How hard would it be to do a grand tour of the Solar system?

[tutrakan4e]

Let's say we have a probe with an ION engine so it can make very suttle velocity changes and burn very little fuel. We want to do a grand tour of the Solar system with it, as in fly by every single planet, using gravity assists (from the Moon first to get us going) to speed up and slow down etc. What sort of supercomputer would we need to calculate the orbital path of the probe? Have we developed that kind of computer yet? Is that possible with a pen and (a million) paper(s)? Is our math advanced enough for that sort of thing?

[KerikBalm]

I'd say it would be pretty hard, but its more of a problem of waiting for the planets to have the right alignment.

Voyager probes basically did what you want for the outer solar system.

Getting the perapsis down to Mercury is going to be hard, even with gravity assists

[Nuke]

we could do a lot with gravity assists, aerobreaking, and minor course corrections. you are going to need an rtg for the outer solar system, and a lot of propellant. computing power is pretty much irrelevant. you are not doing lots of collision tests and structural simulations like you do in ksp and you can focus all cpu power on integrating your trajectory, which mathematically speaking isn't very hard. you dont need anything but your typical rad-hard 32-bit system on a chip module.

[Camacha]

we could do a lot with gravity assists, aerobreaking, and minor course corrections. you are going to need an rtg for the outer solar system, and a lot of propellant. computing power is pretty much irrelevant. you are not doing lots of collision tests and structural simulations like you do in ksp and you can focus all cpu power on integrating your trajectory, which mathematically speaking isn't very hard. you dont need anything but your typical rad-hard 32-bit system on a chip module.

To calculate an accurate trajectory that takes all kinds of subtle phenomena into account you will probably need some serious calculative force. However, the big difference is that you do not do these calculations on board. The eggheads at NASA can use all the fancy equipment they like on Earth and then they will just beam the relevant data up. Some minor calculations might need doing on the fly, but the way a lot of people play KSP is actually very strange. You would never leave Earth without knowing fairly precisely where you are going, when you are going there and how exactly you are going to get there. Only corrections will be done according to the local situation and those are typically very minor.

[TheGatesofLogic]

To calculate an accurate trajectory that takes all kinds of subtle phenomena into account you will probably need some serious calculative force. However, the big difference is that you do not do these calculations on board. The eggheads at NASA can use all the fancy equipment they like on Earth and then they will just beam the relevant data up. Some minor calculations might need doing on the fly, but the way a lot of people play KSP is actually very strange. You would never leave Earth without knowing fairly precisely where you are going, when you are going there and how exactly you are going to get there. Only corrections will be done according to the local situation and those are typically very minor.

Not really... There's a reason we have symplectic integrators, and everything else is differentials that can be done easily with pen and paper. Really It would be pretty simple. All that's really necessary is a VERY long time. You'd be doing an interplanetary network path after all.

Regardless you are right, everything is done beforehand, rather than on the fly

[Armchair Rocket Scientist]

Let's say we have a probe with an ION engine so it can make very suttle velocity changes and burn very little fuel. We want to do a grand tour of the Solar system with it, as in fly by every single planet, using gravity assists (from the Moon first to get us going) to speed up and slow down etc. What sort of supercomputer would we need to calculate the orbital path of the probe? Have we developed that kind of computer yet? Is that possible with a pen and (a million) paper(s)? Is our math advanced enough for that sort of thing?

The computing would probably be possible. The issue is that it's going to be a VERY complicated and difficult mission.

Most likely we'd start with a Venus flyby. Venus can actually give a decent gravity assist, and with repeated flybys can get a probe to Mercury or Jupiter (as was done with Cassini and MESSENGER). We'd probably want to encounter Mercury and Mars early in the mission, before heading for the outer solar system, which would make the trajectory more complicated and take longer. This phase will probably take 5-10 years, with low dV requirements.

At some point, we get Venus and Earth to throw the probe out to Jupiter. At this point, a gravity assist from Jupiter can send the probe to any of the other outer planets provided they're lined up properly. With a Voyager style trajectory, we could complete the mission very quickly, but launch windows would be more than a century apart. Otherwise, we'd need to do a much slower outward transfer, because if we need to loop back around to encounter more planets we can't really do a super-fast solar escape trajectory. This also means the mission will take a VERY long time. I have no idea how long, but it could very well take 50-100 years. Even conventional RTGs will have trouble lasting that long, let alone other hardware. That will be quite the engineering challenge.