Was it multitudinous mathematical trial runs that determined that 1977 was best time within a 176 year period to launch the voyagers? Initial launch was to obtain close encounters with Jupiter and Saturn but, fortuitously or by plan, launch parameters allowed further exploration of more outer planets. Was this potential included in the initial planning calculations?

What programs/math procedures were used to determine the needed launch time and launch parameters to permit the "grand tour"?

thanks, tom kosvic

  • $\begingroup$ I remember seeing a video stating the original computations were done by hand. I would imagine Kepler's equation or even comics were enough to show they were roughly in the right place, though the actual maneuvers would require more precise computations. $\endgroup$ Commented May 26 at 15:19
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    $\begingroup$ There is a paper by Gary Flandro "Fast Reconnaissance Missions To The Outer Solar System Using Energy Derived From The Gravitational Field Of Jupiter" gravityassist.com/IAF3-2/Ref.%203-143.pdf published 1966. In the Acknowledgements Flandro thanks A. Joseph, D. Snyder and Mrs. H. Ling for their assistance in computer programming and trajectory calculations. The programming language FORTRAN was available in 1960, so I guess the programs were written in FORTRAN (Formula Translating System) $\endgroup$
    – Uwe
    Commented May 26 at 20:51
  • $\begingroup$ @GregMiller even comics or even conics? $\endgroup$
    – Uwe
    Commented May 26 at 21:24
  • $\begingroup$ @Uwe, conics, sorry. $\endgroup$ Commented May 26 at 22:32
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    $\begingroup$ Fortran has had excellent math libraries since the mid-late 1970s, but Gary Flandro of JPL discovered the Grand Tour alignment in 1964. $\endgroup$
    – PM 2Ring
    Commented May 27 at 1:49

1 Answer 1


It was a realization that Gary Flandro had in 1964 while he was working at JPL. His original proposal did include all the outer planets (including Pluto), and it became the basis for what NASA called the Grand Tour mission. For budgetary reasons, that was cut back to just Jupiter and Saturn, but everybody working on the project tried to plan for the possibility that they would eventually be allowed to extend the mission. So the only thing fortuitous about it was that they actually got the money. They had a plan from the beginning.

Just getting the idea is something that could have happened visually. The outer planets orbit slowly. If Flandro plotted their locations as of 1964, he would have been able to see that you could draw a plausible sequence of orbital segments from one to the next once Jupiter got into the right place. In his paper (see below or the comments), Flandro says that it was really just getting Uranus and Neptune into position that drove the 176-year gap. That suggests that the window of opportunity would be long enough to get Jupiter and Saturn into position.

It was also pretty easy to tell that the opportunity would come rarely. You have to pass each planet from behind heading towards the next, if you want to pick up energy. Neptune (~165 year orbit) has to be further around the sun than Uranus (~84-year orbit) by just the right amount, and Saturn (~30-year) and Jupiter (~12) have to be in the right places too.

The Gary Flandro paper (gravityassist.com/IAF3-2/Ref.%203-143.pdf) shared by Uwe in the comments is really worth looking at. The concept of a gravity assist is now a standard idea in planning space probes, and that paper seems to be introducing it. He looks at other combinations, considering using Jupiter to go straight to each of the other outer planets.

So this does not definitively answer the headline question, but I feel like it may cover some of the sub-questions.

  • $\begingroup$ Excellent on-point relevant thoughts and references with respect to my question. It appears that the fundamental concepts and math procedures were initiated by a Minovitch also at JPL. I have much to review. Need to find out if old JPL docs are online; don't live in Calif anymore. I will try communicating with the GMAT people to see if they are aware of any modern variant of this code when I can find it's name. thanks again, question solved for me. $\endgroup$
    – tckosvic
    Commented May 28 at 15:01

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