Orbiter missions with no (or little) fuel usage for deceleration, Target planet capturing the spacecraft w/o extensive fuel usage Options

[Anton Martynov]

I was involved in a casual conversation recently about the exploration of bodies in Solar System, in particular about fly-by approach vs. orbiter approach. In particular, I was saying that the main challenge with orbiter missions is that either you have to decelerate once you reach your target (requires tons of fuel on board), or you have to travel along the trajectory that would take an unreasonable amount of time to reach the target. As an example of the latter, I said that you could launch a spacecraft into a trajectory that would be a part of an elliptical orbit around the Sun with the perihelion around Earth and the aphelion around the destination. That way, when the spacecraft reaches its target, its speed relative to the planet will be slow enough for it to be "picked up" by the planet's gravity, and it will start orbiting the planet.

The other person in the conversation pointed out that it's been shown that when two bodies pass each other and influence each other gravitationally, it's not possible for them to start orbiting each other (or, in the case of one object being much more massive than the other (planet vs. spacecraft), simply "one orbiting another"). He said that either the more massive object will simply alter the trajectory of the passing smaller object, but not capture it, or the smaller object will crash into the bigger one.

And this is something that, to me, "intuitively" shouldn't be right, but I don't have enough expertise to prove that it's wrong. My counter-arguments are:

- Some of the natural satellites in the Solar System are believed to be captured by the planet as they were passing by (true, these are mainly hypotheses, but people wouldn't make such hypotheses if this wouldn't be possible?).

- If the object is passing by the planet at the speed less than what is required to enter the orbit, then it will crash down onto the planet. If the object is passing at the speed greater than the escape velocity, then it will continue flying without being captured by the planet. Surely if the object's speed is between these two values, it has to start orbiting the planet? (Not necessarily in a perfect circular orbit of course).

As further proof for the second point, I calculated the elliptical orbit with the perihelion at Earth (1 AU) and aphelion at Uranus (19.2 AU). Sure, it would take 16 years to get to Uranus, but the required takeoff speed would be 41.1 km/s (relative to Earth, that would be 11.3 km/s, so just barely above Earth's escape velocity, so we're good here), and the spacecraft's speed when it arrives to Uranus would be 2.1 km/s relative to Sun, and -4.6 km/s relative to Uranus. This 4.6 km/s speed happens to be the speed of a circular orbit at 266000 km from the center of Uranus.

So, in my understanding, we can launch the spacecraft from Earth at 11.3 km/s into the elliptical orbit, and then some 16 years later it will pass by Uranus and be captured by it. If we make some small course corrections along the way so that it passes 266000 km from Uranus, it will even be a circular orbit.

... but, like I said, maybe I'm missing something that won't allow the spacecraft to be captured by the planet's gravity? My whole point was that in this scenario you don't have to use fuel for anything else other than takeoff. Of course, some course corrections would be inevitable, but at least you won't have to try to decelerate from New Horizons-like speeds.

[tanjent]

In a two body interaction, in vacuum with point masses, etc., can't we say that what happens after closest approach has to be symmetric with what happened before closest approach? The relative approach velocity of the smaller object should accelerate until closest approach and then decelerate with an identical time/distance profile, so if the smaller object wasn't in orbit before the approach, it won't end up in orbit afterwards either. Caveat: there may be some relativistic effects to consider for the accretion disks "orbiting" black holes, but in a planetary-scale Newtonian universe, symmetry should rule out getting into orbit.

But these ideas about multiple-body collisions are fascinating. Under what circumstances is it possible to attain orbit around Saturn with a gravity assist from Titan? Or around Pluto with a gravity assist from Charon? With any body A of a given mass, there must be a limit to the amount of delta-v a spacecraft B can borrow relative to a third body C, without B colliding with A. And if B can be a piece of rock or ice, then collisions are permissible too, like in Triton's case. I'm sure that solutions like these have not been overlooked by the writers of mission proposals, so they must be impossible for the mentioned cases, but impossible by how much?