Can it be predicted if an Interstellar Object will get bound to the solar system by knowing its speed and direction?

Question

Recently I've reading there are only 2 known Interstellar Objects. Suppose another one appears which will cross the solar system at some point, could it be predicted if it will get bound to the solar system by knowing its speed and direction?

Answer 1

Of course! One calculates its total energy (kinetic plus potential) and compare it to zero. If it's $>0$ then it will escape.

In practice, anything heading into our Solar System from outside is unbound. That is how it is established it has come from outside the Solar System. Only a relatively strong interaction with another body in the Solar System might be able to bind it. That would have to be analysed on a case by case basis.

Answer 2

ProfRob's answer is correct but short. I'll add some additional information for those wondering how that analysis takes place.

Suppose another one appears...

So the object is now visible in telescopes and recognized to be moving against the stars. It has a proper motion. Over time (days, weeks, months) if enough precise measurements are made to see some change in speed and direction, it is possible to determine that it is under influence of the Sun's gravity and a proposed orbital trajectory can be constructed, which will include some uncertainty.

As soon as you know the speed and distance of an object (where speed is the magnitude of the velocity in 3D, not just apparent angular velocity) then as prof. Rob points out, the reduced energy is calculated by adding the reduced kinetic and reduced potential energies. "Reduced" means we don't need the mass of the object because we just need the sign of of the total energy.

$$\frac{1}{2}v^2 - \frac{GM}{r}$$

Here $GM$ is the gravitational constant times the mass of the Sun, cf. vis-viva equation.

...will cross the solar system at some point, could it be predicted if it will get bound to the solar system by knowing its speed and direction?

If the calculated reduced energy based on early observations is less than zero, it is already bound to the Sun!

If it is greater than zero, it isn't.

In that case, the only way it could become bound is by losing some kinetic energy. An exotic, unpredictable way would be to become warmed by the Sun's radiation and start shooting a huge jet of steam in the forward direction to slow down.

The other way is to pass close enough to a planet or other object to exchange momentum and energy, or to hit something.

But it is interesting to note that if it were barely bound to the Sun and such a "close encounter" occured, it could just as likely be converted to unbound as the other way around.

Answer 3

Scaling it down one level, it's the same question as asking whether an object in solar orbit will be captured by the planet whose sphere of influence it visits. It's the exact same question.

Largely, the expectation is that speedy thing goes in, speedy thing goes out.

The energy received from entering the planet's sphere of influence ("dipping in") will match the energy expended by exiting the planet's sphere of influence ("dipping out") but slingshot maneuvers do exist and can impart/negate some energy.
It's not impossible (though astronomically unlikely) for some sequence of slingshot maneuvers between the planets and its moons to lead to a stable orbit around the planet. I'm not sure if a slingshot capture around a single body is possible (e.g. a planet with no moons), I suspect it's not but there might be an edge case I'm not thinking of.

Similarly, if it just straight up hits the planet/moon, it trajectory will be significantly altered to the possible point of capture (i.e. not a glancing blow). Zooming out to your original question again, the odds of hitting something in the solar system are low, but not zero.

I'm omitting aerobraking from this analogy since the Sun does not have an appreciable atmosphere for these purposes.

Can this be calculated in advance? Yeah, we understand the governing principles. The main difficulty here is situational awareness, i.e. knowing exactly which players are on the stage. When dealing with a physical impact, it's going to be difficult to get a very precise prediction but ballpark estimates are reasonable.

Answer 4

Of course you can “just” set up a few differential equations…

The speeds, trajectories and masses of all major bodies in the solar system are known with high precision. Last time I checked ( more than ten years ago) good enough to predict paths for the next 25 million years.

If your body is close and its mass is either precisely known or negligible, just solving differential equations is enough. If the path gets close to the sun or one of the planets / large moons you will need very precise initial conditions and take relativity into account. The further away, the higher the speed, the larger the mass, you will need more precision. Hitting an atmosphere will make things tricky. If the body gets hot it could create gases that work a bit like a rocket engine; some comets do that.

And there may be points where the solutions are unstable. So the answer could be “with the given initial conditions and their precision, the solution is so unstable that we cannot predict it”.

I forgot: Solar wind and an artificial object with huge solar sails could be interesting.

Answer 5

Initially, when I saw this question, I formulated the answer in my mind the following way : In addition to knowing the speed and direction of the interstellar object, one must also be aware of the the position, and trajectory(speed and direction) of all other celestial bodies such as comets and meteorites, within the solar sistem. Any collision has the potential to desintegrate, or to dramatically change the trajectory of the interstellar object. However, this aspect has been adressed by other answers.

Later, other aspects came to my mind.

Other data that you may need:

#1: The friction with the medium being traversed (which depends on the evolution in time of the temperature)

One thing than can reduce an object's speed is the friction (the force of resistence) with the medium which it traverses. It is one thing to cross a cloud of water vapours or a cloud of tiny ice particles. The same thing applies to other substances such as methane, carbon dioxide, oxygen. And the aggregation state is dependand on the temperature. Therefore, you must also know "the weather forecast" along the trajectory of the interstellar object.

EDIT: as long as the object passes through a cloud of cosmic GAS, you might need to take aerodynamics into account. Please visualise mentally the profile of a plane's wing: the two sides of unequal lengths cause the airflow to run at different speeds, thus lifting the wing. Of course, in outer space there is no up and down. But when an object has two hemispheres of different shapes, traversing a gaseous cloud could cause a deviation from it's initial trajectory. If the gas density of the cloud is low, then the deviation effect will be low, but even slight deviations from the trajectory could not be neglected, if you want precise calculations.

#2: The evolution in time of the gravitational field

Another aspect is the gravitational field : the force that pulls the object is the resultant force of all individual gravitational forces, from all other celestial bodies (galaxies, stars, meteorites). Of course, distant objects and small objects have a neglectable contribution. However, it is easy to assume that the gravitational field will be constant in time. Yet it is not. I recall from highschool that the gravitational force between two objects depends on the masses of the two objects. Stars' masses are not constant, however. While chemical reactions preserve mass, thermonuclear reactions don't. And it is thermonuclear reactions taking place within stars. As their mass changes, so does their gravitational field. (EDIT: I've googled: Sun's hydrogen turning into helium causes the Sun to loose mass)

#3: variations of Sun's magnetic field (if your object contains iron)

Sun's storms mean not only Sun throwing jets of plasma, but also a high increase of the magnetic field, at least to some directions. Increased Sun's magnetic field, interacting with Earth's magnetic field, causes Aurora Borealis. Does your object contain large amounts of iron ? If so, it's trajectory might be influenced by variations of Sun's magnetic field. But I find it hard to quantify by how much. But this is another reason why the initial variables - speed and direction - are not enough.

#4: is the chemical composition of the object going to stay constant over time ?

Assuming that the object's chemical composition is not going to change throughout the journey, is , well, an assumption that might not be correct. Some chemical substances follow the pattern A -> B + C (substance A decomposing into two other substances). The time range for chemical reactions can vary greatly. Some chemical reactions can take years, like iron turning into rust, which is iron oxydes. (Of course, this particular example requires an atmosphere of oxygen, plus some humidity, which I won't expect in outer space.) However, the point is that your object could start its journey being made up of one particular substance, which in time could decompose, leading, potentially, to the disintegration of the object. In addition to the "self-running" chemical reactions mentioned above, some factors can work as cathalysts, such as high frequency radiation, if your object will get hit by the radiation beam emmited by a quassar or a pulsar.

#5: is the aggregation state (of the object) going to stay unchanged ?

I imagine two scenarios: First one - your object is initially a white object, reflecting most of the light. At some point, it passes through a cloud, being covered with a layer of black dust. As a result, it will absorb more sun light, causing it to warm up, maybe not by much. However, some substances have very low melting points. Second scenario: your object is made up of ice and metal minerals. As mentioned above, your object can get hit by a beam of X rays, gamma rays, which, when being absorbed by the metals, will cause them to heat, to the point of melting the ice, and maybe even dissintegrating your object.

#6: will the mass of the object be constant in time ?

If your object passes through a cloud of cosmic dust, some of this dust might stick to the object. Of course, some substances will have a greater affinity than others for adhering to your object. In any case, the addition of the new material will make your object heavier. A greater mass will mean a higher gravitational force pulling the object.

#7: is the center of mass in the "middle" of the object, or is it shifted outwards ?

Given two objects of the same mass, same sizes and same speed, they will have different trajectories as long as their center of mass is not in the same position. I can name two situations when the center of mass does not coincide with the "geometric" center of the body : 1) the object has CONCAVE SHAPE, which is often the case of meteorites; 2) the object does not have an UNIFORM DENSITY, having heavier material on one side. (see : flipping a biased coin, compared to flipping a fair coin, will, statistically, not produce the same results) My intuition says that having a center of mass shifted to the exterior would produce a helicoidal (spiral) trajectory. However, keep in mind that an object can have 3 individual rotational movements (one along each axis), which, combined with the liniar motion, could result in a complicated trajectory.

I have also identified some potential pitfalls in the way you formulated the problem.

#1: classical mechanics may not be enough to model the movement of cellestial bodies

When you talked about speed and direction, I believe that you operate in the "mental framework" of classical mechanics (also known as Newtonian mechanics, if I am not mistaking). However, this is not enough when operating at a cosmic scale. Often, theory of relativity must be taking into account, particullarly when dealing with speeds which represent a considerable fraction (say, 10%) of the speed of light. This certainly applies in the case of gallaxies departing or approaching one from the other (see redshift, blueshift), but may not necessarily apply to your object.

#2: Does you object have a rotational speed ?

When you said speed (of the object), you probably meant its linear speed. However, objects can also have a rotational speed. Therefore, I would ask : does you object have a rotational speed ? This may not be relevant when travelling through void, but is certainly relevant in case of collision with a different object, to determine the trajectory after the collision. ( see table tennis - top spin and back spin : a ball will have different trajectories after hitting the table, depending on whether it spins forward, backwards, or has no rotational speed at all )

EDIT: I have previously mentioned that friction with the medium being traversed is a relevant factor. Suppose your object traverses a dense cloud of dust. The higher the rotational speed, the higher the friction with the dust particles, thus reducing the linear speed (as well as the rotational speed, too). To give a visual analogy: a car's tire hitting the road can heat due to friction. The more rotations of the wheel, the hotter the rubber gets. For low rotational speeds, or no speed at all, the tire will not get hot.

#3: I really feel that the notion of 'interstellar object' should be better defined.

All this time I had in mind an object like a meteorite. However, would a cloud of cosmic dust quallify as an interstellar object ? Therefore, I feel that you need to specify these things: the SIZE RANGE of the object, and its AGGREGATION STATE.

To sum up, in my opinion the answer is NO. You need more data apart from speed and direction.