An interplanetary coordinate system

Question

On earth, we use a simple but effective coordinate system which determines position unambiguously on the surface (GPS achieving accuracy within 1 meter, which speaking as an engineer, is a remarkable feat in of itself).

For example, Greenwich, England is located at coordinates 51.4800° N, 0.0000°. This disregards tilt of the earth, position around the sun, minor gravitational directional changes due to the pull of the moon, etc. because they are not relevant.

My point is that should we one day inhabit one or more planets outside our solar system, we'll need a new unambiguous system to identify coordinates of the planet in 3d space.

A 3d coordinate system with an x, y, and z coordinate would be relatively impractical since the position of the planet in question would be constantly changing position. There are several factors that come to mind to take into consideration:

• Position of the star it is orbiting
• Any local moons that may alter it's position slightly.
• The tilt of the planet at any given moment (unlike our current system which needs not consider the current tilt of the planet, you would need to know the current tilt in order to find the proper 2d planetary coordinates)

Like most good systems, it must have the following qualities:

• Be precise, in this case lets say within a kilometer of the destination.
• Be concise. Minimize the amount of information you need to provide, in this case in order to unambiguously find the position of the planet
• Be accurate also in the near future. Coordinates which are established on earth must still unambiguously be valid by the time a ship arrives (lets say remain within a kilometer of the destination within 100+ years time)

Assume there are no adverse space-time effects to consider (which would likely make an accurate and practical interplanetary coordinate system nearly impossible).

Assume that we will have computers and thus you do not have to provide information that could otherwise be calculated or remains relatively static (within 100 years time stays the same). For example, given a star's 3d coordinates and angle, a computer would load the planet's distance from the sun and be able to determine roughly where that planet would be, without having to include it in the coordinate system.

Answer 1

Suppose you were given orders to explore an unknown planet's volcano, how would they deliver the coordinates?

"They" would need to give you two things: the coordinates of the planet itself, needed for the interplanetary travel, and the coordinates of the volcano on the planet.

These are two different coordinate systems, with different origins and uses. It is like when you say "42nd Main Street, third floor, office 31". You use a three dimensional system for locating the bunch of offices of the company (42nd Main Street, third floor) and then a different system to locate office 31.

So, to locate the planet, the system does actually exist. Actually, several of them. The simplest method is to give planet's xyz coordinates, but the more stable is to give its orbital parameters. These are enough to know where the planet is just knowing the time.

e.g. Earth has a semi-major axis of 149513000 km, eccentricity of 0.0161700, inclination of 7.155 deg to Sun's equator, and an argument of perihelion of 326.0590 deg. These, together with current time, tell you exactly "Where Earth is".

Once on the planet, the current longitude/latitude system is well defined once you know the origin of longitudes, to say, the Greenwich point.

If you were also in need to locate the star itself, for interstellar trips, you have two options: either the galactic coordinates (galactic latitude, galactic longitude and distance to the galactic center) or those relative to Sun's position.

Answer 2

Disclaimer: I may work on software that has to automatically shift between a dozen frames and coordinate systems on a constant basis to meet user needs and expectations!

I think you might be putting too much into GPS =) I'm going to divide this into two parts. First part is an ephemeris overview, the second is more directly associated with the question.

I think you're actually trying to do several things at once:

• GPS is a way to measure time signals and map them back into space to define a point in space.
• ECEF is a coordinate system (Earth Centered, Earth Fixed) where points on the surface of the idealized Earth don't move. ECI (Earth Centered, Inertial) is an inertial coordinate frame. Points on the surface of the earth move fast in this coordinate system, but the coordinate system is not rotating (more on that later)
• Instructions need to be able to describe where to go.

Each of these is a separate issue. As an example, the output of GPS is a point in space, but it isn't necessarily in any particular coordinate system. You can always convert from one system to another without losses. For example, it is really common to use ECEF to map GPS points onto the earth, because for most common purposes, we'd like "stationary" objects to not move. This can also be converted into latitude/longitude/alt (LLA), which is what people typically think of for "GPS coordinates," using nothing but basic trigonometry.

However, there are situations where this system does not give good results. Consider if your target is moving (such as planets always are). It is not meaningful to give out the "GPS coordinate" of a moving car, because the car rapidly leaves that location. Likewise, the XYZ coordinates of a planet will likely shift over the years, unless your coordinate system is fixed to the planet.

There are also situations where you don't want ECEF or LLA. ECEF is a "rotating" frame because the Earth is rotating, and it is tied to the earth's surface movement. Because it is rotating, you have centripetal acceleration and the Coriolis effect. This means, for objects propagating over long times (like planets would in your example), their motion is actually a remarkably complicated shape. Modern sniper computers actually have to account for the Coriolis effect, making the bullet twist to the side in a non-intuitive manner! For positioning satellites, people talk almost exclusively in ECI. ECI is an inertial frame, so Netwon's laws of motion work roughly like you expect them to (at the price of points on the surface of the earth having large apparent veloicites.

The first major challenge of your problem is defining a coordinate system, so lets look at how we do it today.

An intuitive guess would be that we start with ECEF, and build outwards to LLA and ECI. However, this is not the way they are defined. A coordinate system must have a mathematically sound definition, or positions and motion are ill-defined within the coordinate system. "Points on the Earth hold still" is a poor definition. Consider plate tectonics, which guarantees that a coordinate system perfect for Washington D.C will not be perfect for Berlin.

We, instead, start from ECI. ECI is centered on the centroid of the Earth. This is a relatively fixed concept (though technically changes infinitesimally when we send things to Mars). Anybody can measure the Cg of the Earth, so the center of the coordinate system is reliable. Now we need an orientation for the coordinate system. This is the equivalent of deciding which direction faces up on a map. This is trickier. We know we want an "inertial" frame, but that doesn't specify directions people can agree upon.

To deal with this, we sacrifice a bit. We get "close enough" to an inertial frame, in exchange for a measurable coordinate system. ECI notices that it has two rather reliable datums: the normal for the orbital plane for the Earth, and its rotational axis. Twice a year, at the equinox, these two align, creating a convenient measurement time that occurs every year. We arbitrarily pick the vernal equinox (rather than the autumnal equinox) to base our ECI systems off of. This does mean recreating the ECI frames requires observing seasons.

Now we get into the specifics. ECI is actually a class of frames. Each frame just changes how things are measured. Consider J2000, which is a ECI frame built from the equinoxs and poles of the Earth January 1, 2000 12 noon "Terrestrial Time." Note we even had to agree on a time to make ECI work!

Woof! Now think about ECF. ECF coordinate systems have to rotate, but we don't actually tie them to the earth. We tie them to a mathematically perfect Earth. We declare "ECI and ECF coincide at a date-time," such as Jan 1, 2000 12 noon, and that ECF rotates about the earth's rotational axis at a fixed rate: 7.2921150 x 10^-5 radians/s. This gets close enough to the earth's movement that we can claim spots don't move on the surface of the earth.

Holy cow! What was the purpose of all of that? Defining a coordinate system accurate to a kilometer over the galaxy will be hard, much less measuring it!

As a note: There are more systems than the ones shown. For plotting paths from Earth to Mars, a solar centric model is often used. This is a much more inertial frame, so longer paths are easier to calculate. There are also galactic frames used, which are usually specified via constellations.

Final detail: instructions. We don't always give instructions in coordinates, for the reasons stated earlier. They aren't always enough. We often give instructions in steps. It would be valid to say "go to Lat/Lon, orient yourself towards the tip of the mountain visible from there, and head that way. I'll be along that line." It's also valid to say "here is an ephemeris table describing my position over time. Go there." Instructions are complicated.

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You will have trouble creating a map of the universe with 1km resolution. Consider a major issue: gravity wells. The universe is not flat. Those bends are going to matter a LOT if you want to see 1km resolution over a travel path of 41314127500000km. That distance, by the way, is the distance to Alpha Centauri, which is a relatively short jaunt by galactic distances. For comparason, that is like planning a trip from the moon to the earth, and trying to define a landing site within 10um!

Instead, we would do trips in steps. First we'd use a galactic coordinate system with poor resolution to jump into the right 1000 cubic light-year block. You would find your location using a best fit of visible stars to a 3d constellation map. Then we would take the time to acquire a more local coordinate frame to jump to the right star. Then we would probably use orbital mechanics to determine the right planet. Then we'd analyze landmarks on the planet to determine a local coordinate system. Then we'd jump down and survey to get to km.

The shape of these instructions would vary, based on what you are actually trying to do. Instructions on where a person is on a planet would be different from instructions as to finding an asteroid in an astroid belt (which may have collided with something since coordinates were read).

There's always PO boxes!

Answer 3

The only realistic way to accomplish a coordinate system for stars (and thus planets as well) would be to model the movement of stars through the galaxy. You would need to know both the velocity and acceleration, as position would very quickly become useless. Hence, you would need to actually be able to predict the movement of stars.

The problem is, as it stands, we don't actually understand that. There are a number of theories about how stars move in galaxies, most of which have issues of some form. To my knowledge, density wave is the best, but does not account for all phenomena. For example, density wave would suggest very uniform galaxies, which we rarely observe. The lack of uniformity is likely due to past collisions with other galaxies, non-uniform mass distribution, influence of other galaxies, or even effects we do not understand.

I would suggest that either density wave or measured acceleration values would be sufficient to keep the system accurate. It might need manually corrected every decade or so, but could work with our current technology. However, it is quite likely a spacefairing civilization would know more about galactic movement than we do, and might be able to develop a model which could accurately predict future movement much better than we could now.

As to how this system would physically look, I would expect if this is within a single galaxy (you did not mention multiple), we would use radial coordinates from the galactic core, plus a z axis. Essentially, r, θ, and z. Most likely, θ=0 would correspond to the homeworld of the civilization in question, much like GMT=+0 being in Britain. From there, each star would have its associated position/velocity/acceleration vectors (all likely functions of the model being used linked to measured data), and then each planet would be connected to the star the way we currently measure solar movement (you said to ignore the details on this, so I am, and I don't completely understand them myself, anyway).

All that said, I'm doubtful about your expectation of 1 km accuracy. That's nothing on a galactic scale, and roundoff error would likely cause far greater than that to be lost. That isn't even accounting for the likely error inherent in whatever FTL system in use. On the other hand, solar systems are quite big, and simply getting close enough seems like a workable outcome. There are likely good reasons not to be FTLing around inside a solar system in the first place.

Answer 4

Actually you would need to map in 4d, not 3d. We actually use 3d mapping (latitude, longitude AND elevation). I would expect each planet to have a similar system of terrain mapping as we have here on earth. The planets would be mapped in relation to the sun, the basics would be w(time), x,y with z being less important for most travel in the orbital disc. z will of course become more important as we do more and more travel.

Answer 5

First off I'll note that in the future we may have a way to determine position anywhere in the solar system or throughout the galaxy without assistance using pulsars like stellar GPS satellites. (I know some of the people who worked on this idea and they say it's plausible with today's technology, they just don't have the funding yet.)

For traveling to other stars, you could therefore give heliocentric XYZ coordinates and velocities (since stars are not affected by gravity too much over timescales of human interest).

Now one thing that makes the celestial navigation problem vastly easier is that (unlike points on the Earth's surface) there is not a continuous array of stars and planets: there exist only a finite number in discrete locations. Think of addresses: we don't give the GPS coordinates of a house, we give the city, street name, and street number. In order to identify Earth, for example, we would only have to identify the Sun (and we don't have to be too precise, since the nearest star is light-years away) and then we can label Earth as the third planet. Anybody who can observe the solar system will be able to see and identify the location of Earth.

Finally, I'll leave you with the JPL HORIZONS website. Set Ephemeris Type to ELEMENTS and click Generate, and it will give you the orbital elements of the target body (default is Mars). Six orbital elements are enough to completely specify the orbit of a body. They change slowly over time, but if you just want to identify a planet they're close enough. If you want to precisely predict it's position, then you probably only need to additionally store the rate of change of the parameters.

Answer 6

You can just use names, much like a postal address:

10 Downing Street, London, UK, Earth, Solar System, Orion Arm, Milky Way, Local Cluster, Virgo Supercluster

At the time you will need such coordinate system, Google Sky will be able to convert it to an exact position pinned on a map.

Answer 7

The co-ordinate system you choose would depend on the location you want to specify.

If you want to specify the position of a star within the Milky Way, one option might be to use a polar co-ordinate system centered on the galactic center of mass. Inspired by the terrestrial longitude/latitude co-ordinate system, we would align the North/South axis with the galactic axis of rotation (mean orbital axis of all the stars in the galaxy). This would require a choice of "North", a "galactic prime meridian" (0 degree "galactic longitude" plane), and a choice of right or left handed co-ordinates (in which direction do longitude values increase). We might base the galactic prime meridian on the location of the Sun. Of course the Sun is in orbit around the galactic center, so our co-ordinate system would be slowly rotating. It would also mean that virtually every star in the galaxy will have some motion with respect to this co-ordinate system, so won't have a fixed location. However, that motion might be slow enough that we can assign galactic co-ordinates to stars and they will remain useful for practical time spans.

To specify the location of a remote world, you'd have to identify its host star and its orbital parameters, as described in other answers.

To specify a location on the surface of a remote world (we'll assume worlds with solid surfaces), you'd need to establish a co-ordinate system for each world. Again, drawing inspiration from terrestrial longitude/latitude co-ordinates, it would be a polar system, with the axis aligned to the planet's axis of rotation (assuming it has a stable rotation). Again, there needs to be a choice of "North", a choice of prime meridian, and choice of handedness. On Earth, Grenwich was something of an arbitrary choice, chosen perhaps only because it was the site of an observatory. On a remote world, one might identify the site of a specific colony or a geographic feature and set the planet's prime meridian from that. As with plate tectonics on Earth, the exoplanet surface might be in motion, so whatever feature was used to set the prime meridian may gradually move away, so it would only serve as inspiration.