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Navigation in space

 
 
 
steve_bank said:
I expect that would be a life project evolving over generations.

Start with a model of the solar system that for any [x,y.z] you see the motion of the solar around you. When that is working start expanding incrementally.


It sounds simple, just coordinate and reference frame transformations. I expect complexity wou ldgrow quickly.

Compensation for the finite speed of light and time dilation.
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That seems like an old idea. Some clock makers were making moving models of the solar system (orreries) since the 1300s. Of course the early orreries were geocentric models but later models were heliocentric.

They would have been handy as they would show a planet watcher where to look for any specific planet any time.
 
From relativity there can be no absolute frame, and to identify a point in space it is [x,y,z,t]

In the 19th century the Brits developed a clock with low drift, resistant to temperature, humidity, and ship motion. At least relative to existing clocks.

That really en bled navigation. Synchronize clocks at home in England and with a sextant you can accurately find position on the oceans.

Just within the solar system how would a reference frame be established common to all points in the solar system? What is the time reference? I do not thing it is possible.

You could use Earth as a time and spacial reference point. Once at a point your computer can dispay changing positiin of planets around you.

It is all relative motion. You are at rest at a point in the solar system compared to what?

Light takes time to reach us, so to predict current position of a star you would jave to take into account C. I am weak in astronomy and relativity beyond the basics, but it seems like a difficult model to apply on a galactic scale, maybe impossible.

If theoretically possible how accurate does it have to be given capable soae ships.

I am sure you can go online and find animationsof the solar system and estimates of current positions of pklnets relative to Earth.

You coud but beacons at points in the solar system and potentially work out a LORAN type of system. Deduce position from time of arrival of the different signals.

That is as far as my thinking goes.

More and more it becomes clear that an ET visitor is unlikely.
 
Swammerdami said:
...
Yes, it would be easy to do ... for those who do these things easily! ...

Browsing a folder just now, I see I did some simple star-mapping 4 years ago. I'm attaching one of the resulting lists; I never did anything with it beyond this. The required algebraic manipulations for that were much simpler than drawing constellations.
Click to expand...

I suddenly realized that the C program I wrote to print the table I showed, already does almost all the work needed!

I just define one end of the travel line at a point where Orion is to be viewed, the other end near the center of Orion. The (z, r, theta) for each star in Orion that the code already computes can be trivially converted: (r/z, theta) are the desired polar coordinates! I'll do this next time I'm bored. Anyone want to see those views of Orion?
 
steve_bank said:
From relativity there can be no absolute frame, and to identify a point in space it is [x,y,z,t]

In the 19th century the Brits developed a clock with low drift, resistant to temperature, humidity, and ship motion. At least relative to existing clocks.

That really en bled navigation. Synchronize clocks at home in England and with a sextant you can accurately find position on the oceans.

Just within the solar system how would a reference frame be established common to all points in the solar system? What is the time reference? I do not thing it is possible.
Click to expand...

The stars around us I do not believe are moving at velocities where we need to consider relativistic corrections. We only need to consider it when computing the view from a starship in motion.

As for time--same way they did it in the old days, synchronize your clocks. Just make sure to compute Earth time correctly.

I don't think stellar motions will be big enough we need to consider them for ships at relativistic velocity--slowboats might care. If you care, while still using polar coordinates offset by how far it's moved in the time light takes to get there, and do the same thing the other way around after converting back to polar. Until we have better star maps I don't think that matters, though. You need some sort of maneuvering engine anyway. The worst case is the laser-pumped lightsail because it can't deviate from it's flight path even if it finds it's wrong. A few AU off won't be a mission killer, though, so I don't think this is a big deal.

Note, also, that before we consider such voyages we will have built big telescopes in space and thus have more accurate information as to where the stars are.
 
lpetrich said:
Let's say we use Gaia parallaxes with errors of 10 mcas. At A-Cen, those errors will have become magnified to 3 arcsec. Spacecraft celestial navigation ought to do at least as good as 1 arcsec, and likely much better. For 0.1 arcsec, that means that the Gaia errors will be 30 times larger than the observational errors.
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We should take into account that the database as a whole provides much more accurate readings than the individual observations in it, because the standard deviation of the mean goes inversely with the square root of the number of data points. So if there are 21 million stars whose positions are measured to 1 arcsec, using them collectively would be as accurate as relying on a few beacon stars known 4600 times better than that, about 220 mcas. For a spacecraft within a few parsecs of Earth, this should be good enough to let it determine its own position with an error on the order of 1,000,000 km.
 
“It is the mark of an instructed mind to rest satisfied with the degree of precision which the nature of the subject permits and not to seek exactness where only an approximation of the truth is possible”
~ Aristotle

Applied physicists and engineers understand that 'close enough' works fine in many cases. Spherical cows can often be very useful.
 
Swammerdami said:
The task is to draw pictures of the Orion constellation, as it would be seen from this solar system, and from any of (your choice of) several grid locations, say 12-20 light-years distant from Sol.
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The clamoring for these pictures was less than deafening; and now I'm wondering why I wanted these pictures in the first place!

Lest I regret this detour ... Cheer me up please! Give me an "Attaboy, Swammi!" or "Gee thanks; exactly what I wanted for my birthday."

The picture of Orion from Earth is surrounded by eight pictures, each 20 light-years distant from Sol. Those eight (equally spaced) translation vectors are each roughly perpendicular to the Sol-Orion line. In addition to the eight brightest stars of Orion, nearby bright stars are shown:
  • Ald - Aldebaran (alpha Taurus)
  • Mirz - Mirzam (beta CanisMajor)
  • Pol - Pollux (beta Gemini)
  • Alh - Alhena (gamma Gemini)
  • unn - an unnamed G0III star 42 ly from Sol

orion.png
 
I don't like the word exactness in context. Precision and accuracy are two different things. Precision s how small the divisions are on a ruler. Accuracy is how close the measuremet is to a standard.
With experience there was routine stuff where you knew how detailed you needed to be.

I learned the hard way that when starting a project you have to quantify how tight things have to be. Otherwise you canbe deep into something and find yourself in trouble.


There is always a tradeoff between time, over analyzing, and risk of failure.


So, if looking at navigating space you have to ask given a starting point how close do you need to be at the other end. That leads to a specifcation you can work to.

In the Columbus era and early ocean crossings it wasdead reckoning. Head in a general direction and look for landmarks when you get close to shore.

If I were going to do a formal analysis I would run a simulation which accounted for all potential errors using Monte Carlo techniques to establish an statistical error bound.

That gives you a feasibility estimate.

Will a spherical error probaility of a ly be good enough? f you had warp drive that would b close enough. You can correct for errros with little loss of time. For a slow multi generation ship maybe not so much. Get too far behind a target star and never catch up.
 
skepticalbip said:
“It is the mark of an instructed mind to rest satisfied with the degree of precision which the nature of the subject permits and not to seek exactness where only an approximation of the truth is possible”
~ Aristotle

Applied physicists and engineers understand that 'close enough' works fine in many cases. Spherical cows can often be very useful.
Click to expand...

Well, they're easy to moooove, just roll them!
 
I'll give some size estimates.

  • Aberration, radial velocity: (v/c) for velocity v
  • Parallax: (b/d) for baseline b and distance d
  • Time delay: b/c for baseline b
For pulsars, time delay outside of cislunar space is IMO too large to make them very useful, because of aliasing -- which pulse is one observing? Navigation satellites include timestamp data in their pulses, so these satellites get around that problem.

I'll use Alpha Centauri as a reference, since it is the nearest star outside the Solar System, at 1.3 parsecs. From  List of brightest stars, many of them are about 100 or so times farther, though some are not much farther, like Sirius at 2.6 pc, Procyon at 3.4 pc, Altair at 5.2 pc, and Fomalhaut and Vega at 7.7 pc. Some of them are 500 or more times farther, like Deneb.


Anything outside our Solar System is referred to Solar-System barycentric coordinates, where the origin is at the Solar System's barycenter, and the directions are from the Earth's averaged-out orbit and spin orientations at some time epoch, like J2000 (January 2000).

For Earthbound observations, it is routine to correct for the Earth's position and velocity, so let us see what the numbers look like.

Earth's center relative to SS barycenter: A-Cen's parallax is 0.77 as (770 mas) and aberration is 20.5 as.

Earth observer relative to its center: position ~ 6371 km from its barycenter, velocity at most 460 m/s. A-Cen's parallax is 33 mcas, and aberration is 0.32 as.

For low Earth orbit, I will use the ISS's altitude of 400 km. The ISS's orbital velocity is 7.7 km/s. A-Cen's parallax is 35 mcas and aberration is 5.3 as.

For geosynchronous orbit, the altitude is 36,000 km (total distance 42,000 km) and the orbital velocity 3.1 km/s. A-Cen's parallax is 220 mcas and aberration is 2.1 as.

For the Moon's orbit, the total distance is 384400 km and the orbital velocity 1.0 km/s. A-Cen's parallax is 2.0 mas and aberration is 0.7 as (700 mas)

For the nearby Earth-Sun Lagrange points (L1, L2), the total distance is 1.5 million km and the orbital velocity is 0.3 km/s. A-Cen's parallax is 7.7 mas and aberration is 0.2 as (200 mas)

So using parallax and aberration inside of the Earth's sphere of gravitational influence is not very feasible. That sphere is the Hill sphere, and it extends out to L1 and L2.
 
I'll now consider the Solar System outside of the Earth's Hill sphere. For the inner Solar System, we have numbers similar to those for the Earth, A-Cen's parallax is 0.77 as (770 mas) and aberration is 20.5 as.

One could find velocities with aberration if one wanted to, but one would need very precise measurements, and the results would not be very precise.

For the outer Solar System, I'll take Neptune, the farthest-known full planet, at 30.07 AU and 5.43 km/s. That gives A-Cen parallax = 23 as and aberration = 3.7 as.


So I turn to the nearby stars. They have a lot of velocity scatter, and the Sun has a velocity relative to those velocities' average, the Local Standard of Rest.

A rough summary: lecture11.pdf
Some recent work: [1501.07095] Determination of the Local Standard of Rest using the LSS-GAC DR1
Relative to the LSR, the Sun's velocity is 7.0 km/s inward, 10.1 km/s forward in orbit, and 5.0 km/s northward out of the Galactic plane. That's a total of 13.3 km/s.

From Allen's Astrophysical Quantities, I estimate the velocity dispersions of Sunlike and less massive stars as (inward-outward) 31 km/s, (forward-backward) 19 km/s, (northward-southward) 16 km/s, or a total of 40 km/s.

So to avoid being very restricted in what stars one can go to, one must depart from the Solar System at 100 km/s or more.
 
The star's position: xs = d*{1,0} + t*{vr,vt}
The spaceship's position: xt = v*t*{cos(a),sin(a)}

For them to meet, xs = xt, and I find

sin(a) = vt/v
t = d/(sqrt(v^2-vt^2) - vr)


 List of artificial objects leaving the Solar System
The spacecraft: Voyager 1 17.0 km/s, Voyager 2 15.4 km/s, New Horizons 13.9 km/s, Pioneer 10 & Pioneer 11 11.9 km/s.

I thin that one will need at least 50 km/s departure speed, or likely 100 km/s, to avoid being very restricted.

Since 1 km/s ~ 1 parsec / million years, that means 1 pc / 10^4 years

That means an aberration of 1 minute of arc.

It would take 13,0000 years to make it to A-Cen.

Once there, stars like Sirius and Vega would be displaced by several degrees, most of the brighter ones would be displaced a lot less, like half a degree, and Deneb around 1/10 of a degree.
 
The best case for nuclear-energy propulsion I estimate at 0.1 c, giving an aberration of about 6 degrees and a radial-velocity shift of about 0.1.

Going much faster with onboard fuel will require antimatter, and that's full of problems. Though antimatter provides the highest-efficiency energy release, it is very hard to make and very hard to store.

I've tried to find the efficiency of making antimatter, and numbers are hard to find. But I once found 10^(-3) for positrons and 10^(-8) for antiprotons.

Antimatter's properties are easy to predict, since antimatter is not some sort of bizarro matter but just like ordinary matter with some properties mirror-imaged, like electric charges. Masses are not mirror-imaged, however. This mirror imaging cancels out of most familiar macroscopic properties, and one can use that to estimate how easily one can store antimatter.

Storing it is a HUGE problem, since antimatter tends to prematurely react with the ordinary matter around it, destroying itself and that matter in the process.

At first thought, it seems easy. Make lots of positrons. But they are just like electrons, and they electrically repel each other. To stabilize them, one must make antinuclei, and the easiest ones to make are antiprotons. That makes antihydrogen, and it boils at the same temperature as ordinary hydrogen: 20 K. Keeping it frozen will be a challenge.

One can make antimatter substances that boil at higher temperatures, but one has big problems. One can add antineutrons, but there are no stable nuclei at 5 and 8 nucleons. So getting past those gaps is challenging.
 
One problem with speed is reaction forces when changing couse and velocity. The change in inertia has to show up somewhere.

STNG had 'structural integrity fields' that kept the structure from tearing itself apart.

It would get worse if you had a rotating drum for artificial gravity.
 
[If this tangent is too distracting, please ask the Mods to delete this post, or hide it with Hide tags.]

Perverse perfectionism ranks somewhere on my List of 30 Biggest Faults. I am unable to proceed without posting a flaws-corrected version of the Nine Views of Orion. Again the eight views other than the central view from Earth are taken every 45 degrees along a circle of radius 20 ly centered at earth and perpendicular to the Earth-Orion line.

Many more stars are shown than in the previous effort (263 stars over the nine pictures). A bug feature is that faint stars are colored black or dark grey; they are visible in the image if magnified.

Here is a list of the 16 stars brighter than 2.4 which occur in these images. These include the 7 brightest stars in Orion, 7 stars shown with labels, the second brightest star of Castor (a sextuple-star system), and the second brightest star of Capella (a quadruple-star system). Amusingly(?) Capella's companion was BARELY in a viewing frame of my earlier effort, while Capella itself was NOT -- I didn't note the connection then and labeled this companion as "unnamed star."

The first number in the entries following shows how many of the 9 views contain the star; the second number is the star's relative magnitude.

CAP : 1 Capella [-0.6] alpha Aurigae
--- : 9 Rigel [0.2] beta Orionis
--- : 1 Capella companion [0.3]
--- : 9 Betelgeuse [0.4] alpha Orionis
POL : 1 Pollux [0.5] beta Geminorum
ALD : 2 Aldebaran [0.7] alpha Tauri
CAS : 1 Castor [1.1] alpha Geminorum
aln : 1 Alnath [1.5] beta Tauri
--- : 9 Bellatrix [1.6] gamma Orionis
--- : 9 Alnitak [1.7] zeta Orionis
--- : 9 Alnilam [1.7] epsilon Orionis
alh : 4 Alhena [1.9] gamma Geminorum
mir : 7 Mirzam [2.0] beta Canis Majoris
--- : 9 Saiph [2.1] kappa Orionis
--- : 9 Mintaka [2.3] delta Orionis
--- : 1 Castor-companion [2.4]

orion2.png


I have my own blog under a different name I keep separate from 'Swammerdami.' Therefore I never post both to my blog AND TalkFreeThought; and have therefore lost the opportunity of posting this to my blog. :( I will avoid this mistake in future! :)

 
lpetrich said:
The best case for nuclear-energy propulsion I estimate at 0.1 c, giving an aberration of about 6 degrees and a radial-velocity shift of about 0.1.

Going much faster with onboard fuel will require antimatter, and that's full of problems. Though antimatter provides the highest-efficiency energy release, it is very hard to make and very hard to store.

I've tried to find the efficiency of making antimatter, and numbers are hard to find. But I once found 10^(-3) for positrons and 10^(-8) for antiprotons.

Antimatter's properties are easy to predict, since antimatter is not some sort of bizarro matter but just like ordinary matter with some properties mirror-imaged, like electric charges. Masses are not mirror-imaged, however. This mirror imaging cancels out of most familiar macroscopic properties, and one can use that to estimate how easily one can store antimatter.

Storing it is a HUGE problem, since antimatter tends to prematurely react with the ordinary matter around it, destroying itself and that matter in the process.

At first thought, it seems easy. Make lots of positrons. But they are just like electrons, and they electrically repel each other. To stabilize them, one must make antinuclei, and the easiest ones to make are antiprotons. That makes antihydrogen, and it boils at the same temperature as ordinary hydrogen: 20 K. Keeping it frozen will be a challenge.

One can make antimatter substances that boil at higher temperatures, but one has big problems. One can add antineutrons, but there are no stable nuclei at 5 and 8 nucleons. So getting past those gaps is challenging.
Click to expand...
Ultimately, the problems of antimatter production go away at around the time we have the technology to produce large quantities of anti-matter, which would require something around the sun, absorbing gargantuan amounts of energy. In order to have level of tech, we'd presumably have the tech to use magnetic fields to isolate antimater particles. The trouble becomes, you'd still need a large amount of anti-matter (100+ tons) to go any decent percentage of c. Anti-matter takes you farther at lower speeds, but then you aren't getting anywhere.

I ponder if anti-mass (not anti-matter) propulsion is possible. Even if it is, we continue to run into the problem that is the universe... it is too big. It might simply be an issue of being stuck in space, much like we can't just swim to bottom of the Pacific.
 
Swammerdami said:
[If this tangent is too distracting, please ask the Mods to delete this post, or hide it with Hide tags.]

Perverse perfectionism ranks somewhere on my List of 30 Biggest Faults. I am unable to proceed without posting a flaws-corrected version of the Nine Views of Orion. Again the eight views other than the central view from Earth are taken every 45 degrees along a circle of radius 20 ly centered at earth and perpendicular to the Earth-Orion line.

Many more stars are shown than in the previous effort (263 stars over the nine pictures). A bug feature is that faint stars are colored black or dark grey; they are visible in the image if magnified.

Here is a list of the 16 stars brighter than 2.4 which occur in these images. These include the 7 brightest stars in Orion, 7 stars shown with labels, the second brightest star of Castor (a sextuple-star system), and the second brightest star of Capella (a quadruple-star system). Amusingly(?) Capella's companion was BARELY in a viewing frame of my earlier effort, while Capella itself was NOT -- I didn't note the connection then and labeled this companion as "unnamed star."

The first number in the entries following shows how many of the 9 views contain the star; the second number is the star's relative magnitude.

CAP : 1 Capella [-0.6] alpha Aurigae
--- : 9 Rigel [0.2] beta Orionis
--- : 1 Capella companion [0.3]
--- : 9 Betelgeuse [0.4] alpha Orionis
POL : 1 Pollux [0.5] beta Geminorum
ALD : 2 Aldebaran [0.7] alpha Tauri
CAS : 1 Castor [1.1] alpha Geminorum
aln : 1 Alnath [1.5] beta Tauri
--- : 9 Bellatrix [1.6] gamma Orionis
--- : 9 Alnitak [1.7] zeta Orionis
--- : 9 Alnilam [1.7] epsilon Orionis
alh : 4 Alhena [1.9] gamma Geminorum
mir : 7 Mirzam [2.0] beta Canis Majoris
--- : 9 Saiph [2.1] kappa Orionis
--- : 9 Mintaka [2.3] delta Orionis
--- : 1 Castor-companion [2.4]

View attachment 33332


I have my own blog under a different name I keep separate from 'Swammerdami.' Therefore I never post both to my blog AND TalkFreeThought; and have therefore lost the opportunity of posting this to my blog. :( I will avoid this mistake in future! :)

Click to expand...

Your images are all upside down.
 
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