# Orbital mechanics: is ballistic capture possible without acceleration?

James Demers
All spacecraft that have been put into orbit around other planets have required engines to decelerate them and inject them into their orbits. So-called "ballistic capture", from what I've read, always seems to call for at least a minimum application of force to change the trajectory; I get the impression that while it might be possible to temporarily orbit via a purely ballistic capture, the resulting orbit is chaotic and will not persist.

Deimos and Phobos have every appearance of being captured objects - but one can imagine collisions providing the needed orbital injection forces. Other examples, if they exist, are pretty rare, given the billions of years of opportunity.

Newtonian trajectories are conic curves (hyperbolic, parabolic or elliptical), and transitioning from one to the other would seem to call for the application of force. My main question is, can an inert object be captured from a hyperbolic/parabolic trajectory into a stable orbit, or is acceleration required? (Would an observer locked within the object be able detect the event with an accelerometer?)

Relatedly - more as a question of orbital mechanics than of physics - as object A approaches planet B on a hyperbolic/parabolic trajectory, could the gravity of a third body C put object A into orbit around B? For an object approaching, say, the Earth-Moon system, stable orbits are hard to come by, but given three bodies and no initial orbits, can an orbit be produced?

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### Orbital mechanics: is ballistic capture possible without acceleration?​

All of your scenarios imply a change in trajectory, which implies a change in velocity, which IS acceleration, so ... no.

James Demers
All of your scenarios imply a change in trajectory, which implies a change in velocity, which IS acceleration, so ... no.
The OP is explicitly asking about proper acceleration, not acceleration by gravity alone:
... or is acceleration required? (Would an observer locked within the object be able detect the event with an accelerometer?)

• phinds
Newtonian trajectories are conic curves (hyperbolic, parabolic or elliptical), and transitioning from one to the other would seem to call for the application of force.
Yes.
Relatedly - more as a question of orbital mechanics than of physics - as object A approaches planet B on a hyperbolic/parabolic trajectory, could the gravity of a third body C put object A into orbit around B?
You mean a stable orbit? Maybe two objects approaching a third one from opposite sides (symmetrically), could both end up orbiting it? Not sure though.

Gold Member
Since several planetary moon in the solar system is believed to have been captured (without impacts), it seems to follow that capturing may be possible in a multi-body system if the configuration of orbits of all the involved bodies are just right, but I guess modelling such a capture using patched conics (as implied by OP) may prove to be impossible since this method usually assumes that the total trajectory is divided into piecewise two-body orbits.

Regarding the "degree of stability" of a particular capture I would guess it is inversely proportional to how like it is to occur (everything else being equal). Or in other words, I have trouble imagining a very stable impact-free capture unless it involved a third body that since has been ejected from the system.

• Dale
Keith_McClary
Summary:: Can inert objects be captured into stable orbits?

as object A approaches planet B on a hyperbolic/parabolic trajectory, could the gravity of a third body C put object A into orbit around B?
Maybe if C is ejected (with escape velocity).