If I remember correctly, The construction and launch of the Voyager spacecrafts in the early 1970s had an urgency as there was to be an unusual lineup of the outer planets (Jupiter, Saturn, Uranus and Neptune). At that time, we had only been "space-faring" for about 10 years!
Does this planetary lineup really occur infrequently? And if so, when is the next time that a Voyager-like mission (using today's technology), could be mounted?
The lineup occurs once every 175 years. The launch window the last time this alignment occurred was from 1976 to 1980 [1], so the next time it would open would be around 2151-2154.
Another Voyager-like mission could be mounted at any time really. We have the technology to do it, but the cost of mounting such a mission outside of the Grand tour launch window would be much higher, because the spacecraft would need more propellant to be able to alter its trajectory to get from place to place. Such a mission would also take longer, citing from the same source as above, the Grand tour would take "...eight to thirteen years, depending on the trajectory, compared to thirty years for a direct flight to Neptune alone-by employing a maneuver called gravity assist"
The beauty of the gravity assist is that you use the gravity field of a large body to change course. A common misconception is that the gravity assist increases speed, but it actually leaves speed unchanged. It's more accurate to say that the gravity assist changes direction, since velocity is both a magnitude (speed) AND a direction.
If I recall correctly from a study I made of these trajectories a couple years ago, the Voyagers saved something like 30 km/s of delta-v by employing gravity assists. I can't find a source for this at the moment, but I will dig up my notes and see if I can confirm. But 30 km/s is a huge savings, as most outer solar system probes only launch with a few hundred m/s of delta-v that they can spend performing maneuvers [2]
[1] http://history.nasa.gov/SP-4219/Chapter11.html
[2] Delta-v of deep space maneuvers in deep space missions like Voyager or Pioneer
A four-planet lineup is rare, as @Nickolai said. 3-planet lineups are a bit more common. New Horizons used a single gravity assist (Jupiter) to get to Pluto.
Grand Tour-type missions are going to be rare: the focus has shifted to missions that study a single planet in more detail. Many of these missions were designed to answer the questions raised by the Voyager flybys.
You could argue that Dawn is conducting a tour of the asteroid belt, and there's a mission plan for another probe that will visit 6 asteroids. Not as grand as the 4 outer planets, but the same basic idea: initial exploration that will be followed up by more detailed investigations.
Alignment for a grand tour will occur next in about 175 years as a consequnce of the orbital periods of the four outer planets. The dominant factor is the ~165 year orbital period of Neptune, which sets the "low frequency" interval that defines the overall period. The long orbital period of Uranus also plays heavily, but the fact that its period is 84 years (or almost exactly half that of Neptune) helps keep a lot of things "resonant" in the sense that in 168 years or so, Uranus comes back to the same spot where it was and in that amount of time, Neptune is also in almost exactly the same place. Saturn's orbital period is between 29 and 30 years, and Jupiter's is about 12 years, so they return to the same places relative to the sun more frequently, so their effect on stretching the "grand tour" period is a bit lower. But consider what might happen if, say, Saturn's orbital year was 70 earth years. It'd be back to where it started in just 70 years (too early for Uranus and Neptune to be aligned), 140 years (also too early for Uranus and Neptune to be aligned), and 210 years (too late to be on the tour). In a way you can think of the phenomenon of alignment a bit like strumming a chord on a guitar. The notes aren't the same on every string, but if they're at the right intervals, you get something that sounds good and you have a kind of resonance. Uranus and Neptune are about an octave apart. Jupiter and Saturn are at higher notes on the staff, but they work, and the period for the tour gets to be something reasonable.
Part of what makes taking a tour like this attractive -- other than not having to travel to one side of the sun to get to one planet and to the other side to get to the next one -- is that gravity assist to change momentum becomes possible. Remember that a momentum vector has both direction and speed, and with a gravitational interaction between probe and planet, the probe can exchange momentum with the planet, thus changing both its direction and speed. (It also, to a miniscule degree changes the direction and speed of the planet as it goes by, since energy is conserved, and the extra energy the probe may pick up has to come from someplace. But you'd have to send a staggering number of probes past a planet before you changed its orbit in any significant manner.)
When you travel past the planet ahead of it, the planet's gravity is behind you, and it tugs on your mass (and your momentum vector, pulling you back and slowing you down). If you come into an orbit on the back side of its direction of travel, your mass (to an infinitesimally small degree) exerts a gravitational pull slowing the planet down, while at the same time, the planet pulls on you, transferring energy to you and slingshotting you forward. You momentum vector then has a change in both speed and direction, and you're off to the next planet that much more quickly.
You can liken this effect to towing one car behind another with a rope. If the car in front has a running engine and the one behind doesn't, the one in front is expending energy to accelerate the one behind. And the one behind is stealing energy from the one in front, which would be getting much better gas mileage if it weren't being used as a tow vehicle.
It's worth mentioning this "momentum exchange via gravity" because it also factors into how the Apollo missions got to the moon. One of my favorite mission patches is the one from Apollo 8, which depicts a figure 8 around the moon. (Apollo 8 was the first mission to go all the way to the moon.) You could just write this off as cool graphics and a play on the number 8, but in fact this is the actual trajectory the spacecraft took. It effectively did its translunar injection (TLI) burn to get into what would have been a very high elliptical orbit around the earth had it not also put the spacecraft in the path of the oncoming moon. Instead, far enough away from earth, the ship was captured by lunar gravity as it went ahead of the moon. And it was this negative exchange of energy to the the moon from Apollo 8 that slowed the ship down by enough that it was captured into orbit. Had Apollo 8 approached from the other side (behind the moon), lunar momentum would have been transferred to the ship, and it would have continued on into deep space. Coming home, the engine burn on the ship got Apollo 8 enough momentum to get out of the lunar gravity well and far enough back into its original high orbit around Earth to be recaptured by the Earth's gravity well, where final engine burns could slow it to atmospheric re-entry speeds.
The lineup occurs once every 175 years. The launch window the last time this alignment occurred was from 1976 to 1980, so the next time it would open would be 2151-2154.
Source: Grand Tour program
