable "down".

 

"or if a traditional sextant with a
mighty-big dip correction (in the neighborhood of 12+ degrees at 100 nm
altitude) might suffice.  While using the diameter of the Earth and sextant
reading of it's angular diameter to find distance off (altitude) initially
occurred to me, my guess was the 120d-130d range of a standard sextant would
not cover the horizon-to-horizon range of a craft in the 100-200 mile range
(a SWAG) above an approximately spherical body 6900 nm in diameter.  Then
again, NASA is probably not "standard." "

 

The trouble with the Earth at low altitudes (a few hundred miles) is that it has no distinct horizon. There was at least one experiment on a Gemini flight where this was verified. This is exactly the same reason that you can't use the horizon in air navigation --it's lost "in the fog" in the distance. But what about higher altitudes, maybe thousands of miles from the Earth? From those altitudes, the Earth has a sharp enough horizon or limb, so we should be ok. In principle, you could get position fixes on trips from the Earth to the Moon and nearby planets using a sextant and angles measured between a set of nearby objects like the Earth, Moon, and nearer planets and maybe some asteroids (whose positions in 3d space would be required) and a set of very distant objects (the ordinary navigational stars would do just fine). Measuring the angle between a nearby object and a background star puts you on a "cone of position" whose apex is at the center of the nearby object (and at the points where that cone intersects the Earth's surface you get a traditional circle of position). You can get two cones (intersecting in a ray) by using the same nearby object, and then a single point fix by using another sight from a second nearby object. If the nearby object is near enough to show a disk, you could measure the semidiameter directly. This would be equivalent to measuring dip. Notice also that this system can be extended very easily to interstellar space. You need an "almanac" of nearby objects and a set of "background" objects (this categorization is not essential but it simplifies things). If you were flying to a star a few dozen lightyears away, you would usually be within five lightyears of a few minor stars. By measuring their positions relative to distant objects with an ordinary sextant (assumed accurate to 0.1' of arc) you could find your starship's location to within (0.1/3438)*5ly which is approximately the distance between Saturn and the Sun. At 90% of the speed of light, the ship would cover this distance in about an hour and a half. Note that the aberration correction at this speed would be huge (see my post on December 31st on sextant science and the speed of light), but straight-forward.

 

By the way, there's an interesting problem with using a traditional sextant in space (in case you decide to bring one along when orbital space tourism takes off ten years from now): the windows are in the way. You would need some sort of optical dome or a sextant built into the spacecraft hull with its optics on the outside in order to make proper observations.

 

I should emphasize that there is no reason to do any of this, except for entertainment. Sextants on spacecraft have been intended to be used almost exclusively as a backup means of determining orientation of the vehicle, not for position fixing. And in fact, those "sextants" that have flown (at least after 1967) were sextants in name only and were mostly used as telescopes.