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I'm modeling this on the Voyager 2 flight path. I want to have this flight at this particular time, and not wait for a more advantageous launch window.

Based on this orbital configuration (1st image below) the day a spacecraft leaves Earth, could a spacecraft slingshot around Jupiter, enter a single highly elliptical orbit around Saturn, then fire its engines near periapsis to redirect it to Uranus?

enter image description here

Since it took Voyager 2 four years to reach Saturn, the next image shows what theskylive.com indicates the position position Saturn would be when the craft reaches Saturn. I assume a craft could not simply slingshot by Saturn (like Voyager 2 did) and head to Uranus based on the positions of the planets. In my story the craft needs to flyby Saturn on the way to Uranus.

enter image description here

I don't need a detailed answer, just a yes or no, and minor details (if any) would help.

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    $\begingroup$ You included the science-based tag, so I'm not going to attempt an answer. But, in principle, yes. The details depend on the exact placement of the planets, the exact speed and angle the spacecraft arrives at, and exactly how much delta-V the spacecraft has available for this purpose. For such calculations, possibly this instacalc.com/42836 Hohmann transfer calculator will be useful. $\endgroup$
    – puppetsock
    Commented Jul 10, 2019 at 13:24
  • $\begingroup$ @puppetsock Should I have used the reality-based tag? $\endgroup$
    – Bob516
    Commented Jul 10, 2019 at 13:26
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    $\begingroup$ This isn't really a worldbuilding question, if we're talking about orbital mechanics in our actual solar system. I feel like this is a question for space.stackexchange.com $\endgroup$ Commented Jul 10, 2019 at 13:32
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    $\begingroup$ There can be a lot of overlap, but it really depends on whether your question involves anything speculative or not. I suspect that the people who are really knowledgeable about orbital mechanics probably frequent both places, so you'll probably get the same answer either way. $\endgroup$ Commented Jul 10, 2019 at 13:38
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    $\begingroup$ A few notes: (a) To enter into an orbit around Saturn, you have to fire your engines (or brake in the atmosphere) to reduce your kinetic energy. You then have to fire your engines again to leave orbit. This seems wasteful; if you don't need to hang out at Saturn for a while, it'd be better to do a slingshot maneuver around Saturn instead. (b) Note that having the planets in a straight line (as in your picture) won't necessarily help, since they'll keep orbiting (at different speeds) while you're in transit. Aim for where the planet's going to be, not where it is now. $\endgroup$ Commented Jul 10, 2019 at 17:41

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Based on the orbital configuration in the image below

Orbital configurations are not static, they're dynamic.

So it would be more accurate to say there are configurations that would allow this done in principle.

could a spacecraft slingshot around Jupiter

Not quite trivial, but doable.

enter a single highly elliptical orbit around Saturn

Slingshot to Saturn from Jupiter is of course harder to arrange. Exactly how easily this could be done depends a great deal on the position of planets when you launch and the propulsion capability you have during slingshot (and after for course correction).

Getting to Saturn is relatively easy.

Getting into any orbit around Saturn is harder. What you'd likely do for efficiency is aero-brake - aim to skim the upper atmosphere and slow down enough to be in an orbit. You'd correct this path again to avoid re-entering the atmosphere.

, then fire its engines near periapsis to redirect it to Uranus?

This is not needed.

You're either gong to wait for a configuration that allows you to sling shot either directly from Jupiter to Uranus or to slingshot from Saturn (possibly via Jupiter) to Uranus. There is no reason to "stop" at Saturn (enter orbit) unless there is a very specific issue with configuration of planetary positions that make slingshots impossible.

If you started, for whatever reason, in orbit around Saturn you can try various methods to slingshot using Saturn, it's moons and possibly even Jupiter, to get to Uranus. It depends on what propulsion capability you have and how long a journey time is allowed. With the wrong combinations it may be impractical or impossible.

At Uranus you again aero-brake and correct to enter a stable orbit.

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