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There is an extraordinary amount of math involved. They plan out the exact path of the vessel, as well as the paths of all planets involved.

The approximate path of the vessel is calculated with conic sections (ellipses and hyperbolas) around a planet or star.

The best way to predict a path, albeit with an extraordinary amount of math, is actually very simple. We use the conic sections to predict planets' orbits, since they don't tend to change much, and then we do a very simple calculation to see how much they each tug on the vessel. We then add all of these tugs together and see what direction it is pulled overall. We move it a tiny forward, and repeat the calculation again. Move it again. Calculate, move, calculate. Over and over ten billion times to get a good prediction of the path the vessel will follow. Computers are great for that.

We do not know that, just that it will ake a very long time before it could because of the enormous distances.

Voyager, I do orbit something, the core of the galaxy just like the solar system. It is the combined effect of all matter in the solar syst.

Sure but just because it's unlikely for a commet or asteroid to hit them or something doesn't mean that it's impossible, did they do anything with the orbital paths of the planets around the sun to know that when they launched it it wasn't going to be swept into the orbit of another planet? If so, what did they do?

And thank you I didn't know that about Voyager I!

As well as all the fancy math the book smart people do, space is vast and empty. Like REALLY vast and empty. Unconceivably vast and empty. Now I know your picturing in your head something vast and empty, but its nowhere near the level that space is. You can fit every planet in our solar system, equator to equator, between Earth and the Moon, and that's not even a drop in the bucket compared to the space of...well...space

OP's question also brings to mind the story of the Curiosity Opportunity rover on mars.

It's original tenure was only supposed to be a 90 day mission on the surface, but through a combination of good construction and non-catastrophic conditions, it instead served for 14 years. It didn't stop until a harsh dust storm knocked out its ability to recharge.

Similarly, something like the Voyager is a combination of "let's get it as far as we can" and "let's see how far it will go". With enough computation and simulation, a path can be plotted out of our star system so that it doesn't hit Pluto and crash. However the farther it goes, the more Chaotic Entropy comes into play. We can project paths of celestial bodies, but longer predictions bring on more deviations until it stops being viable.

Once Voyager cleared the system, it was reasonable to say "alright, we've set it up as best we can, let's see where it goes" and keep collecting data as long as it transmits

I don't know how to give best answer of if that's even a power that I have on my post but this is definitely it so far, thank you! This is exactly the type of comprehensive breakdown that I was looking for.

It was more the math itself and the simulations and that kind of thing that I was looking for, but I probably could've made that more clear, sorry. I appreciate your answer though, the exact vastness wasn't something that dawned on me outside of basic planetary science taught in school.

In space unless you aimed REALLY well you aren't hitting anything. No matter how empty you think it is it's a billion times emptier.

They didn't do any crazy math to make sure they weren't going to hit anything. They did crazy math to make sure they got within very precise distances of each planet they visited to get a gravity assist. Each gravity assist sped up the probe until Voyager 1 was going about 17km/s and Voyager 2 was going about 15.5km/s. No rocket is capable of getting them to those crazy speeds.

After they each finished visiting planets they were on their way out of the solar system. There just isn't any risk of them crashing into anything.

Planets are hard to miss and they do not take unexpected turns like some drunk git on a highway. If you know where Mars is now and its velocity, you can predict where it'll be in exactly a thousand years, probably down to a few tens of meters of accuracy.

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Their orbits are planned out before the mission to begin with. If they weren't no mission would be possible.

The orbits of the planets in our system are well studied, so we know their shape around the sun and the speed the planets have along each part of their orbit, so modelling their orbits into the future is relatively simple. If you've ever wondered how we know before hand when conjuctions will happen or when a comet will pass by or how astrological predictions are made for future dates, that's how. (Astrology isn't a real science but it relies on our good understanding of our solar system).

We also know their mass and their gravitational force, so complex calculations are made that can chart a spacecraft's exact course through space which also determines how much fuel the spacecraft itself needs for maneuvers and how much of its course will rely on the gravitational pull of other celestial bodies. Space is mostly empty, and vast, so the chances of a random piece of debris or asteroid hitting the spacecraft are not zero but they're highly impropable.

Nowadays these calculations are carried out by complex computer modelling but it's not a simple calculation that one can simply write out here. But what you can do is get Universe Sandbox, which is a game that models our solar system fairly well and allows you to change variables or simulate missions which helps visualise and give a much more intuitive understanding of how these things work. In fact there's a whole host of such software but this one I think is a great one for people interested in learning about our solar system, space and how missions work

It's not impossible, however it would be like dropping 8 beach balls and a few dozen tennis balls in random parts of the pacific ocean, and then plotting a random course across the pacific ocean without hitting any of those balls. Sure it's POSSIBLE you could hit one of those balls, but given the vast size of the ocean and the comparatively tiny size of the balls, the chances are pretty darn close to zero.

Only instead of like that, about a million times less likely.

> OP's question also brings to mind the story of the Curiosity rover on mars.

> It's original tenure was only supposed to be a 90 day mission on the surface, but through a combination of good construction and non-catastrophic conditions, it instead served for 14 years. It didn't stop until a harsh dust storm knocked out its ability to recharge.

You're referring to Opportunity, not Curiosity. Curiosity was activated under 11 years ago, is still operational, and doesn't recharge because it uses an RTG.

Opportunity was deployed for 14 years and relied on solar power.

For the planets, absolutely. The Voyager probes actually relied on planetary flybys to get a "gravity assist" to slingshot them out of the solar system. Lots of calculations involved to make that happen right.

Beyond that though, colliding with a random comet or asteroid is a) insanely improbable and b) impossible to account for if you don't know about them in the first place.

As for a running into another star system, it will take about 40,000 years for either Voyager probe to come within a couple light years of another star (but we do know which those will be)

“Space is big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space.”

― Douglas Adams, The Hitchhiker's Guide to the Galaxy

Scale is really hard for our meat brains to understand. Here's a fun video that can help a bit to understand, via a medium of printer paper standards.https://www.youtube.com/watch?v=pUF5esTscZI

The rotation can sometimes be surprisingly chaotic, though. Saturn's moon Hyperion wobbles so wildly that it was impossible to plan for a probe flyby to cover unexplored areas.

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The asteroid belt is not like in movies. The average distance between objects is about 1 million km, a bit less the 3x the distance to the moon. If you were on an asteroid it is extremely unlikely you could see another with your naked eye.

If you could see another astroid you are likely to be close to one of the four larger asteroids Ceres, Vesta, Pallas, and Hygiea, they contain 60% of the total mass of the asteroid belt. The total mass of the asteroid belt is about 3% of the mass of the moon.

We do know where the planes in the solar system are and it was because of how they lined up that Voyager I and II were launched.

Voyager, I did flybys of Jupiter and Saturn and exploited their gravitational field to do a gravity boost and increase the speed.

Voyager II did flybys if Jupiter, Saturn, Uranus, and Neptune.

Both have thrusters that were used for small maneuvers so the flyby was exactly as what desired.

There are no unknown objects in the solar system that has enough gravity to capture an object that moves at the speed of the probers.

It it what they encounter in thousand, million or billion of year that is not exactly known

Here's a website that explains the math to calculate an orbital trajectory. The math isn't really something that can be explained like you're five though. You'll need to have a solid understanding of algebra and trigonometry to be able to use it.

>If you were on an asteroid it is extremely unlikely you could see another with your naked eye.

I remember science fiction shows when I was a kid, and they'd go through "The asteroid belt!!!' or a "meteor storm!!!" and were avoiding what looked like dozens of balls of crumpled-up foil, banging into their space ship. I think a lot of nerdy kids pictured the asteroid belt as a shotgun blast of planet chunks bouncing off each other. If one really want to bump into a lot of stuff in space, they might choose Saturn's rings though.

I'm not sure which of us is confused. Conic sections are solutions to two body problems or similar (the Earth is orbiting the centre of mass of the solar system, not the sun itself).

Three body problems rely on second by second force simulations. Instantaneous force simulations lead to accelerations which lead to changes in velocity and location, which feedback to the force simulations.

Euler's method and similar are ways to solve differential equations like above.

People have already correctly noted the extreme emptiness of space and the careful mission planning, but there's another fundamental reason why a probe like Voyager isn't going to start orbiting something (that it isn't already orbiting, like the center of the galaxy).

Newtonian orbits are what's called "conservative". That means they don't gain or lose any energy during the orbit, they just exchange kinetic energy (the energy something moving has) for gravitational potential energy (the extra energy something gets from going uphill against gravity) and back again.

One of the effects this conservation of energy has is that if a probe falls into the gravity well of a celestial body of some sort, the probe will just exchange potential energy for kinetic as it falls into the gravity well, and then exchange kinetic back to potential as it flies away out of it. If it fell towards the celestial body from a very large distance (where the gravity of the celestial body was effectively zero) and had some initial speed, then it wasn't initially gravitationally bound to that celestial object and it won't be gravitationally bound to it in the end, either. It has enough total energy (kinetic plus potential) that it will simply fly away from the celestial body just like it flew towards it and won't go into orbit!

Now, if the probe fires its thrusters, or if it interacts with the planets atmosphere, or if it interacts with a third body, then it is still possible for it to go into orbit of the planet. But the first takes active intervention by the mission controllers, the second requires incredibly precise flying to interact just right with the atmosphere so as not to burn up (and it would come around and interact repeatedly until its orbit did decay), and the third requires an even more improbable and specific three-body interaction where the two-body interaction is already fantastically unlikely.

Conic sections are just an approximation. The fairly minimal tidal gradient makes stitched together conical sections a decent approximation - when you're near Earth you follow a conic around Earth and your path around the sun otherwise mimics that of Earth.

The Earth orbits the solar system's barycenter, which approximates fairly nicely to the sun but if we ignore the sun and patch our conics around the barycenter it works even better.

The method is aptly named "patched conics".