From launch to land could a person travel in space with only mechanical devices like a sextant? With enough experience what would be the minimum devices needed? Which vehicle currently would be easier to fly this way?
Depends on that do we call a "computer". Would a slide rule count? This extremely simple, hand held device can do multiplication, division, and also functions such as exponents, roots, logarithms and trigonometry. Some included specialized features for aviators. Or may I bring my Curta into spacecraft? It also has been highly favored by commercial and general-aviation pilots. Such simple, mechanical devices would make work of human much easier and, I think, possible.
Where the time is critical, it may often be possible to use prepared plans and pre-computed tables for adjustment. Where errors are critical, three or more humans can work in parallel, picking the result that coincides.
Apart the speed of calculations, there is fundamentally nothing in the math that computer can do and human cannot.
You can travel in space without any navigation devices or computers at all, establishing suborbital flight and orbital flight is done by the rocket, it's accuracy there that matters and early manned rockets had no computers. De-orbiting is a matter of setting up the spacecraft to the right attitude for retro fire, which can be done by eye if need be, early spacecraft used gyros for that with a manual backup.
If you want to get anywhere specific in space you have to be accurate. A spacecraft must be held in a specific position and engines must fire at exactly the right time and for the right amount of time. Gyroscopes and timers can give you a fair amount of accuracy, so you don't need a computer for that (although it really helps).
The biggest challenge without a computer would be the mathematical calculations, which can be done by hand as long as you have a room full of human computers to back you up. Just by yourself it will take you longer perform some calculations than they are worth - by the time you have the answer you're past the point you needed them.
Yes, as long as you don't care where you end up
Early spacecraft used electrical controls, but had no computers:
- Six Vostok each carried one person to orbit. The first flight carried the first man and the last flight carried the first woman into space.
- Six Mercury flights each carried one American astronaut into space, four of these into orbit. Although the vehicles had no computers, they were supported by IBM 701 computers on the ground (offline and not real-time control).
- Voskhod flew two unmanned and two manned flights. The first manned flight carried three cosmonauts. The second manned flight carried two cosmonauts for the first spacewalk.
None of these flights had a precise target location, either in space (no rendezvous with a space station, lunar module, or satellite) or at re-entry (no runway or landing pad). As long as you landed somewhere in Siberia or the Pacific, an entire army or fleet of ships would find you.
Ascent - serves as a backup guidance system. The switchover is manually controlled by the astronauts.
Orbital flight - provides a navigation capability to the astronauts to determine the time of retrofire and to select the landing site for safe reentry in the case of an emergency. (on extended missions ground data may become unavailable when ground data network rotates out of the orbital plane.)
Rendezvous - serves as primary reference by providing guidance information to the astronauts. The orbit parameters are determined by the ground tracking which are then sent to the spacecraft; the guidance computer was responsible for processing the information along with sensed spacecraft attitude. The information was presented to the astronauts in terms of spacecraft coordinates.
Reentry - feeds commands directly to the reentry control system for automatic reentry or provides the guidance information to the astronauts for manual reentry.
Most of these weren't strictly needed for the Gemini missions, but rather testing the technology so it could be used for Apollo. However,
- Gemini had a radar system, which essentially needs a computer to be useful. This was used to practice rendezvous and docking, which would be needed in the Apollo missions between the CSM and the LEM. Apollo also used radar to measure the distance to the lunar surface; otherwise it would have likely crashed.
- Rendezvous is nearly impossible without a computer. Nearly every manned mission now uses rendezvous with another spacecraft in some way.
- If you want to land in a precise area (e.g. shuttle runway, SpaceX landing pad), you need computer control.
One of the other answers is wrong about Apollo. The CSM and LEM each had a guidance computer, the LEM had an abort computer, and the Saturn booster had another computer.
So, if you don't care where the spacecraft goes, you don't need a computer.
Is it possible? Certainly, and it has been done as stated.
It just takes a lot more time to calculate your burns and trajectories by hand than it does using computers, and performing them by hand rather than relegating things to a computer controlled automated flight control system requires a very steady hand and excellent timing.
Mind that the calculations aren't rocket science, and could probably be taught to anyone with a decent aptitude for mathematics and spatial insight. But they're not trivial either, having some preprinted worksheets to fill in your numbers and guide you through the calculations would speed things up enormously.
That said, using computers it's just a lot more convenient and reliable.
Robert A. Heinlein is a Science Fiction author well known for the use of extremely accurate calculations in launching and flying spacecraft. His novel The Rolling Stones is particularly noted for the use of a slide rule as the means of calculating space navigation.
Now weirdly, this future was already obsolete by 1977. Calculators had been invented, just about. But I didn’t notice that. I just took a sliderule for granted as a futuristic whatnot. Source; Pass the slide rule: Robert Heinlein’s The Rolling Stones
Fictional work or not, if Heinlein says you can calculate space navigation with a slide rule, then you can.
Related sister site question Heinlein slide rule calculations