Navigation in space

[Wiploc]

It is quite possible that I'm being thick, but the Mercator projection isn't any more real than the cylindrical projection. How do you take an actual sphere and link Cleveland with Chicago, without impacting Toledo?

The map is not the territory. You don't get to think of it as an actual sphere while at the same time thinking of distorting it so that Cleveland is next to Chicago. You can't hold both of those thoughts in your mind at once.

You think of Toledo as being impacted because -- I'm guessing -- you imagine Chicago moving along the surface of the earth toward Cleveland. I grant that this would smoosh Toledo.

But the concept being illustrated is that we don't slide things along the surface but rather bend the surface until distant places touch.

So here's one analogy. This is San Fransisco:


-- sanfran

We see that San Fransisco is far from Oakland by land, but not so far by bridge. Building the bridge didn't smoosh Menlow Park, didn't hurt it at all. Probably helped Menlo Park by reducing the traffic load.

Folding space to, effectively, go faster than light is science fiction, so it's fiction. But it's also science fiction, so we have get used to dualities. It's not possible to think of light as particle and wave at the same time, but we have to accept there is some sense in which it is both. In the twin paradox, it's not possible to think of both twins as younger than the other, but we have to accept that, from John really is the younger one from his perspective, and Jane really is the younger one from hers.

People talking about gravitons do not seem to disagree with those who talk in terms of gravity waves. And then others jump in and say that gravity doesn't really exist; gravity is an illusion caused by the curvature of space. Scientists who talk about curved space and the nonexistence of gravity don't seem to be contradicting the ones who talk about gravitons and gravity waves. I'm a layman, so it seems obvious to me that the three theories can't all be true.

But scientists think these conflicting theories are all true enough to be useful ways of describing reality.

Think of imaginary numbers. Those are obviously impossible, and yet we couldn't design computers without them.

So there is one sense in which it is true that Chicago and Cleveland are on the surface of a sphere and are far apart. But there is another sense -- if faster than light travel is possible -- in which they can be functionally close together on a distorted surface. In this latter sense, Toledo is not smooshed between them; it is where it always was.

I don't know if any of this helps. In the twin paradox, we have to give up the idea of privileged viewpoints. It's not as if John is really right and Jane is wrong. Nor is Jane really right in the sense that John is wrong. Both are right from their own perspectives, and both perspectives are equally valid.

So, in a world in which Han really did the Kessel run in less than twelve parsecs, we have to accept that, while we normally view the run as longer than that, there is also an equally legitimate sense in which Han bent space so the endpoints of the run so that they were less than twelve parsecs apart. This didn't change or affect anyone simultaneously making the run at a slower speed. It didn't smoosh Toledo.

I hope this helps, but I have no idea.

 

[Loren Pechtel]

If evolution is a conat resylting in prey and predator, then unyil we get photon torpedos and warp drive the last thing we want is let oters know we are here.

That was Stephen Hawking's position too. But I believe he was looking beyond photon torpedoes and warp drive as a defense as those could be seen as primitive toys to a truly advanced race of space farers.

Personally, I don't think we could hide the fact that Earth is teaming with life from an advanced race even several hundred lightyears away... even if we had never used radio, tv, or radars. An analysis of Earth's atmosphere as we passed between them and the Sun would give them plenty of evidence that the Earth was crawling with life.

Yeah, there's no hiding from an ET determined to kill other aliens.

 

[Loren Pechtel]

The old pre GPS LORAN system might work in some form. Multiple transmitters at known locations sending pules in a known order with known timing.

Even if the locations are moving you might still derive relative position.

We have a pre-existing, galactic system for that. They're called Pulsars.

Pulsar emission isn’t isotropic though, so you would have to keep a large catalogue that you keep accessing as you move around.

So it would seem to me that the plaque showing Earth’s location relative to pulsars would only work if you’re actually at earth’s location and can see that set of pulsars that are beamed toward you. Like telling someone where you live by describing what you can see outside your window.

An ET with such a catalog of pulsars can use the plaque to figure out where we are even without our having the catalog.

 

[Shadowy Man]

Pulsar emission isn’t isotropic though, so you would have to keep a large catalogue that you keep accessing as you move around.

So it would seem to me that the plaque showing Earth’s location relative to pulsars would only work if you’re actually at earth’s location and can see that set of pulsars that are beamed toward you. Like telling someone where you live by describing what you can see outside your window.

An ET with such a catalog of pulsars can use the plaque to figure out where we are even without our having the catalog.

But my point is that because pulsar flashes are beamed you can’t see them unless you are aligned with them. So the only way you can see all the pulsars listed on the plaque is if you are basically where Earth is, modulo the beam opening angles of the pulsars. So they won’t be on your catalog because you’ve not seen them until you got to Earth’s position.

 

[skepticalbip]

Pulsar emission isn’t isotropic though, so you would have to keep a large catalogue that you keep accessing as you move around.

So it would seem to me that the plaque showing Earth’s location relative to pulsars would only work if you’re actually at earth’s location and can see that set of pulsars that are beamed toward you. Like telling someone where you live by describing what you can see outside your window.

An ET with such a catalog of pulsars can use the plaque to figure out where we are even without our having the catalog.

Or even more simply, they can note the trajectory of the probe. Surely a space faring species would have an understanding of motion equivalent to Newton's laws of motion. If they know the direction it is traveling then they know the direction of where it is traveling from.

 

[Jimmy Higgins]

It is quite possible that I'm being thick, but the Mercator projection isn't any more real than the cylindrical projection. How do you take an actual sphere and link Cleveland with Chicago, without impacting Toledo?

The map is not the territory. You don't get to think of it as an actual sphere while at the same time thinking of distorting it so that Cleveland is next to Chicago. You can't hold both of those thoughts in your mind at once.

You think of Toledo as being impacted because -- I'm guessing -- you imagine Chicago moving along the surface of the earth toward Cleveland. I grant that this would smoosh Toledo.

But the concept being illustrated is that we don't slide things along the surface but rather bend the surface until distant places touch.

So here's one analogy. This is San Fransisco:

View attachment 32762
-- sanfran

We see that San Fransisco is far from Oakland by land, but not so far by bridge. Building the bridge didn't smoosh Menlow Park, didn't hurt it at all. Probably helped Menlo Park by reducing the traffic load.

Folding space to, effectively, go faster than light is science fiction, so it's fiction. But it's also science fiction, so we have get used to dualities. It's not possible to think of light as particle and wave at the same time, but we have to accept there is some sense in which it is both. In the twin paradox, it's not possible to think of both twins as younger than the other, but we have to accept that, from John really is the younger one from his perspective, and Jane really is the younger one from hers.

People talking about gravitons do not seem to disagree with those who talk in terms of gravity waves. And then others jump in and say that gravity doesn't really exist; gravity is an illusion caused by the curvature of space. Scientists who talk about curved space and the nonexistence of gravity don't seem to be contradicting the ones who talk about gravitons and gravity waves. I'm a layman, so it seems obvious to me that the three theories can't all be true.

But scientists think these conflicting theories are all true enough to be useful ways of describing reality.

Think of imaginary numbers. Those are obviously impossible, and yet we couldn't design computers without them.

So there is one sense in which it is true that Chicago and Cleveland are on the surface of a sphere and are far apart. But there is another sense -- if faster than light travel is possible -- in which they can be functionally close together on a distorted surface. In this latter sense, Toledo is not smooshed between them; it is where it always was.

I don't know if any of this helps. In the twin paradox, we have to give up the idea of privileged viewpoints. It's not as if John is really right and Jane is wrong. Nor is Jane really right in the sense that John is wrong. Both are right from their own perspectives, and both perspectives are equally valid.

So, in a world in which Han really did the Kessel run in less than twelve parsecs, we have to accept that, while we normally view the run as longer than that, there is also an equally legitimate sense in which Han bent space so the endpoints of the run so that they were less than twelve parsecs apart. This didn't change or affect anyone simultaneously making the run at a slower speed. It didn't smoosh Toledo.

I hope this helps, but I have no idea.

I'll cede to that. Thanks.

I suppose the next dumb question to ask is if you fold spacetime as such, does time passage get impacted due to the curvature change (if any)?

 

[Loren Pechtel]

Pulsar emission isn’t isotropic though, so you would have to keep a large catalogue that you keep accessing as you move around.

So it would seem to me that the plaque showing Earth’s location relative to pulsars would only work if you’re actually at earth’s location and can see that set of pulsars that are beamed toward you. Like telling someone where you live by describing what you can see outside your window.

An ET with such a catalog of pulsars can use the plaque to figure out where we are even without our having the catalog.

But my point is that because pulsar flashes are beamed you can’t see them unless you are aligned with them. So the only way you can see all the pulsars listed on the plaque is if you are basically where Earth is, modulo the beam opening angles of the pulsars. So they won’t be on your catalog because you’ve not seen them until you got to Earth’s position.

Anyone that plucks the probe out of interstellar space has considerable interstellar travel capacity. I think they've been around enough to know all the pulsars, not just the ones visible from their home system.

 

[steve_bank]

I had an idea for a cartoon.

Two Ets are buzzing along in their spaceship. The pilot suddenly jerks the spaceship to one side muttering, 'Those god damn idiots keep sending out those freaking probes'.

Think about it,

 

[bilby]

Star Trek, like a great deal of Science Fiction, is basically just a bunch of stories about naval exploration and adventure of the eighteenth and nineteenth centuries, with a layer of technobabble added to place the stories in the future, rather than the past. The advantage being that by doing so you largely avoid accusations of either defamation of historical persons, organisations, or nation states; or of historical inaccuracy or anachronism.

You could translate all of Trek in all its forms into an historical drama, and change nothing substantial at all.

Certainly the scriptwriters weren't interested in bothering to imagine space as a three dimensional vacuum where motion is subject to the laws of Relativity (except when the limitations of lightspeed needed to be handwaved away). They wrote what they knew - naval actions on the two dimensional surface of a planet - and just changed the setting to "outer space" with no particular care for the actual differences between deep space and a planetary surface.

This is why spacecraft with an obvious "right way up" are ordered by their captains to come to a "full stop". Because that's what ships do. That spaceships don't is completely irrelevant, particularly as the setting is of little importance to the story being told.

Star Trek and Master and Commander - The Far Side of the World are only set in different centuries in the most superficial way possible. The details of the two settings are identical, apart from a handful of trivial matters of appearance.

Steady as she goes, Mr Sulu.

 

[Tigers!]

Star Trek, like a great deal of Science Fiction, is basically just a bunch of stories about naval exploration and adventure of the eighteenth and nineteenth centuries, with a layer of technobabble added to place the stories in the future, rather than the past. The advantage being that by doing so you largely avoid accusations of either defamation of historical persons, organisations, or nation states; or of historical inaccuracy or anachronism.

You could translate all of Trek in all its forms into an historical drama, and change nothing substantial at all.

Certainly the scriptwriters weren't interested in bothering to imagine space as a three dimensional vacuum where motion is subject to the laws of Relativity (except when the limitations of lightspeed needed to be handwaved away). They wrote what they knew - naval actions on the two dimensional surface of a planet - and just changed the setting to "outer space" with no particular care for the actual differences between deep space and a planetary surface.

This is why spacecraft with an obvious "right way up" are ordered by their captains to come to a "full stop". Because that's what ships do. That spaceships don't is completely irrelevant, particularly as the setting is of little importance to the story being told.

Star Trek and Master and Commander - The Far Side of the World are only set in different centuries in the most superficial way possible. The details of the two settings are identical, apart from a handful of trivial matters of appearance.

Steady as she goes, Mr Sulu.

Damn the phasers. Full speed ahead.
(With apologies to Admiral Farragut)

 

[Bomb#20]

Certainly the scriptwriters weren't interested in bothering to imagine space as a three dimensional vacuum where motion is subject to the laws of Relativity (except when the limitations of lightspeed needed to be handwaved away). They wrote what they knew - naval actions on the two dimensional surface of a planet - and just changed the setting to "outer space" with no particular care for the actual differences between deep space and a planetary surface.

My favorite example:

Spock: "He is intelligent, but not experienced. His pattern indicates two dimensional thinking."

Kirk: "Z minus 10,000 meters."​

For the direction the Enterprise needed to move along in order to get out of the plane of Khan's two dimensional movements to be the Z axis, the Enterprise would need to have started out lined up with that plane. I.e., Kirk's pattern also indicates two dimensional thinking. Kirk's experienced; what's his excuse?

 

[Loren Pechtel]

Certainly the scriptwriters weren't interested in bothering to imagine space as a three dimensional vacuum where motion is subject to the laws of Relativity (except when the limitations of lightspeed needed to be handwaved away). They wrote what they knew - naval actions on the two dimensional surface of a planet - and just changed the setting to "outer space" with no particular care for the actual differences between deep space and a planetary surface.

My favorite example:

Spock: "He is intelligent, but not experienced. His pattern indicates two dimensional thinking."

Kirk: "Z minus 10,000 meters."​

For the direction the Enterprise needed to move along in order to get out of the plane of Khan's two dimensional movements to be the Z axis, the Enterprise would need to have started out lined up with that plane. I.e., Kirk's pattern also indicates two dimensional thinking. Kirk's experienced; what's his excuse?

Against a competent opponent it probably doesn't matter.

 

[Jayjay]

In Star Trek universe, space itself seems to be two-dimensional, not just the thinking of inexperienced captains. Observe the shock wave in the beginning of Undiscovered Country:

 

[Shadowy Man]

In Star Trek universe, space itself seems to be two-dimensional, not just the thinking of inexperienced captains. Observe the shock wave in the beginning of Undiscovered Country:

The 2-d explosion is an annoying sci-fi trope. Was really bothered when Lucas added it to the original Death Star explosion.

 

[steve_bank]

It is strange how you can hear explosions in space, but what do I know.

In STNG they had sub space beacons, a navigation system. I suppose sub space is like the space beneath a floor in a house. Wires you don't see.

 

[Loren Pechtel]

In Star Trek universe, space itself seems to be two-dimensional, not just the thinking of inexperienced captains. Observe the shock wave in the beginning of Undiscovered Country:

The 2-d explosion is an annoying sci-fi trope. Was really bothered when Lucas added it to the original Death Star explosion.

I always pictured the 2D boom being that the Death Star basically came apart at the trench, a lot of the blast energy came out where the trench was. There had to be something of a weakness there since the thermal exhaust port had a straight line down to the reactor in it's heart--and I can't believe there was only one such port. They just shot at one to avoid splitting their forces.

 

[Shadowy Man]

In Star Trek universe, space itself seems to be two-dimensional, not just the thinking of inexperienced captains. Observe the shock wave in the beginning of Undiscovered Country:

The 2-d explosion is an annoying sci-fi trope. Was really bothered when Lucas added it to the original Death Star explosion.

I always pictured the 2D boom being that the Death Star basically came apart at the trench, a lot of the blast energy came out where the trench was. There had to be something of a weakness there since the thermal exhaust port had a straight line down to the reactor in it's heart--and I can't believe there was only one such port. They just shot at one to avoid splitting their forces.

If you watch the edited Episode 4 I believe you’ll see that the explosion doesn’t line up with the tench.

 

[Elixir]

Certainly the scriptwriters weren't interested in bothering to imagine space as a three dimensional vacuum where motion is subject to the laws of Relativity (except when the limitations of lightspeed needed to be handwaved away). They wrote what they knew - naval actions on the two dimensional surface of a planet - and just changed the setting to "outer space" with no particular care for the actual differences between deep space and a planetary surface.

My favorite example:

Spock: "He is intelligent, but not experienced. His pattern indicates two dimensional thinking."

Kirk: "Z minus 10,000 meters."​

For the direction the Enterprise needed to move along in order to get out of the plane of Khan's two dimensional movements to be the Z axis, the Enterprise would need to have started out lined up with that plane. I.e., Kirk's pattern also indicates two dimensional thinking. Kirk's experienced; what's his excuse?

He thought it was a taser?

 

[lpetrich]

[1107.1688] Measuring emission coordinates in a pulsar-based relativistic positioning system
More-or-less using pulsars like navigation satellites: GPS, GLONASS, Galileo.

The main problem with this scheme is that pulsars' pulses do not vary much over time. This means that they will have a big aliasing problem, and that will create big complications for anything out of cislunar space.

[1704.03316] Pulsar Positioning System: A quest for evidence of extraterrestrial engineering

[1711.08507] Characterization of Pulsar Sources for X-ray Navigation

[2002.04051] Advances in Deep Space Exploration via Simulators & Deep Learning

[2103.10389] Lost in space? Relativistic interstellar navigation using an astrometric star catalogue

The exploration of interstellar space will require autonomous navigation systems that do not rely on tracking from the Earth. Here I develop a method to determine the 3D position and 3D velocity of a spacecraft in deep space using a star catalogue. As a spacecraft moves away from the Sun, the observed positions and velocities of the stars will change relative to those in a Earth-based catalogue due to parallax, aberration, and the Doppler effect. By measuring just the angular distances between pairs of stars, and comparing these to the catalogue, we can infer the coordinates of the spacecraft via an iterative forward-modelling process. I perform simulations with existing star catalogues to demonstrate the method and to compute its performance. Using 20 stars and a modest angular distance measurement accuracy of 1", the position and velocity of the spacecraft can be determined to within 3 au and 2 km/s respectively. If a measurement accuracy of 1 mas is achievable then the navigation accuracy increases by a factor of 1000. Using more stars and/or including also onboard measurements of the stars' radial velocities improves the accuracy further.

That's good. I like it.

 

[lpetrich]

For pulsar-pulse navigation, I will see if the aliasing problem can be resolved.

One can find one's position with a least-squares fit:
\( E = \sum_i w_i (n_i \cdot x - t_i)^2 \)
for error E, individual pulsars i with arrival time t(i) at the coordinate origin and weighting w(i), and position x. A good choice of weight is
w = 1/(pulse_size)^2

E can be found from a quadratic equation in x:
\( E = T - 2(X.x) + (x.N.x) \)
where
\( T = \sum_i w_i (t_i)^2 ,\ X = \sum_i w_i t_i n_i ,\ N = \sum_i w_i (n_i \otimes n_i) \)

The least-squares solution is
\( x = N^{-1} \cdot X \)
with error
\( E = T - X \cdot N^{-1} \cdot X \)

The aliasing problem is essentially which pulse is one observing. For pulse periods P and pulse count m we have
\( t_i \to t_i + m_i P_i \)

This gives us
\( E = E(0) + 2 \sum_i m_i E'_i + \sum_{ij} m_i m_j E''_{ij} \)
where
E(0) is E for all the m's = 0,
\( E'_i = w_i P_i (t_i - n_i \cdot N^{-1} \cdot X) \)
\( E''_{ij} = w_i (P_i)^2 \delta_{ij} - (w_i P_i) (w_j P_j) (n_i N^{-1} n_j) \)

One can do a least-squares solution here also,
\( m = - (E'')^{-1} E' \)
but it has the problem that the m's are constrained to be integers. But one can take such a solution and round it to create an initial one, and then search around it. This problem is sometimes called a problem in integer quadratic programming.