Sextant Navigation for Exploration Missions (Sextant Navigation): The crew performed checkout and the second session of operations of the Sextant Navigation hardware based upon selected observation targets during orbital night. The investigation focuses on stability and star sighting opportunities in microgravity. Astronauts on board the ISS tests a hand-held sextant that is intended for use on future Orion exploration missions. The results from this investigation can aid in the development of emergency navigation methods for future manned spacecraft.

This is interesting. I wonder how the calculations are handled… Seems like spherical trig with the earth’s center as a reference point would be out. Obviously this goes well beyond sight reduction tables and an almanac.

The sextant’s readings are fed into a small computer that handles the calculations. For more information see video from 4:05 min. The explanation is a bit unsatisfactory with only one sextant reading fed into the computer.

I understood it was an update on celestial distances using the disk of the earth. From memory I think it was Apollo 8 that last used it and the tables were formulated by a USN Officer.

Could be. The sun’s diameter D is known and with the measured angle A you can simply calculate the distance d. The same can be done with the Earth. Seen from earth the angle is 5°.

…your had a problem with the decimals.
The angle of visibility from the earth is about 0.5° or 30+ arcminutes for the sun (…and for the moon too).

This will make it very difficult, you must read the diameter of the sun in fractions of an arcsecond. The sun is gaseous with no exactly defined surface… and looking into the sun for more details is dangerous.

Oops, thanks for the correction! It is somewhat amazing that in this space age they have to fall back, for backup that is, on the good old trusted sextant. Who could have thought that when the sextant was dropped almost immediately with the introduction of GPS.

The sun’s exact position is not always as easy to understand, as it may seem.

At first, the earth does NOT orbit around the sun, but “orbits” around the common barycenter Earth+Moon; this barycenter orbits around the sun.

The barycenter is always inside the rotating earth at the sublunar point; 1400 – 2000 km below the earth’s surface (depends on the moon’s distance). Hence, depending on the moon’s position, distances to the sun may be greater from the earth or from the barycenter.

Some not really useful, but maybe interesting data for this year 2019:
(Perihelion and Aphelion are the shortest and the longest distance to the sun in a given year)

Perihelion earth on January 3, 9h UTC at 147099770 km
Perihelion barycenter on January 3, 22h UTC
Aphelion earth on July 4, 18h UTC at 152104275 km
Aphelion barycenter on July 5, 13h UTC

Apparent angular diameter sun on Perihelion = 32’ 32”
Apparent angular diameter sun on Aphelion = 31’ 28”
This gives a difference of 64 arcseconds, or a mean daily variation of 0.35 arcseconds.

However, the variation is not linear… around aphelion, for 20 days, the diameters’s rounded arcsecond does not change, around perihelion the same is valid for 15 days.

Space nav would not be using a horizon and HO 229, more like angles between various planets and maybe stars. In many ways it is easier to do, you always have a perfect view of them and hopefully the spacecraft is not rocking and rolling.
Speaking of nav, there is no technical reason the GPS system couldn’t resolve positions at points past the orbit of the satellites as well as inside the orbit. I wonder if there ever has been a GPS programmed to work out that far.

I just read the first experiment in what could be a solar system wide “space GPS” system was launched, so space navigators will be as lazy as the rest of us soon enough.

Basically, the existing GPS is a spherical triangulation by the distances (i.e. the time used by the signal) from the satellites’ positions to the receiver. If the altitude ASL does not matter, three satellites in different directions are needed.

In the outer space, even if the signal should be strong enough, this becomes rapidly inoperative.
Even from the nearby Moon, the orbits of the GPS-satellites have an angular diameter of 8.7° only.

Measuring all three satellites at their perpendicular extreme ‘positions’ would show all three at the same distance.

Taking satellites inside their extreme orbital positions will reduce the angular diameter. Their real distances will vary only by their relative distance to a perpendicular plane through the earth’s center.

Yes, exact times are essential for all spatial navigations.
It seems they are testing a single clock for now.

Even with our GPS, they must take care of some relativistic effects. In deep space, with the extreme absolute and relative speeds and distances, this must be even more complex.

However, Einstein and me… we are not very close friends…

Stationary relative to what?
Outside a planet’s attraction, it must orbit around the sun like a planet; otherwise, it will fall into the sun.

The velocities on their orbits are 30 km/s for the Earth and 24 km/s for Mars, as examples.

To have the relativistic speeds this must be considered too:
220 km/s is the orbital speed of the Sun around the center of the Milky Way, and
552 km/s is the orbital speed of the Milky Way around the Big Bang, the origin of all.

Against the light’s speed of 300000 km/s that seems not to be much.
However, our GPS works with nanoseconds, these future applications maybe with picoseconds.

yes, so what time do they use as items moving in space slow time down
One of the issues to be corrected in GPS sats as the orbits change their speed changes so the time is not accurate.
Theory of Relativity