= ASTRONAUTICAL EVOLUTION =

When will Voyager 1 leave the Solar System?

Stephen Ashworth, Oxford, UK

Searching for a boundary

As Voyager 1 reports on changing patterns of particles and fields at the edge of the heliosphere, claims are appearing that it is on the verge of leaving, or may already have left, the Solar System:

• An article by Tia Ghose in Space.com claims: “NASA’s Voyager 1 Probe May Have Left Solar System” (20 March 2013).
• But according to the latest NASA update, “It is the consensus of the Voyager science team that Voyager 1 has not yet left the solar system or reached interstellar space” (20 March 2013).
• Jonathan Amos and David Shukman provide coverage on the BBC website, together with a fanciful artist’s impression of Voyager 1 against a blue-sky (!) Milky Way (20 March 2013).
• Paul Gilster recently discussed the Voyagers in Centauri Dreams, “Looking Back from Deep Space” (25 February 2013).
• Meanwhile an earlier NASA news item reports on the changing signs that the Voyager science team are watching for (3 Aug. 2012).

Voyager 1 is currently humanity’s most distant probe, 123.7 AU from the Sun at the time of writing (the exact distances of Voyagers 1 and 2 from both Sun and Earth are given on their homepage, updated at half-second intervals). It is a notable feature of their slow progress that for part of the year, their distances from Earth are actually decreasing because for part of its orbit Earth, moving faster, is catching up with them. But their distances from the Sun, and from Earth year by year, are of course always increasing.

The domain of the Sun is the region of space which is dominated by our star’s gravitational and magnetic fields. Here, too, the Sun is brighter than any other object in the sky. But does this domain have a clear boundary which a spacecraft can cross? Does it actually make sense to draw a line in the sky and define the space on one side as interplanetary and on the other as interstellar?

There appears to exist a reasonably well-defined magnetic boundary. The Voyagers are clearly close to this boundary: JPL states that they are in the heliosheath (the outermost layer of the heliosphere), but have not yet crossed into interstellar space. But a graphic of their current location suggests that the distance from the Sun to the edge of the heliosphere is wildly different in different directions. Even in any particular direction, that distance will surely vary over the 22-year solar cycle as the Sun’s magnetic strength waxes and wanes.

The Sun’s gravitational dominance extends well beyond its magnetic influence. The small world 90377 Sedna, discovered in 2003, is currently close to its perihelion of 76 AU (which it will reach in 2076), but over the course of the next 5,700 years it will retreat to an aphelion of around 937 AU, or more than seven times further from the Sun than Voyager 1 is at present, and so presumably well outside the heliosphere in that particular direction.

A few other small bodies are known with similarly large aphelia: minor planet (87269) 2000 OO₆₇ has aphelion at 1068 AU, while (308933) 2006 SQ₃₇₂ goes out as far as 1570 AU. There must be many more waiting to be discovered.

Are we to say that Sedna and similar worldlets spend part of their orbit in the Solar System, but the rest of the time are outside the Solar System, in interstellar space? This would be bizarre: these are Solar System bodies, therefore the Solar System must extend out at least to 1600 AU. And what about the hypothesised Oort Cloud? Although no bodies in the Oort Cloud have yet been directly observed, it is believed that vast numbers of icy asteroids (which form long-period comets when occasionally disturbed into falling into the inner Solar System) exist out to a distance of up to a light-year. Do the unperturbed majority spend their entire lives orbiting the Sun in interstellar space?

These are, however, small bodies, smaller than Pluto. Perhaps the outer boundary of the Solar System should be marked by the orbit of its outermost planet?

For the present the outermost known major planet remains Neptune; the largest body currently known beyond Neptune is tiny Eris, both smaller and lighter than Neptune’s largest moon Triton (which is in turn the smallest of the Solar System’s seven planet-sized moons). The distance of Eris from the Sun varies from 38 to 98 AU, thus well within the heliopause. But it remains possible that one or more larger worlds, even a planet, could be discovered in a stable circular orbit well beyond the heliopause, and even more so that such worlds may be found orbiting other stars.

The orbit of Neptune defines a pancake 30 AU in radius but only 1.9 AU thick (due to the inclination of that orbit at 1.77° to the ecliptic), which can be regarded as the domain of the major planets.

We thus find three possible definitions for the boundary of the Solar System:

1. Magnetic, where the solar wind gives way to an interstellar flow of charged particles: apparently somewhere near 125 AU out in the direction in which Voyager 1 is travelling, but according to the JPL graphic much greater in other directions, and in all directions likely to fluctuate in time depending on the fluctuating strength of the solar magnetic field.
2. Gravitational, at the orbit of the outermost major planet: that of Neptune at 30 AU in the direction of the ecliptic plane but only 0.93 AU towards the poles of the ecliptic; values that are stable over time but would change if a new trans-Neptunian ninth planet is discovered.
3. Gravitational, at the aphelion of the outermost small body that may continue to orbit the Sun for the lifetime of the Solar System, which, depending on close encounters with other stars, may be in the region of 0.1 to 1.0 light-years (6,000 to 60,000 AU) away; identifying this body is, however, totally impractical: for a very long time to come it will always be possible to find an even smaller asteroid orbiting at an even greater distance than the current record-holder.

Clearly, none of these definitions by itself is satisfactory, and they are mutually inconsistent by orders of magnitude. Taking the criterion of the Sun being the brightest object in the sky is not very helpful, either, as this would abolish the whole concept of interstellar space and divide space up among the interplanetary spaces of different stars, the larger part of which volumes would not in fact contain any planets.

James Jason Wentworth offered a suggestion in the comments to the Centauri Dreams article on the Voyagers: “In his 1979 book Planetary Encounters, Robert M. Powers usefully defined an intermediate region of space between the planetary region of the solar system and interstellar space, which he called ‘ultraplanetary space’. Its outer boundary is 0.1 light years (6,320 Astronomical Units [AU]) from the Sun.”

How he arrived at that outer boundary is not clear without reading the book; presumably it is impressionistic rather than physical, a round-number approximation to the distance at which an orbiting body would not be likely to be disturbed by stellar close encounters over the life of the Solar System. While the inner edge of ultraplanetary space would be clearly defined (in our case) by the orbit of Neptune, its outer edge is fuzzy in the extreme.

The realm of the Solar System, then, merges gradually into that of the stars, with no clear boundary line where one could set up a border control and a passport checkpoint for humans leaving or aliens entering the Solar System.

Redefining the boundary

So how can we say that our spacecraft have or have not made the crossing from interplanetary to interstellar space?

The problem, I suggest, is that people are still thinking in terms of what they are used to on planet Earth. Here on the ground, location is all-important, as every estate agent knows. Every country has a precise boundary, often physically marked with a wall or a barbed-wire fence, a river or a coastline, and crossing the border is a big deal which politicians expend much rhetoric on, while police forces watch the queues at airport arrivals with eagle eyes.

In space, it is different, because nothing stays still, everything is moving under the influence of gravity. The location of a body by itself is of little account because it is constantly changing. A space “station” is not stationary, but always in motion. The role of fixed points on the ground is played in the Solar System by fixed heliocentric orbits: the path followed by a body around the Sun when it is not influenced by rocket propulsion or by the gravity of another orbiting body such as a planet.

Left to itself, then, an orbiting planet, asteroid or spacecraft in a perfectly circular orbit around the Sun maintains a constant speed and constant distance from the Sun; but that perfect circle is an ideal, and in general closed orbits take the form of ellipses. As the body approaches the Sun it speeds up and as it recedes away from the Sun it slows down, thus both its distance from the Sun and its speed are constantly changing as well as its position in space.

If we ask what feature of an orbiting body remains constant, a useful answer is the specific mechanical energy of that body. That is, if we take its kinetic energy at any point and its gravitational potential energy at that same point, add the two and divide by the body’s mass, we arrive at the total energy per unit mass of any body in that orbit (as well as in a family of related orbits).

Gravitational potential energy is usefully defined to be negative everywhere, while kinetic energy is always positive. This convention leads to the following result: if the body’s total energy works out to be negative (gravitational greater, in negative numbers, than kinetic), then that body is in a closed orbit (circle or ellipse) around the Sun. But if the total energy is zero or positive (kinetic equal to or greater than minus potential), then that body is not bound gravitationally to the Sun, and after a single flyby of the Sun it will recede forever on a parabolic or hyperbolic trajectory (the difference being that on a parabola, with zero total energy, the body approaches zero velocity at infinite distance from the Sun, while on a hyperbola it is moving faster, even when theoretically infinitely distant from the Sun).

To be precise: if it has velocity v and distance r from the Sun, whose mass times the universal gravitational constant is G M, then a body’s specific mechanical energy E is:

E = 0.5 v² – (G M / r)

This, then, is how a trajectory specialist would think of crossing into interstellar space: not by flying past some boundary line in space, but by accelerating to positive total energy relative to the Sun. On Earth location is all-important, but in space that role is played by energy.

So when can we say that Voyager 1 has left the Solar System? When it was accelerated by its flyby of Jupiter, which raised its total energy above zero. Whether Voyager is in or out of the Solar System is not a function of location but of energy. A spacecraft could be closer to the Sun than our Earth is, but if it is moving too fast to remain bound to the Sun, then it is already in interstellar energy space, like Arthur C. Clarke’s fictional starship Rama. An icy asteroid may be drifting up to a light-year away from the Sun, but if it is in orbit around the Sun then it is still in interplanetary energy space.

Conclusions

(1) There is no clear geographical boundary to the Solar System. We cannot think of the Solar System as we do of a country on Earth, with borders marked on a map and a passport office and a customs post set up on the border: the Solar System is not like that. There is nowhere we can set up a notice saying: “You are now entering the Solar System (twinned with Alpha Centauri). Please fly carefully.”

(2) The Solar System possesses a heliosphere, which is the domain where the Sun’s magnetic field is stronger than the interstellar field, and controls the flow of charged particles emanating from the Sun. The boundary of the heliosphere is variable in time and direction, and at 123.7 AU distance in one particular direction Voyager 1 is now close to becoming the first probe to cross that boundary.

(3) The Solar System posseses a region of interplanetary space between the orbits of Mercury and Neptune. This space can be completely enclosed within a flat cylinder 30 AU in radius and 1.9 AU in depth, aligned with the ecliptic plane. Thus Pioneers 10 and 11 and Voyagers 1 and 2 left interplanetary space some time ago, travelling on hyperbolic trajectories. The NASA/ESA Ulysses probe also left interplanetary space in 1992, while still remaining in an elliptical orbit around the Sun, through a Jupiter gravity assist which put it into a highly inclined orbit which took it several AU north and south of the ecliptic. Ulysses has passed into and out of interplanetary space at regular intervals ever since.

(4) The Solar System possesses a region beyond interplanetary space in which stable heliocentric orbits are possible, but no major planets are found. Robert Powers usefully named this region ultraplanetary space. It is populated with small bodies (variously termed asteroids, comets, minor planets, dwarf planets, Kuiper Belt objects, Trans-Neptunian objects, Oort Cloud objects, and so on – in my view, it is sensible to use the word “asteroid” as a catch-all term for all bodies smaller than planets and major moons, but larger than meteoroids). These speculatively exist out to a distance of a light-year or so, but identifying the outermost one down to any particular size is not practical due to their extreme remoteness and faintness.

The outer boundary of ultraplanetary space is therefore unknown, and it merges imperceptibly into interstellar space. That boundary cannot even be defined clearly, since there is a vast region beyond say about 0.1 light-year where orbiting bodies are only weakly bound to the Sun, and are progressively more likely with increasing distance from the Sun to be disturbed out of the Sun’s gravity altogether by encounters with other stars.

(5) There does exist, however, a precise distinction between a Solar System body and one which is not in the Solar System; that distinction depends not on location but on energy. Pioneers 10 and 11, Voyagers 1 and 2 and now New Horizons have become our first interstellar spacecraft, because all five have accelerated above solar escape velocity. All now possess so much kinetic energy that they no longer remain bound to the Sun.

Let us celebrate Voyager 1’s crossing of the heliopause, when it happens, without too much rhetoric about it “leaving the Solar System”. It left the Solar System already after its Jupiter flyby. Later it passed Neptune’s orbit and thus departed from known interplanetary space, and is now passing through the heliopause and thus departing from the heliosphere. But it will be a long time yet while it traverses solar ultraplanetary space, and the date of its final crossing into true interstellar space must remain a mystery.