Real life, Real time, on-station orbit calculations

[Grover]

I've been puzzling over a question of mine for some time now, i was wondering how it is that real spacecraft (such as the shuttle or Apollo) calculated their orbits, and thus worked out burn data for orbit syncing, base alignment, de-orbit etc

obviously there could be a difference between how Apollo did it and how modern spacecraft do it, but doing it at all is a great feat.

does anyone know? or is this a great NASA/ESA/Roscosmos/whoever secret?

 

[garyw]

I'd recommend reading this book as well as some of the NASA mission reports as a lot of the information is contained in those.

You could also have a look at the shuttle checklists and post mission burn calculations.

 

[Grover]

i cant afford to buy things im a student now, i have £8 a week left to buy clothes, phone contract and getting anything fixed, £18 on a book is alot for me

 

[kwan3217]

Well, the guidance computer in the spacecraft calls VESSEL::GetGlobalPos() and VESSEL::GetGlobalVel()...

The real answer is lots and lots of help from the ground, and lots of radar and radio data. That and a mathematical algorithm called the Kalman filter. This is a magical little program that given your old course (position and velocity), the physics of gravity, and some measurements (such as radar distance to the spacecraft) calculates the most likely value for your current course.

Most of the time the orbit is calculated on the ground and sent up to the spacecraft -- not because the spacecraft computer isn't good enough, but because it is easier to calculate the answer on the ground and send it up than to send all the raw measurements from the ground to the spacecraft and have it figure it out.

Some maneuvers are calculated on-board, such as the Space Shuttle (and I imagine other spacecraft, manned and automatic) docking with the Space Station, and things like a lunar landing. In these cases the computer again starts with a course, usually sent up from the ground, then uses physics and its own instruments, such as star trackers, gyroscopes, accelerometers, and radars, to generate measurements. No one measurement is good enough to get the current course, but combined with the magic of the Kalman filter, the spacecraft is able to keep track of its course.

So, let's take an example like the Apollo lunar landing. Before Powered Descent Initiation (PDI) when the spacecraft is still in lunar orbit, the spacecraft is tracked by its radio signal. The ground sends up a signal which among other things contains a pseudo-random noise signal. Think of it as a very accurate timing signal. When the spacecraft receives this signal, it immediately copies it into its own downlink, so that when the signal is again received on the ground, the ground equipment knows exactly how long the signal traveled from the Earth to the spacecraft and back. This becomes a measurement. By combining a bunch of these measurements, using computers on the ground running the Kalman filter program among other things, the ground guys are able to put together the "track" of the spacecraft, which is why this process is called "tracking".

So, with this track, the ground guys are able to calculate a "state vector", which is the position and velocity of the spacecraft relative to the moon at a particular instant. By using a gravity model, this state vector can be "propagated" forward or backward in time. The spacecraft computer is easily able to handle this task. Of course since the measurement is made tools made by humans, it is imperfect and will become more imperfect, so they have to keep tracking the spacecraft and sending up state vector updates.

So again with a lunar landing, the spacecraft uses the uplinked state vector to figure out where it is. Eventually it will calculate that it is at the correct place and time to fire its engines and start towards the surface. Now that the engines are firing, the accelerometers in the spacecraft detect this, and this becomes a measurement which once again feeds a Kalman filter program running on its own computer. Since the spacecraft is not just coasting anymore, it needs to use a physics model which includes both gravity and thrust. As the spacecraft falls out of orbit, the vehicle is still tracked by the ground, but it also tracks itself. When the spacecraft gets close enough to the ground, it uses a radar to measure its altitude, but perhaps more importantly its speed both vertically and horizontally. These measurements are also fed into the filter.

So, a lander makes its way to the surface by a combination of lots of help from the ground, measurements from its own sensors, and the Kalman filter. Generally when a vehicle is far from anything floating in deep space, it will use the most help from the ground. When it is maneuvering or near some object like a space station or the surface, it will use its own sensors.

The space shuttle uses state vectors from the ground to execute a deorbit burn, but from there acts much like a lunar lander, using its own accelerometers to feel lift and drag through the atmosphere. Since it is landing on the Earth, it is also able to use GPS, and since it is landing in the United States, it is also able to use the same military navigation beacons on the ground that the Air Force uses. There are lots of different kinds of data, and the physics of flying are different, but the Kalman filter still supports it all.

None of this is secret, just complicated. I could explain further, but the next step requires linear algebra and matrix equations.

 

[Grover]

i think i understand: its like public GPS in reverse (and incredibly more complicated)

the ground stations send and/or recieve a signal, and using their timings, they can calculate the distance from the station to the vessel. with 3 of these, that puts it to a single point (but more improve accuracy)

this is all done in realtime, every few moments, and this is sent in a seperate signal to the spacecraft.

though modern craft might be able to handle this now, the older craft would rely on computations made on the ground to calculate the orbital properties of the craft, ApA, PeA, Inc etc, as well as its position (and further measurements can be used to measure perbutations, i remember one mission was launched to map Earth's gravitation field (may or may not have ACTUALLY launched))

then the spacecraft puts this info together to calculate burn data (in Apollo missions, this was calculated on the ground)

but speaking of Apollo, the LOI burn and most of the PDI would have been performed on the far side of the moon, but how did the signal get to the craft through the moon (i know the live footage of Armstrong and Aldrin managed to get back, possibly via the CSM)

is it possible for a modern spacecraft to make these measurements on-orbit, rather than relying on ground stations. it could use other GPS satalite signals to locate itself, like a car GPS does, then use a powerful computer (about as powerful as a HC gaming rig) to calculate its orbital properties?

thanks man, i get it now

 

[Hlynkacg]

but speaking of Apollo, the LOI burn and most of the PDI would have been performed on the far side of the moon, but how did the signal get to the craft through the moon (i know the live footage of Armstrong and Aldrin managed to get back, possibly via the CSM)

is it possible for a modern spacecraft to make these measurements on-orbit, rather than relying on ground stations. it could use other GPS satalite signals to locate itself, like a car GPS does, then use a powerful computer (about as powerful as a HC gaming rig) to calculate its orbital properties?

thanks man, i get it now

Easy, you calculate it out before hand and then establish a countdown.

Based on current trajectory we will be at "point X" in 1 hour 12 minutes and 15.5 seconds. Upon reaching point x we will burn retrograde to change our velocity by _____km/s.

...and hope we got it right.

 

[kwan3217]

though modern craft might be able to handle this now, the older craft would rely on computations made on the ground to calculate the orbital properties of the craft, ApA, PeA, Inc etc, as well as its position (and further measurements can be used to measure perbutations, i remember one mission was launched to map Earth's gravitation field (may or may not have ACTUALLY launched))

Even the older spacecraft such as Apollo and Gemini had computers sufficiently powerful to calculate all that stuff on board once they have a state vector. In other words, once the spacecraft had its position and velocity at time X, it was simple to calculate on board all the orbit elements as well as its position and velocity at any other time Y. It's just that accuracy degrades over time (hours or days).

but speaking of Apollo, the LOI burn and most of the PDI would have been performed on the far side of the moon, but how did the signal get to the craft through the moon (i know the live footage of Armstrong and Aldrin managed to get back, possibly via the CSM)

LOI was performed on the far side, yes. The ground guys would make sure that there was a good state vector and burn plan up on the spacecraft before contact was lost. The spacecraft is able to propagate the orbit for the few hours it is out of contact, by using the old track and updates based on its own accelerometers during the burn. In other words, the spacecraft doesn't need a new state vector continually, just every once in a while. The radio tracking is much more accurate than the accelerometers, but as you stated, only available when the spacecraft is in contact. The Apollo computer during LOI was able to calculate ApD, PeD, etc in real time during the burn so that the astronauts could monitor it while out of contact. They didn't just point in a certain direction and run the engine for a certain time with a stopwatch.

PDI was done on the near side, in contact with the ground. But, the onboard computer was in charge, since it was collecting the data from its accelerometers and radar directly. One of the things they did for the Apollo 12 super-accurate landing was send state vectors calculated on the ground up to the lander, at least once during powered descent.

is it possible for a modern spacecraft to make these measurements on-orbit, rather than relying on ground stations. it could use other GPS satalite signals to locate itself, like a car GPS does, then use a powerful computer (about as powerful as a HC gaming rig) to calculate its orbital properties?

thanks man, i get it now

Don't knock the old computers. Modern computers may have GHz speed, but they need it mostly to calculate millions of triangles per second to create a 3D image. Strip away the graphics, and it is amazing what can be done with MHz or even kHz. 80kHz doesn't sound like much, but it was used effectively. Have a look at the Virtual AGC for more detail than anyone should care about.

Modern spacecraft in low-earth orbit often do carry GPS receivers, especially ones with radar altimeters or lasers used to measure sea level, ice level, and such. They calculate their own positions onboard in real time (millisecond-level delay) with meter-level accuracy, which is more than enough to control themselves. But they also send down the raw GPS measurements so that the orbits can be calculated on the ground in non-real-time (hours to days delay) at centimeter-level accuracy, because the orbit accuracy directly translates into altitude accuracy and therefore mission measurement accuracy.

It's all a matter of bandwidth. When the ground stations have a better track of the spacecraft, state vectors are calculated on the ground and sent up. When the spacecraft has a better track by itself from its own sensors, the spacecraft does things itself. Spacecraft computers have been good enough to do this since the early 60s. Even with Gemini, once the spacecraft got close enough to the target to see it by radar, maneuvers were calculated on board.

 

[Grover]

so its a good idea now, to have the spacecraft to calculate its own orbital parameters, but have a regular update with ground control to check that its still accurate?

 

[MikeB]

Somewhat off-topic, but I hope close enough:

Extrapolating forward in time, say 50-100 years, when many commercial spacecraft are cruising among the asteroids and visiting bases at Earth/Mars/Jupiter, how will they navigate?

Surely they won't rely on Earth-based tracking stations, especially if the Sun is in the way. Should we plan on a GPS-like system of beacons from Venus to Neptune? Should each ship use its own sightings of planets/moons/asteroids against the stars? I would like to think that ships would be able to maintain their own state-vectors, as Orbiter assumes and provides through its standard MFDs. But how might it be done? :hmm:

 

[kwan3217]

Somewhat off-topic, but I hope close enough:

Extrapolating forward in time, say 50-100 years, when many commercial spacecraft are cruising among the asteroids and visiting bases at Earth/Mars/Jupiter, how will they navigate?

Feeling optimistic today, aren't we?

Surely they won't rely on Earth-based tracking stations, especially if the Sun is in the way. Should we plan on a GPS-like system of beacons from Venus to Neptune? Should each ship use its own sightings of planets/moons/asteroids against the stars? I would like to think that ships would be able to maintain their own state-vectors, as Orbiter assumes and provides through its standard MFDs. But how might it be done? :hmm:

Asteroids are an excellent navigation source. The Deep Space 1 spacecraft was almost entirely a set of engineering demonstrations and one of the things demonstrated was Autonav - the spacecraft used its camera to photograph star fields with known asteroids in it.

Also, I have heard of a proposal to use pulsars as natural navigation beacons. Pulsars are extremely accurate and precise. In principle they can be used to navigate anywhere in the solar system (or even outside) with GPS-like accuracy. The two limiting factors I can think of are 1) glitches and 2) pulsar pulse width. Glitches are an observed natural phenomenon where a pulsar suddenly changes its pulse rate. These would have to be detected, probably on Earth, and then a warning message would have to be sent out stating that a particular pulsar is unusable until its rate is re-measured. Pulse width has to do with measuring the exact peak time of a pulse. Every nanosecond of uncertainty represents 29.97cm (about 1 foot) of uncertainty. In deep space, microsecond precision is probably good enough, and you may be able to improve this by measuring many pulses.

There are several papers on using pulsars in navigation - a place to start is here (I had to save the PDF and view it outside of my browser).

 

[MikeB]

Fascinating. I think I'll wait for the MFD.

 

[Grover]

i thought pulsars were almost totally reliable, since theres not much that can change the rotation speed of a neutron star (unless ive got my names mixed up :S)

 

[kwan3217]

i thought pulsars were almost totally reliable, since theres not much that can change the rotation speed of a neutron star (unless ive got my names mixed up :S)

That's what the observers of pulsars thought, too, until one watching the Crab Nebula pulsar glitch. He had this great theory to explain it too, as some kind of impact or something like that, until it glitched again within a couple of years. See here (abstract only). It is thought that all pulsars are neutron stars, but perhaps not all neutron stars are pulsars. Come to think of it, I don't know if any non-pulsar neutron stars have been observed.