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A spacecraft in a circular LEO orbits at ~7.7km/s. If it performs a retrograde burn and cancels this velocity (within the Earth reference frame) it will start falling towards the Earth center along a straight line and hit the Earth's surface.

A spacecraft in a circular orbit around the Sun at 1Au radius would orbit at ~29.78 km/s. If it performs a retrograde burn and cancels this velocity (within the Sun reference frame) it will start falling towards the Sun center along a straight line and, unless Venus or Mercury would happen to perturb its trajectory, will burn after getting close enough to the Sun's "surface".

The Solar System is traveling at an average speed of 230 km/s within its trajectory around the galactic center.

Let's imagine a spacecraft that is launched from Earth in direction opposite to Earth motion around the Sun, and performs a burn to cancel both velocities: a) due to Earth's spin and b) the ~29.78 km/s around the Sun, hence becoming "stationary" in the Solar system.

Straight after this the spacecraft performs another burn in direction opposite to direction of Solar system motion in the Milky Way galaxy (and I'm not sure what this direction is, as this related question remains unanswered) in order to cancel the galactic 230km/s speed, hence becoming "stationary" in the Milky Way galaxy reference frame (I know it's practically not possible yet).

Question(s):

  • Will the spacecraft in this case start falling towards the Galactic Center?

  • Will it reach the Galactic Center if happenned to be not perturbed heavily by nearby stars on its way? Or maybe motion in galactic scale is affected by the nearby stars so much that the perturbation effects can not be neglected?

Sergiy Lenzion
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    This is an interesting exercise. Questions about the interstellar and galactic gravitational potential and its lumpiness are probably more likely to receive authoritative answers in Astronomy SE than they might here, and galactic trajectories might not even be on-topic here since they don't reflect aspects of Space Exploration normally discussed here. But let's see what happens! – uhoh Feb 02 '20 at 06:17
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    @uhoh we already have 5 spacecrafts that are bound to the galactic gravitational laws, so I hope that if not the gravitational potential, than at least galactic trajectories might be loosely on topic here. And if not, might need to transfer to Astronomy. – Sergiy Lenzion Feb 02 '20 at 06:42
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    Those spacecraft are not bound to the Sun, but the Sun's gravity is still by far the strongest force affecting their trajectory. All of them are still constantly slowing down with respect to the Sun, it's just that it's not enough to stop them completely. – uhoh Feb 02 '20 at 06:50
  • Here's the closest I've gotten to an answer here about space outside the solar system: Local expansion measured, near zero via Lunar Ranging - what about deep space probes? It's not necessarily related, but it's the only question I know of here that's close spatially. – uhoh Feb 02 '20 at 06:56
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    The first burn is wasteful, you just need to cancel your galactic velocity, which would be more efficiently done in a single burn. The spacecraft would immediately receive a gravitation assist from Earth (briefly) and the Sun, so it would no longer be at rest WRT the the galactic centre.. –  Feb 03 '20 at 09:41
  • @JCRM, I understand that direction of single burn to cancel all velocities (around Earth, Sun and galaxy) can be calculated and will be more efficient. I just described hypotherical step-by-step process to ensure my thinking about idea of coming to a complete stop in galaxy is not misinterpreted. The second part of your comment is part of the answer: a "one millionth of microsecond" after complete stop it will start to move. The question was in what direction? And given the estimate in BobJacobsen answer of galactical "pull" being so miniscule, the Sun will start "dragging" it quite stronger. – Sergiy Lenzion Feb 03 '20 at 10:17
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    @uhoh Astronomy has ruled that questions about spacecraft are only allowed when they are about doing astronomy with a spacecraft, or questions about observing satellites' orbits. In this case, I don't think the question should be moved there. – called2voyage Feb 03 '20 at 14:28
  • @called2voyage the question is about the gravitational acceleration experienced by an inert object. That the OP calls it a spacecraft is a red herring; it doesn't matter how it got to where it is, it's stopped. An asteroid, a spacecraft, and an actual interstellar herring would all follow roughly the same trajectory which is determined by the interstellar gravitational potential which is something that astronomers know about and space explorers mostly do not. Can you bring my comment to the attention of "Astronomy" and see if they don't agree? – uhoh Feb 03 '20 at 15:32
  • @called2voyage I'm trying to figure out how to work "So long, and thanks for all the fish" into that part about the herring... – uhoh Feb 03 '20 at 15:36
  • @called2voyage the actual question here is only "What is the trajectory of an interstellar object initially at rest in galactic coordinates; assume it starts in the vicinity of Sol but outside of the solar system." The answer will be "It depends where exactly it starts; from some locations it will fall back into the Sun or a nearby star, in other locations it may travel quite a distance towards the center of the galaxy." The answer with then talk about the interstellar gravitational potential in more detail. – uhoh Feb 03 '20 at 15:45
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    @uhoh I think Astronomy would prefer that it not be framed around a spacecraft, even if that might as well be a placeholder. So if the OP wants to ask over there but replace mentions of spacecraft with "object", that should be fine. That said, as there is already an answer here, migration would be the preferred route to accomplish this, so if the OP does want to make such edits and migrate, they can perform the edits and flag the question for me to migrate. – called2voyage Feb 03 '20 at 16:20

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The period of Earth's orbit around the galactic center is about 225-250MYr or about $750 \times 10^{15}$ seconds. The peak velocity is $230 \times 10^3$ m/s. So the central acceleration is:

$$a = 2 \pi v / T = 2 \times 10^{-12} \rm{m/s/s}$$

That's a very, very small acceleration. To put it in perhaps more understandable units, it's about 6 m/s per thousand years. Almost any other effect on a spacecraft will be larger: The much-studied Pioneer anomaly is a factor of 100 larger.

Bob Jacobsen
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  • Good start; how does this compare with the acceleration towards a random star, say of 1 solar mass at 10 ly distance? – Russell Borogove Feb 02 '20 at 16:38
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    Well at 1AU it's $6\times 10^{-3} ms^{-2}$ and 10ly is roughly 640000 AU. So we are looking at $1.5\times 10^{-14} ms^{-2}$ or about 1% of the overall galactic acceleration. Conveniently that means 1 solar mass at 1 ly matches the galaxy. – Steve Linton Feb 02 '20 at 17:52