Weird question I thought of about space trajectories

That makes me think of two cars on the road–one is travelling at 50 mph, the other at 100 mph. At some point they will be exactly side by side as the faster car passes the slower car, but jumping from one to the other at that point would be…messy.

Wait, why is that particular sequence required? Once you’re able to escape from Earth’s sphere of influence, you can get pretty much anywhere you want, with only a minuscule amount of fuel.

You could hit all of those planets on one trajectory in many, many different ways. Those ways might be more complicated than Voyager’s path, or take a longer total time, but how much weight do those have in our figure of merit? And there are many other things one might include in a figure of merit: For instance, how fast (relative to the planet) is the probe going at flyby (thus determining how long it will spend close enough to make good observations)? And how far away will the probe be able to get before its RTG cools off too much to allow for communications (relevant for the interstellar science you can get from the probe)? Granted, interstellar science wasn’t the primary mission of the Voyagers, but they’ve still returned some good data on that.

The Voyager probes (which are actually just redesignated Mariner platforms with some additional instrumentation) have no propulsion systems except for some tiny Trajectory Correction Maneuver thrusters that are just intended for fine-tuning in swing-by maneuvers, so no actual ability to change speed or direction post-transplanetary injection except via planetary swing-by maneuvers. Sure, it is theoretically possible to, say, head for Saturn, do a giant ellipse that takes it past Neptune and way out into the Oort Cloud, come back in and pass by Uranus to kick over to a Jupiter intercept, but such a trajectory would take many decades if not multiple centuries, long beyond any expected operational lifetime of the spacecraft even setting aside the limited power generation lifespan of a radioisotope thermoelectric generator (RTG). The ‘Grand Tour’ trajectory allowed a direct path for Voyager 2 to visit Jupiter, Saturn, Uranus and Neptune within the span of about a decade (using Voyager 1 as a pathfinder to refine ephemerides for Jupiter and Saturn) which could not be feasibly achieved without that conjunction. I don’t understand what you mean in this context by “figure of merit” but we certainly could not launch a single mission today that would be able to visit all four planets in any expected operational lifespan, or indeed, in a human lifetime.


A “figure of merit” is a number that measures how good something is, for purpose of being able to optimize that number. “Number of planets visited” is, of course, one possible figure of merit, but it’ll result in a lot of ties, since a small integer isn’t a very precise figure, and get you some missions that vary wildly in other ways that probably ought to be considered relevant.

I know what a figure of merit is, but you referred to “our figure of merit” even though one was not identified and the term doesn’t really make sense in this context. The Voyager “Grand Tour” trajectory is the only trajectory that would allow one spacecraft to perform a flyby of all four outer planets in one outward sweep in the span of a ~12 year mission duration using just non-propulsive swing-by maneuvers (accept for the small approach adjustments noted above). @k9bfriender was correct that there is no other conjunction of those four planets that would permit that kind of mission until the middle of the 22nd century. There are, of course, an essentially infinite number of mission trajectories using low-energy transfers (e.g. the so-called “Interplanetary Transport Network”) but outside of this planetary conjunction the shortest of them would still take on the order of a century, and most would take many millennia, which are obviously not viable durations either for the operation of the spacecraft or for mission support on the ground.


… but you fuck one goat…

Ghosts aren’t confined to normal dimensions and trajectories.

Can you elaborate, please?

Kerbal Space Program is fantastic.

Just had to say that. If you are not into rocket science might not be your cup of tea.

Picture that you spilled rice on the smooth kitchen floor and you grab the vacuum cleaner to get it up, but the floor attachment is missing, so you’re making do with the long rigid want that just ends in a pipe opening.

You sweep this through the densest regions of the spill, which of course gathers some up, but it also slingshots some of the grains because it attracts them but moves out of line too quickly.

That’s how I picture solar system exploration trajectories. The rice picture is very inaccurate because it’s dominated by friction, but it’s still a demonstration of motion somewhat like a slingshot maneuver.

Now, from an Einsteinian relativistic point of view, most of the traveling spacecraft do is in a straight line, the exception being when they are firing their rockets, but that’s more of a tweaking thing and not the main way of making progress. If you think of the arrangement of 3D points several years in the future when you want your probe to get to Saturn (or wherever), and then play their positional histories backwards through a series of infinitesimal time steps, you will find that some tiny fraction of the points that will be next to Saturn then are actually here now. They’re moving, yes, but if you fire your rockets to put your spacecraft on one of the point locations now, matching the point velocity too, then all you have to do is wait, and the spacecraft will be at Saturn.

I actually have a degree in physics and astronomy, and have studied advanced mechanics and a bit of celestial mechanics, so I appreciate these are not trivial things. Moreover, the above handwaving ignores for example how difficult it is to figure out where all these things are, based on what we see from our own Earth, or for example what kind of mechanical engineering you have to do to get a kilogram from here to Saturn. Still, those points all swirling around kind of like rice grains – that’s real.

The space “game” I am familiar with is this one:

I say “game” because, while you are in a spaceship and can push buttons and so on, if you want to make it to Mercury or Saturn you need to do some calculations well in advance— the in-game plug-ins are adequate as far as they go but do not completely automate the task of coming up with complex trajectories like BepiColumbo’s

Orbital mechanics can be very counter-intuitive.

For example, if you are in a handy-dandy spaceship in orbit around the sun, and you want to get rid of your trash, you might think all you need to do is fire it towards the sun. Intuitively, you might think that the trash is just going to spiral in to the sun. But that’s not what happens. Instead, from your point of view, the trash is going to move towards the sun, stop, and then come back and hit you in the face.

The reason for this is that your spaceship, like the planets, is whizzing around the sun at a rather high velocity. If you want to go into a higher orbit, you need to increase your orbital velocity. If you want to go into a lower orbit, you need to decrease your orbital velocity. By firing your trash towards the sun, you haven’t really changed its orbital velocity by a significant amount. All you did was change its direction. This will leave its average orbital distance basically unchanged, and all that you have done is made its orbit more elliptical. And since its orbit is now more elliptical, from your point of view in a more circular orbit, the trash is going to want to oscillate above and below your orbit (which is why you need to get out of the way or it’s going to come back and smash you in the face).

To put it in perspective, it actually takes less energy to escape from the solar system than it does to get to the sun. Launching your trash into the sun just isn’t a very practical idea.

So how do you get to Mars?

One way is to just go faster around the sun. If you increase your orbital velocity, you are eventually going to attain a Mars orbit. It’s not the most fuel-efficient way to do it, but it’s theoretically possible.

Another way is to make your orbit more elliptical. Just like the trash example, from the Earth’s perspective your orbit is going to want to oscillate above and below the Earth’s orbit. Make it elliptical enough and your elliptical orbit will intersect with the orbit of Mars. Note that your elliptical orbit will cross the Earth’s orbit twice, so you can either aim towards the sun or away from the sun. Either way you can still end up at Mars.

And if there happens to be a planet conveniently located inside of your elliptical orbit (i.e. Venus) then you can slingshot around it, essentially converting your orbital velocity into a faster and easier path to Mars.

One interesting idea proposed for any sort of Martian colony is the idea that you can make a relatively efficient supply ship run by essentially using an elliptical type of orbit with its inner and outer ranges at Earth and Mars respectively. This would basically be a stable orbit that would require no real effort to continually go between Earth and Mars. You could launch supplies from Earth, rendezvous with the supply ship while it is close to the Earth, then detach the supplies when the supply ship is close to Mars and have them drop down for a landing on the surface of Mars.

Orbital mechanics are interesting.

Of course not; everybody knows you dump your trash inside the ergosphere of a rotating black hole, that way you extract free clean energy as a bonus!

you have that backwards!?
Maybe you mean orbital energy.

I don’t think so.

You increase your speed in your current orbit, and your orbit will move outwards into a higher orbit. Your speed in the higher orbit will be slower though.

ETA: Yes, orbital energy is a better way of phrasing it.

If you’re at Earth’s distance, in Earth’s orbit, and speed up, you’ll go into an elliptical orbit that eventually reaches Mars’ orbit. Once there, if you speed up again, you’ll be back to an (almost) circular orbit, at Mars’ distance. And despite both of your rocket burns speeding you up, you’ll be going slower than you were at the start, because during the trip in between those two rocket burns, as you’re rising in the Sun’s gravity, you’ll be slowing down even more than your two rocket burns sped you up.

However you are right (+ @Chronos). If you give yourself a quick speed boost (increasing your energy in the process) then you will kick yourself into a higher (elliptical) orbit, but for non-circular orbits your speed is constantly changing, according to

\frac{v^2}{2} - \frac{\mu}{r} = -\frac{\mu}{2a} = \text{specific energy},

where a is the length of your semi-major axis.