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I understand that every probe launched has been launched into an orbit. The further you want to go into the solar system, the faster it needs to be moving. And everything orbits the sun until it finds a different mass to "capture" it.

But I noticed that Pluto is REALLY far away and the orbit of New Horizons is not a circle nor an elliptical shape and it doesn't look like the probe will ever come back - it will just keep going. It doesn't even look like it is orbiting the sun! How is this kind of orbit possible?

Same with the voyager probes. It looks like they will keep going into interstellar space and never come back. Is their trajectory even remotely some kind of a circular orbit around the sun at this point? If not, how is this kind of trajectory possible?

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    $\begingroup$ The Voyagers are not in an elliptical orbit around Sun, they exceed the escape velocity necessary to leave the solar system forever. The probe just should be fast enogh. $\endgroup$ – Uwe Sep 24 at 15:55
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This relates to the concept of escape velocity, which is the speed needed to escape an object's gravity well. Even though gravity has an infinite reach, the fact that its force reduces quadratically with distance means that it only takes a finite amount of energy to climb out of a planet's gravity well. For some fixed energy cost, you can get arbitrarily far away from the planet. If your speed is higher than escape velocity, you can get as far away from the planet as you like, and still have some speed carrying you away - in other words, you are never coming back.

You are correct that cyclical orbits are round and repeating. But not everything in space has to be in a cyclical orbit. Objects that are moving at least as fast as escape velocity are not in a cyclical orbit, they are on an escape trajectory. New Horizons has sufficient speed that it is on an escape trajectory from the sun - it will leave the solar system and never come back, although it may fall into orbit somewhere else around another celestial body.

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    $\begingroup$ A parabola or hyperbola is a perfectly valid orbit, but not "cyclical". $\endgroup$ – DrSheldon Sep 24 at 16:13
  • $\begingroup$ @DrSheldon Interesting, it seems that while orbit is typically used to refer to a repeating trajectory (NASA's own site states that all orbits are elliptical), it can also be used to describe a non-repeating trajectory. I've updated my answer to reflect the broader usage. $\endgroup$ – Nuclear Wang Sep 24 at 16:28
  • $\begingroup$ @NuclearWang Excellent and clear answer, thanks! $\endgroup$ – export_all_errors Sep 24 at 18:24
  • $\begingroup$ @NuclearWang But are we trying to exceed the escape velocity of the Sun or of the Earth? Or both? $\endgroup$ – export_all_errors Sep 24 at 18:25
  • $\begingroup$ @export_all_errors The objects we have sent beyond the Sun's reach -- Pioneers and Voyager -- had to escape from Earth first, then the Sun. Two recent objects, 'Oumuamua and asteroid 1I/2017 U1 came near the Sun but already were moving in excess of the Solar escape velocity. $\endgroup$ – bitchaser Sep 24 at 19:20
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I think your problem is just a matter of terminology. Almost all of the orbits you hear about are elliptical. Some are almost exactly circular, but that counts as a special case of elliptical. Orbits like that keep going round and round, and stay within a certain distance of the primary. You might have the impression that's part of the meaning of "orbit".

But technically, it is still called an orbit if it is not a closed curve. Orbits where the object doesn't come back are hyperbolas, rather than ellipses. These space probes are on hyperbolic orbits. If you remember your geometry, a hyperbola has two asymptotes that the curve approaches as it extends off to infinity. By now, the space probes are so far from the sun that they are very close to the hyperbolic asymptote, and basically moving in a straight line out of the solar system.

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