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Is the GPS data reliable or meaningful only on Earth or below the geo-stationary Earth orbit? For GPS navigation, does a rocket has to fly below the geo-stationary orbit? If GEO is a physical limitation; for longer distance navigation and for the purpose of vertical landing especially on other planets, what is the alternative to GPS navigation?

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There are a couple of questions here, I will try to answer them all.

Q1: Is GPS only valid below GEO orbits?

A1: For the most part yes, because GPS satellites transmission are pointed at earth. (Minor Technical correction: GPS satellites are not in fact in Geosynchronous orbits. They are in MEO orbits which are only half way to GEO by altitude)

However the GPS transmitter use fairly wide beams which can be heard from the other side of the planet on their side lobes (see image). These transmissions can be and have been used for localization on spacecraft above the GPS constellation (This is sometimes called the "inside out solution"). The GPS position calculation has to be changed from my understanding, but otherwise works fine and actually has pretty good accuracy (10s of meters). Go here to read the nitty gritty details of how this works.

enter image description here

Q2: What are alternative to GPS based navigation above GEO.

A2: For near earth operation the GPS solution above still works, however signal strength loss will kill that option after a certain distance away from earth.

For free space operations generally spacecraft use rate-range and angles to do navigation. You can read about ESA's range-rate navigation here.

Range rate navigation can be slow since you have to 1) send a signal to the spacecraft and wait for it to return to get the time of flight. 2) Calculate the position from this and the rate (velocity) based on the measured Doppler shift and finally 3) send this position back to the spacecraft. This method works fine for anything where the dynamics happen over the course of hours (basically any orbit). It breaks down when you try to land on another extraterrestrial body like the moon or Mars.

In those cases something called terrain relative navigation is used. It uses computer vision to localize itself based on what a camera see versus what maps show as there. TRN is what curiosity used to land on Mars

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...for the purpose of vertical landing especially on other planets, what is the alternative to GPS navigation?

Terrain recognition and imaging, and if there's a landing pad, some radio and optical beacons and possibly even a big "X" or other reflective (optical) or topographic (radar) marker if somebody with a company with an "X" in the name already put an "X marks the spot" up there.


Optical

NASA's Terrain-Relative Navigation explains vertical landing of the Mars 2020 mission" which includes the Perseverance rover and Mars Helicopter Ingenuity

How Terrain-Relative Navigation Works

  • Orbiters create a map of the landing site, including known hazards.
  • The rover stores this map in its computer "brain."
  • Descending on its parachute, the rover takes pictures of the fast approaching surface.
  • To figure out where it's headed, the rover quickly compares the landmarks it "sees" in the images to its onboard map.
  • If it's heading toward dangerous ground up to about 985 feet (300 meters) in diameter (about the size of two professional baseball fields side by side), the rover can change direction and divert itself toward safer ground.

There is a lot more information in this answer to how and why is image processing used on spacecrafts?, but here's the NASA GIF

NASA Illustration of Terrain-Relative Navigation

above: Illustration of Terrain-Relative Navigation. "Terrain-Relative Navigation helps us land safely on Mars - especially when the land below is full of hazards like steep slopes and large rocks! From here.

See How did Chang'e-4 hover, rotate, and then descend so gracefully? (Video) for more about this!

Radar

Radar might be helpful for terrain recognition and it works at night, but the problem is that with a wavelength so much longer than optical you can't directly image very easily. Instead what's usually used is side-looking radar especially combined with synthetic aperture techniques. Since you generally have to look sideways to image terrain with radar, this might be most helpful when you still have some forward motion to scout for a landing site, but final vertical descent can't really use side-looking radar.

For more on this see How can ICEYE-X1 capture 2D high resolution SAR images in "tens of seconds"? and this answer to Detailed radar imaging of Tiangong-1; how do they do that? where the equivalence to side-looking is understood from

...The motion of the target is what provides the baseline.

Beacons etc.

If a landing site has been prepared ahead of time, it could be equipped with blinking lights or other optical beacons, and possibly radio beacons as well. Early developments of the use of radio is detailed in Arthur C. Clarke's excellent Glide Path.

For an example of what this could look like from orbit, see What is this huge, red, blinking light structure on Earth seen from the ISS in this video?

Progress MS-10 cargo spacecraft launched on 16 November 2018 at 18:14 GMT from Baikonur cosmodrome, Kazakhstan, taken by ESA astronaut Alexander Gerst from the International Space Station

From YouTube Progress launch time lapse seen from space

Inertial

This answer to During final descent how will InSight know cardinal directions in order to land with proper orientation? begins with

By integrating inertial measurements, initialized from the final star tracking about 20 or 30 minutes earlier.

and although the question and answer are related to attitude, an inertial guidance system will provide some information about current 3D position and velocity relative to the surface. Combined with and constantly calibrated against Terrain-Relative Navigation discussed above, inertial measurements can provide critical information, especially if exhaust blows up a huge amount of dust as the craft approaches the surface during the vertical landing phase.

Radar and gamma rays for a gentle touchdown

The timing of radar pings can give the distance to the surface to pretty high accuracy, and this might be important for a gentle touchdown. I don't have any proof, but I would expect that the Falcon-9 landings might use radar for proximity to the landing surface as additional feedback for engine throttling, since they need a gentle landing to avoid breaking a leg.

Some spacecraft use backscattered gamma rays from a radioactive source to automatically trigger retropropulsion at the last split-second to make the landing more gentle for humans. For more on that see:

For reference:

Soyuz MS-08 landing

GIF from Soyuz MS-08 landing

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    $\begingroup$ Great answer +1. Visual landing will be difficult due to poor visibility issue especially the dust kicked off by the rocket thrusters. $\endgroup$ – seccpur Sep 16 at 1:20
  • $\begingroup$ @seccpur thus "...inertial measurements can provide critical information, especially if exhaust blows up a huge amount of dust as the craft approaches the surface during the vertical landing phase." And of course radar will still provide precise distance measurements to the ground. I'll add more about that in a minute. $\endgroup$ – uhoh Sep 16 at 1:22
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So, you have basically 2 questions:

1.) vertical landing ... 2.) Navigation outside of earths shere of influence

Let us start with 1.) : Typical extra-terrestial landers are equipt with radar altimeter:

A Doppler radar altimeter on the ExoMars 2016 Schiaparelli Entry, descent, and landing Demonstrator Module...

The lander's [...] radar altimeter...

... LUNAR MODULE LANDING RADAR ...

The Apollo LM had a radar altimeter

Radar altimeter can give you a quite precise altitude over Ground AND thanks to Doppler also the velocity you have relative to the ground.

The 2.) is not so easy: Navigation outside earths shere of influence:

Typically you can quite good determine your atitude by star trackers. Basically cameras looking on specific stars telling you in which direction they are.

Due to the typical long duration of extra-terrestial space missions, inertial navigation is not the first choise so you end up in trusting Isaak Newton:

It is common to use earth based radar and telescopes to gather as much measurements about the spacecraft as possible, then you put them into an orbit determiantion software and the result is a calculated/determined Orbit. In most cases you can also calculate the uncertainty of the determined orbit. this procedure is re-done regulary so you calculate the position.

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  • $\begingroup$ Those work if you aren't targeting a specific site. If there's a pre-prepared flat, clean landing spot then radar ranging isn't enough. That's why for example SpaceX uses GPS to land on those little boats in the ocean, or pads on land. $\endgroup$ – uhoh Sep 11 at 10:20
  • $\begingroup$ I am quite sure, this landers had no requirement to land on a stamp, yet. $\endgroup$ – CallMeTom Sep 11 at 10:25
  • $\begingroup$ @uhoh: Airplanes have been landing on pre-prepared flat, clean landing spots long before GPS, any other kind of NAVAIDs, or even radar existed. NAVAIDs may have existed when they started landing on boats, but radar and GPS definitely didn't. $\endgroup$ – Jörg W Mittag Sep 11 at 10:34
  • $\begingroup$ @JörgWMittag I loved the novel Glide Path! I'm not sure your point exactly. My comment is that distance to ground measurement by timing alone of a radar pulse would not be sufficient to land on a predetermined, small area. There are plenty of ways that radar could be used to do this, but they are not currently described in this answer. It would be great if an answer did! $\endgroup$ – uhoh Sep 11 at 11:02
  • $\begingroup$ Sry, either I understand something wrong, or you guys: the topic is about landing a vechicle horizontally on another planet? $\endgroup$ – CallMeTom Sep 11 at 13:22
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Laser telemetry, stellar navigation from a landed telescope

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  • $\begingroup$ This is a great idea, but as a Stack Exchange answer it's too short. Can you expand it a little? Does it require that landings only happen at night? Can they see at least a few stars or planets during the day? Since the fixed telescopes know exactly where they are relative to the landing site, why do they need stars at all? I think this can be an excellent SE answer but eight words is not enough. $\endgroup$ – uhoh Sep 17 at 6:37
  • $\begingroup$ To add to the uhoh's comment, don't hesitate to look at the help center to understand how to write a good answer. $\endgroup$ – Manu H Sep 19 at 15:44
  • $\begingroup$ In most cases I like short answers, they mostly teach the OP how to use a fishing rod and do not give her/him a fish ... but in this case: can you explain a bit in detail, what "landed telescope"s are? Do you mean ground based telescopes or to you mean telescopes landed on other planets? In the last case, I do not thing something like that existst at least not for tracking other S/C. $\endgroup$ – CallMeTom Sep 21 at 5:59

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