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After the Pioneer, Voyager and New Horizons spacecraft complete one orbit of the Milky Way (in approx. 230-250 million years or one "galactic year"), how close will they then be to our solar system?

(Editing my question for clarification) The reason for asking the question is to understand whether these spacecraft that are now in orbit around the center of the galaxy will behave analogously to an object that was thrust away from the ISS and then meets up with the ISS exactly one orbit later. I am assuming that the gravitational pull of the galactic core will prevent the spacecraft from rising above or below the galactic plane for ever and that they will be in a similar orbit to the solar system, just inclined to it. Is that correct?

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Oversimplifying by taking the current velocity of each probe and multiplying it by 250 million years, I get:

Admittedly this ignores slowing down due to the sun's gravity (definitely significant). It also ignores any gravity effects from any stars it passes along the way (probably significant, but as as @GdD mentions we don't know).

For comparison, Wikipedia puts the diameter of the Milky way at 150,000 to 200,000 light years.

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    $\begingroup$ This is pretty good answer actually. "Somewhere in Milky way, and still on the same side of it as earth." $\endgroup$ – jpa Jun 2 at 17:43
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    $\begingroup$ @jpa unless it gets a gravity assist from a freak black hole that shoots it out of the galaxy at 10% the speed of light. While definitely extremely unlikely, it's possible! $\endgroup$ – John Dvorak Jun 2 at 19:37
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    $\begingroup$ @JohnDvorak Wouldn't that require a black hole moving at 5% the speed of light? $\endgroup$ – lirtosiast Jun 3 at 8:00
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    $\begingroup$ Aren't those velocities heliocentric? If they are, it should be noted that in 250 million years the probes are expected to have completed a galactic orbit, although being still near the Sun. $\endgroup$ – Pere Jun 3 at 8:36
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    $\begingroup$ @SoronelHaetir to quote hitchhiker's guide to the galaxy: "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." (One of the rare occassions Adams was probably underestimating a fact). The chance that you run into something outside of our solar system is almost zero, so you can with almost certainty say none of the spacecraft will hit something large enough in a given timeframe. $\endgroup$ – paul23 Jun 3 at 11:14
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We don't know as there's no way to calculate it exactly. To do so we'd have to have extremely accurate data on every gravitational interaction these space probes will ever be exposed to. This would require accurate information on the location, mass and vector of every single body in the galaxy, that means every star, every gas cloud, nebula, planet then all the way down to small rocks. Then we would have to perfectly model every gravitational interaction between every single one of these bodies in order to map stellar shift and the movement of objects for the next several hundred million years, and be able to account for the gravitational influence of extremely distant objects. Then we could plot the spacecrafts' paths through this gravitational map.

We don't have nearly enough data to do this. The milky way galaxy has an estimated 250 billion stars plus or minus 150 billion. We don't even know how many stars are in the galaxy, much less their exact mass, position or other direction of movement. That's just stars, we can estimate the number of planets from our existing observations, without knowing their positions and mass. Even if we had the data we don't have the computing power to calculate it.

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  • $\begingroup$ I commend you for even making an effort to write this answer. I know there are no stupid questions but I don't know what OP was expecting. $\endgroup$ – OrangeDurito Jun 2 at 11:10
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    $\begingroup$ And we could add the problem of dark matter & dark energy, discrepancies in estimates of cosmological constants,... Hey I know! We'll use TensorFlow! :-) $\endgroup$ – Carl Witthoft Jun 2 at 11:27
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    $\begingroup$ Well, you would hope we will have those solved in 200 million years @CarlWitthoft. $\endgroup$ – GdD Jun 2 at 11:43
  • $\begingroup$ @GdD At which point we could observe; we wouldn't need to predict their position :-) $\endgroup$ – Carl Witthoft Jun 2 at 12:22
  • $\begingroup$ @CarlWitthoft ok, first let's measure the universe 500000 times from big bang to heat death, so we have enough data for learning our neural network. $\endgroup$ – leftaroundabout Jun 2 at 15:07

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