This post started out as a thread on X. Here I’ve edited it into a blog post. The image below and the fact cited can be found in JPL Publication 89-24.
In 1960 it didn’t seem that it would be possible to explore the solar system beyond Jupiter without greatly improved propulsion.
Then the gravitational assist (“slingshot”) maneuver was discovered in 1961. With this new discovery, NASA began making plans to take advantage of an alignment of the outer planets in the 1970s. This led to the Voyager missions.
(Fun fact: In a gravitational assist, the velocity of a spacecraft with respect to the planet doesn’t change, but the velocity relative to the sun changes greatly.)
Note that before encountering Jupiter, Voyager was moving well below solar system escape velocity. As a result of gravitational assists at four planets, the spacecraft is traveling at well over solar system escape velocity.
In a gravitational assist, speed (relative to the sun) increases or decreases, depending on which direction you approach the planet. At the end of the tour, Voyager 2 no longer had a reason to increase speed—it wasn’t possible to visit Pluto—but decreasing speed allowed it to visit both Neptune and its moon Triton.
It may seem that a gravitational assist violates conservation laws: where does the additional momentum come from? From the planets. When Voyager 2 passed Jupiter, Saturn, and Uranus, each of these planets lost some momentum, transferring it to the probe. When the spacecraft passed Neptune, the planet gained some momentum and the probe lost momentum. The changes in momentum were infinitesimal relative to the momentum of the gas giants, but large relative to the momentum of Voyager.
Related post: Error-correcting codes using on Voyager missions
The slope of Voyager’s velocity post Neptune is really close to the slope of the escape velocity curve. Is it known whether Voyager 2 will escape the solar system?
I think the hard part is saying what the boundary of the solar system is. Maybe it has already left?
But I suppose “solar system” here means “captured by the sun’s gravity” and so there’s a definite answer, but I don’t know what it is.
The escape velocity curve shows the speed needed to escape the Sun’s gravity at different distances from the Sun. So the slope of the 2 curves doesn’t determine if Voyager 2 will escape the solar system, just the fact that Voyager 2’s speed is above the escape velocity curve.
The slope of Voyager 2’s curve is actually closer to 0 at any given distance from the Sun (greater than Neptune’s distance). If it were less than the slope of the escape velocity curve, it would catch that curve and not escape, which would also mean there must be some force slowing down Voyager 2 to prevent it from escaping.