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All 4 outer planets line up once every 175 years. 2 of them line up at least once every orbit Jupiter makes, about every 12 years. But how often do 3 of the outer planets line up?

Here's a simple orrery which I hope is reliable, that shows the planets' (angular) positions at a given date. But how do they have to line up to be useful for a flyby mission? For example, are Saturn and Uranus close enough in November 2020?

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    $\begingroup$ You don't want them truly in line. The probe is on an elliptical approach to (say) Jupiter. Jupiter's gravity accelerates the probe along its motion (in the sun reference frame), so you want the next target ahead of Jupiter in orbit. By choosing how close you pass, you can choose how much of this happens. $\endgroup$ – Ross Millikan Apr 2 '15 at 15:44
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    $\begingroup$ @RossMillikan I suspect the frequency of "truly in line" and "in a perfect configuration for Grand Tour 2.0" be the same (but of course not when they occur). $\endgroup$ – gerrit♦ Apr 2 '15 at 22:10
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    $\begingroup$ There's some flexibility in the flight path - see picture. i.imgur.com/d0US12a.jpg obviously you wouldn't want one of the planets to be on the other side of the sun, so there are better and worse times to launch, but certainly a good launch date will happen sooner and more frequently than every 175 years. $\endgroup$ – userLTK Apr 3 '15 at 10:53
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I used this solar system simulation to look for planet positions in an arc, more or less as shown in this image of the Grand Tour (provided by @userLTK).
Grand Tour

When I entered Voyager 1's launch date in the simulation, I got this image: 1977
Jupiter-Saturn-Uranus are spread around 135 degrees, Jupiter-Saturn-Neptune are spread around 180 degrees. I basically checked positions every few years, looking for those angles.

In 2074, Jupiter, Saturn, and Uranus look to be nicely aligned:

2074

The window for a 3-planet flyby is probably several years wide (just like a Grand Tour window).

Those 3 planets will be in conjunction in 2080. Saturn and Uranus align around 2036 as well, but Jupiter's too far away for a 3-planet tour.

And right now there's a favorable position for Jupiter, Saturn and Neptune:

2015

(Google's search results for '3-planet conjunction' and similar terms were useless, by the way; you end up knee-deep in astrology)

There are more permutations for 3-planet tours than the two shown here, I didn't check all of them.

Now, this is just a first-order approach. You'd have to use trajectory calculation software to get exact answers. I found some Matlab scripts, but I don't have access to Matlab...

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