Capture would be like a reverse gravitational slingshot? This planet happened to meet the sun at an angle where it lost enough energy to fall into orbit instead of slinging back out like those comets that come around on long cycles?

It would be like a reverse gravitational slingshot, in a different way.

There is no way to capture with just 2 bodies - it would have to leave on gthe same hyperbolic orbit that it arrived on. However if it drove by and had a close enough interaction with a third body, like Jupiter, it could lose angular momentum to the planet, resulting in entering an orbit around the Sun. Further gravitational interactions with planets could then smooth that orbit out over time.

Alternately this could be the more straightforward scenario of interstellar object hits planetoid, they merge, and the new combined object is now in orbit.

AFAIK, it could be in a 2 bodies slingshot, multi-body interaction with some other stuff on the Oort cloud, or tidal interaction (what could happen way more easily with a nebula).

A comet coming back on a long cycle is an orbit

gravitational capture

You don't need to lose energy to enter orbit any more than you need to lose energy too roll a ball down a hill.

But a ball needs to lose energy to not roll right back up a hill to the same height it came from. And if that "ball" is a mass from outside our solar system, it will roll right back out of the solar system just as easily as it rolled in unless there is enough forces to slow it down enough to capture it.

Not true. An obit is not an infinite "plain" with a finite "hill" on but rather a finite "valley". The ball will exit the valley on the other side unless it loses excess kinetic energy somewhere in the valley.

Anything that approaches the sun will do so with faster than escape velocity because the gravitational potential energy gets converted into kinetic during the approach. Newtonian mechanics is time-reversible - just like it's impossible for an object in orbit to spontaneously escape without gaining energy from somewhere first, it's impossible to enter orbit without losing energy to another body.

Small nit: this is for objects approaching from infinity in a two body system. Otherwise the object can be in orbit and already be “captured” there. For example, the moon also approaches earth slightly over the month while speeding up, then slows down while moving away. Or it could just be a 3 body system, which is chaotic and can’t be modeled accurately and can have objects spontaneously eject from the stable system (even though the physics is indeed reversible)

Your first nitpick only makes sense with a weird definition of "approaches" for the context, so I think it just adds confusion. They're pretty clearly talking about something that is headed in the direction of the sun and not already in orbit.

And the comment you're responding to already mentioned that other bodies can make a capture happen. Nobody was saying capture is impossible.

I thought the context is orbital mechanics, for which the term approach is the common term for a portion of the trajectory where the bodies move towards each other. Take any Wikipedia article for an orbiting solar body and search approach eg: https://en.m.wikipedia.org/wiki/Halley%27s_Comet

That is not true. If it approaches with less than escape velocity it will gain all the velocity necessary to escape in the process of approaching the Sun.

You could think of it as speeding up as it falls toward the sun, it then slows down by the exact same amount as it leaves the Sun.

In order to stay near the sun it needs to lose some of that speed, and given that momentum is conserved, the only possible way is to either hit the Sun or send that momentum to a third object.

To all other readers: this is wrong.