# Calculating where an astronomical object has been , Voyager specifically

I know that it’s possible to predict the path of an object sent from Earth, that’s why we can hit things um…very far away with astonishing accuracy. Excuse the lack of technical jargon, I’m not even going to try because it’s so far out of my league.

But would be possible for someone who just stumbled upon Voyager this afternoon to observe it for a a few hours and then trace its path all the way back to earth, but figuring out what bodies where close, gravity effects, etc?

It seems enourmously complex to me, but so does a simple trip around the moon, so…

No, Voyager had thrusters on it which allowed it to make minute adjustments. Without knowing the timing of the thrusters, it’s impossible to reverse engineer it’s trajectory.

Darn…hm, ok. Then let’s say we threw out something from Earth in…hm…THAT direction points and it was allowed to continue without any artificial course adjustments.

Would it be possible then?

No, anymore than you could figure which direction a golf ball came from if you found it on the ground (although you might be able to make some educated guesses…).

An important factor that is not available from an object on the ground is WHEN.

Yeah, but that’s different, innit? The ball is sitting on the ground. Voyager, you can say “Ok, it’s here now…but now it’s here” and at least start with a reverse azimuth.

When you say “stumbled upon” do you mean* in flight*? Because, that’s a whole lot different than finding it after it’s landed…

Yeah, while it’s till moving!

If you want to go into that, then the aliens could still measure how much tank space there is for fuel, and use that to determine a trumpet-shaped region of space from which the probe could have come. And it’d be a very narrow trumpet, narrow enough that they’d probably still be able to track it back to our Solar System. And if you’re positing an interstellar civilization that’s interested in our Solar System, they’d be sure to be able to narrow it down further from there.

Effectively, no. For a situation where a body in in a free path starting from earth (say), there are more than two bodies to calculate (n-body problem), and there are no easy mathematical solutions, only approximations. For a small object at low speed, the errors accumulate with every interaction, so an accurate reverse trajectory is very hard.

For something like the Voyagers, you might be able to project back to the last gravitational slingshot (Voyager 1: Saturn, Voyager 2: Neptune). I suspect there have been no major course corrections since then (just attitude). You have no chance from there.

Si

I would argue, effectively yes, although it might count as cheating since you have to deal with more than just the spacecraft’s movements. It seems pretty clear that from knowing where the Voyagers now are, you could limit their origin to the solar system (because that is the thing they are close to), and consequently, to one of the planets or moons. Which gives you, say, a couple hundred places to look, and from there, the most likely place of origin is the Earth because it’s the place with all the toolmakers.

Now, granted that this doesn’t really rely on the exact trajectory at all, but that’s what I’d do if tasked to figure out the origin of the Voyagers.

But couldn’t you also figure out that Jupiter (or whatever) must have been in the same area as Voyager when you trace its path back that far? And couldn’t you then figure out where the slingshot came from? Or do the approximations just fall apart here, leading to just a too large area of the solar system that Voyager could have come from? I mean, after all, people did figure out how to plan and accomplish the slingshots to begin with. I can’t think of, at least offhand, any reason why doing it backward would be that much harder.

Sure, tracing back past any orbital slingshot would be very difficult or impossible. But the complexities of the n-body problem wouldn’t be relevant at any point beyond our Solar System. And like I said, once you’ve got it narrowed down to a particular star, an interstellar civilization wouldn’t have any problem in finding us.

When you’re doing a maneuver like that forward and in real time, you can continually observe precisely where the spacecraft is (not just where it should be), and if it’s not precisely where you want it, you can fire thrusters to correct it. When you’re calculating backwards, you don’t have any such way of compensating for accumulated errors.

Although, very clever aliens might be able to correctly guess all of the slingshots, if they were able to deduce (based on what instruments are present) that the craft’s primary mission was to study multiple other planets, and also deduce (based on habitability) what planet was the point of origin of the craft. It’d be tricky (plotting good orbits for such things is something of a black art, very difficult to explain how you’re doing it even while you are doing it), but maybe the aliens have a better knack at it than us (or can program their computers to have a better knack than ours).

Thanks.

I don’t think it would be that narrow a trumpet if you take into account slingshots. The entire point of slingshots is that you can control where you want the spacecraft to go (to the next slingshot) very precisely with only a minimal amount of fuel used. This means your error bounds grow hugely every slingshot.

One way they could do it though is to reverse engineer based on the timing. There’s only a few good windows open every decade where you can take advantage of multiple slingshots and get the furthest from Earth with the minimum amount of fuel. If they assume you would only launch a craft during an optimal period, that would limit down to earth.

Isn’t this the problem faced by the astronomers in the distant past?

They made observations of the motions of the planets, and then from these correctly predicted both the path and the shape of their orbits.

How is this problem different from that in the OP?

The probes are tiny, so their path is influenced by small things (or big things at a distance). For example, the Pioneer Anomaly is a velocity change experienced by Pioneer 10 caused by uneven radiation of heat from the probe.

The planets are much larger, and (for a first approximation) can be treated as a 2 body calculation (sun and planet). This gives an elliptical, stable orbit. It isn’t until later with close observation that perturbations were identified (such as the one that pinpointed Neptune).

There is a reason NASA only gives future probabilities for near-earth asteroid passes - they cannot predict the orbits of such objects more than a few years out.

Just looking back at Voyager again. If Voyager passed close to an object out beyond Pluto and changed direction out of the orbital plane - before long, the observed track would point past the solar system, and the diverting object would not be visible. An observer would have to guess as to the source.

Si

Voyager is only about 0.002 light years from Earth, and heading away from the Solar System; if some one found it today and didn’t manage to track the origin back to the Solar System and induce that it came from Earth, they wouldn’t be trying very hard.

No, it wouldn’t be, at points beyond the slingshot. But interstellar space is, for all practical purposes, empty. The Voyagers will almost certainly never have another slingshot again. If aliens ever find them, they’ll be able to back-track their trajectory all the way back to our Solar System, because that’s where the last slingshot is.