How did Pluto end up in it's current orbit?

Since the discovery of Pluto and the discovery of its strange orbit several models were made to explain that orbit.
Most of those models were later dissmissed, because they were based on wrong assumptions, for example a wrong mass.
All the models have in common that they assume that Plutos current orbit was formed due to an interaction of Pluto, Neptune and Triton (Neptunes largest moon).
This assumption is made because of two things:
• Triton has a retrograde orbit, which clearly designates it as a non-natural satellite.
• Pluto has an eccentric orbit, which brings Pluto within the orbit of Neptune.

A survey of the models is given below. The models are arranged by date. First the principle of the model will be discribed and then the problem(s) that came with the model.

Dormand & Woolfson - 1977
Model
The model of Dormand and Woolfson was based on a collision between large planets in the early Solar system.
Pluto was a moon of one of those planets and was ejected into a heliocentric orbit during the collision.
It's orbit led it to Neptune. There Pluto interacted with Triton, which was a natural moon of Neptune. The interaction reversed Tritons orbit into a retrograde one and Pluto was pushed into an orbit similar to it's present.
Problem(s)
Numerical analysis of this model showed that it was possible, but there were also three problems.
The first problem was that the present orbits of Neptune and Pluto are such that the minimum distance between the planet is about 18 AU.
This problem could be solved by the existence of resisting medium in the early Solar system that was the prime cause of the planetary collision in the first place.
The early planets had eccentric orbits with small inclinations. Because of the non-central gravitational forces on the planets due to the medium there was rotation of the lines of apses of the orbits, so that from time to time the orbits did intersect.
The same precession of the lines of apses would have occured for Neptune and Pluto and by the time the resisting medium disappeared the orbits could have become well-separated, due to the inclination of Pluto
The second problem was that the main disturbing influence transferring Plutos orbit from a small perihelion distance to its present orbit was as a result of Neptune and such a transfer of orbit seems precluded by Tisserand's criterion.
The third problem was a problem Dormand and Woolfson couldn't consider. In 1977 Charon wasn't discovered yet. Therefore the model didn't include Charon and the mass of Pluto was greatly overestimated.
The discovery Charon completely ruled out this model.

Harrington & Van Flandern - 1979
Model
Harrington and Van Flandern proposed that both Pluto and Triton were natural satellites of Neptune.
Their orbits were disrupted by a body with a mass of about 5 Mearth which passed through the satellite system. The disruption caused Tritons orbit to reverse, ejected Pluto and disturped Nereid (moon of Neptune) into it's current eccentric orbit.
The formation of Charon is ascribed to the tidel action by the passing body.
Problem(s)
The passing of such a body is possible and independent of the masses of Triton and Pluto, but Harrington and Van Flandern didn't discuss the origin and destination of the massive body.

Farinella et. al. - 1979
Model
The model created by Farinella and his colleague's is based on the assumption that Pluto was a natural satellite of Neptune and that Triton was in a heliocentric orbit.
Triton was captured by Netune into a orbit around it. Its orbit around Neptune then evolved until it underwent an interaction with Pluto. Pluto was ejected into a heliocentric orbit and tidally disrupted by the interaction, which caused Charon to form.
Problem(s)
The weakness of this scenario is that it requires a direct capture of Triton. Such a capture is dynamically very difficult and requires a great deal of "luck". It would also require that Triton and Neptune were in similar heliocentric orbits so that the approach velocity of the two bodies was just right.
However, it is possible.

Dormand & Woolfson - 1980
Model
With the new estimated mass of Pluto Dormand and Woolfson created a new theory. Their model had some similarities to that of Farinella et. al.
They began with Triton in a heliocentric orbit and Pluto as a natural satellite of Neptune.
Again Triton is captured into an orbit around Neptune.
A close interaction pushed Pluto out of its orbit into a heliocentric orbit and Triton went into a retrograde orbit about Neptune.
Problem(s)
The orbit of Pluto around Neptune had to have a very large radius compared to the radii of the orbits of satellites we find nowadays.
The final orbit of Triton around Neptune also was very large (radius 0.9AU). In this orbit it would be heavily disturbed by the sun.
These problems were mostly due to the wrong estimation of mass of Triton. Dormand and Woolfson used an estimation of 10-7 Msun. The present known value is 1.111 X 10-8 Msun.

The collison model - Woolfson
Most of the models suggested a close approach between Pluto and Triton. Therefore a current, not ready rejected, theory is that Pluto and Triton not only approached eachother, but actually collided.

Model
This model also starts with the assumption that Pluto was a satellite of Netptune and that Triton was in a heliocentric orbit.
The relative positions and velocities of Neptune, Triton and Pluto are given in figure 1.
Pluto has the velocity it needs to be in an orbit around Neptune and Triton strikes Pluto coming from the outside the orbit of Neptune.
Integrating this four-body system (the sun is also included) backwards in time shows that the orbit of Pluto was is an almost circular orbit with a radius of 544,840 km about Neptune. It also gives that Triton was in a heliocentric orbit with an axis of 29.087 AU and an eccentricity of 0.9122.
Figure 2 gives the velocities of Pluto and Triton immediatly after the collision.
Nummerical integration forward in time gives that Pluto goes into a heliocentric orbit with an axis of 39.49 AU and an eccentricity of 0.2534. These values are very similar to it's current orbit, which has an axis of 39.51 AU and an eccentricity of 0.2482.
According to this integration Triton went into a retrograde orbit around Neptune with an axis of 436,500 km and an eccentricity of 0.8805. It's current values are 354,800 km and 0.000
The eccentricity of the orbit of Triton disappeared because of interactions with other satellites of Neptune. This would also explain the highly eccentric orbit of Nereid.
In the calculation Triton had mass 1.111 X 10-8 Msun and the mass of Pluto is taken as the estimated combined mass of Pluto and Triton, 7.43 X 10-9 Msun.

This model also explains the formation of Charon.
Figure 3 shows the approach velocity of Triton relative to Pluto. Triton doesn't hit Pluto head-on, but merely grazes Pluto. This blow removes material from it (at the darker-shaded side) and sends it into a orbit around Pluto.
The formation of Charon wasn't calculated in this model, but such calculations have been done by Benz, Slattery and Cameron (1986). In that scenario a Mars-mass body hits the Earth, removing material that goes into the orbit of what now is the Moon.

Problem(s)
This model gives orbital parameters for Pluto and Triton which are very similar to what they are today. The only thing this model doesn't discuss are the inclinations.
That is because the calculations leading to this model were two-dimensional.
But this model is easy to alter in order to get inclinations. A small depature in planarity could lead to an interaction in which the Pluto-Triton centre-to-centre line at the closest approach was highly inclined. This could have ejected Pluto into an inclined orbit and captured Triton into an orbit inclined from the orbital plane.

Conclusion
The mechanism for producing Pluto in its present orbit accompanied by Charon and also Triton as a retrograde satellite cannot be uniquely defined by modelling. Nevertheless, the collision-model with Pluto as a natural satellite of Neptune and Triton as a body originally in a heliocentric orbit is strongly indicated.