# Orbital mechanics: is ballistic capture possible without acceleration?

• James Demers
In summary: So in summary, while it is possible to orbit via a purely ballistic capture, the resulting orbit is chaotic and will not persist.
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?

James Demers said:

### 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.

phinds said:
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:
James Demers said:
... or is acceleration required? (Would an observer locked within the object be able detect the event with an accelerometer?)

phinds
James Demers said:
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.
James Demers said:
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.

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
James Demers said:
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).

James Demers said:
Summary:: Can inert objects be captured into stable orbits?

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.
Early on in the formation of the Solar System, the situation would not have been as apparently stable as it is now. There could have been objects with highly eccentric orbits which would have been 'weeded out' after they had made their disturbances to the others. What we observe is a near - final result and that doesn't tell us everything about the distant past.

Looking at what goes on in Saturn's rings and in the Asteroid belt, you could expect external effects on the mutual orbits of two small bodies 'of interest' which could put them into or take them out of a temporary stable mutual orbit.

## 1. What is orbital mechanics?

Orbital mechanics is the branch of physics that studies the motion of objects in orbit around a larger body, such as a planet or a star. It involves understanding the forces and equations that govern the movement of objects in space.

## 2. How does ballistic capture work?

Ballistic capture is a technique used in orbital mechanics to transfer a spacecraft from one orbit to another without using a significant amount of fuel. It involves using the gravitational pull of a planet or moon to capture the spacecraft into its orbit.

## 3. Can ballistic capture be achieved without acceleration?

No, ballistic capture requires some form of acceleration, whether it is from the spacecraft's thrusters or the gravitational pull of a celestial body. Without any acceleration, the spacecraft would continue on its original orbit and not be captured into a new orbit.

## 4. What factors affect the feasibility of ballistic capture?

The feasibility of ballistic capture depends on several factors, including the mass and velocity of the spacecraft, the mass and gravitational pull of the celestial body, and the distance and relative velocity between the spacecraft and the celestial body.

## 5. Is ballistic capture a common technique used in space missions?

Yes, ballistic capture is a commonly used technique in space missions, especially for transferring spacecraft to and from planets and moons within our solar system. It is a fuel-efficient method and has been successfully used in several missions, including the Cassini-Huygens mission to Saturn.

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