How does a planet's gravity push away smaller bodies that would otherwise intersect its orbit?

Question

I was reading an article about dwarf planets online where I stumbled upon the following definition of a planet:

The International Astronomical Union defines a planet as being in orbit around the sun, has enough gravity to pull its mass into a rounded shape (hydrostatic equilibrium), and has cleared its orbit of other, smaller objects.

The article put a lot of emphasis on the last line, but given that gravity is an attractive force, how do big planets push away smaller objects from their orbit that would otherwise intersect it?

The article I read: https://www.space.com/amp/15216-dwarf-planets-facts-solar-system-sdcmp.html

Answer 1

I feel the need to correct some issues that were brought up in the other answers.

Yes, gravity is an attraction-only force.
But due to its relative weakness, objects in space can attain large velocities, before getting the chance to collide with any single target. In physics we would speak of excess angular momentum, which is hard to get rid of in space, but I will try to avoid that terminology here.
What 'large velocity' means, can be expressed in terms of comparing the vectorial velocity of a body $\vec v$, with respect to a potential target, and the scalar escape velocity of that potential target $v_{\rm esc}$.

If $|\vec v|>v_{\rm esc}$, and orbits intersect, then one can think of our body experiencing only a slight deviation from its initial path due to the target's gravity, and the collision probability is given by the geometric cross-section of the target, which is always small, even for stars. This is in fact the normal case in the solar system, as opposed to what other, wrong, answers were presenting.

If $|\vec v|\approx v_{\rm esc}$, and the objects are nearly co-orbital, then it is hard to intersect the orbits and the body will end up mostly on a horseshoe-orbit around the target or be ejected, see also a thorough discussion of this case in the fantastic "Solar System Dynamics" by Murray & Dermott.

If $|\vec v|<v_{\rm esc}$, and orbits intersect, then the usual outcome is that the object is captured on an eccentric orbit around the target as a satellite. Again, a collision is extremely improbable, because the range of velocities in space is just enormous. To exactly hit the target object and not miss it, the velocity has to be fine-tuned to a very small range of values.

Synthesizing all this, we can say
Intersection of orbits does not imply collisions. In the overwhelming majority of cases orbit clearing works via swing-bys and not via accretion onto the clearing planet.

Furthermore, the popular picture of planet growth via collisions is that the young protoplanet gets bombarded a lot via asteroids and comets and thus grows. This picture seems to be broadly correct (e.g. Raymond et al. (2006), Alibert et al. (2018)), but with the caveat as stated above: This process is extremely inefficient, and most asteroids/comets will miss the young protoplanet. This is what makes planet formation with large impactors hard, and in modern times alternatives with gas-assisted drag of much smaller solids are considered (e.g. Morbidelli et al. (2015)) in order to build the terrestrial planets in the solar system.

Answer 2

There are two ways in which a massive orbiting body, such as a planet, can clear a smaller object from the vicinity of its orbit. One, obviously, is by colliding with it. The other, more common way is called the gravitational slingshot effect.*

This is a trick that many space probes have used to gain (or lose) extra speed and thus get further away from (or closer to) the sun, but it's also something that happens completely naturally.

Basically, when the smaller object passes close to the planet, the gravitational pull of the planet will cause the small object's path to curve.** Viewed from the planet's reference frame, the small object will follow an (approximately) hyperbolic fly-by trajectory, arriving and leaving at the same speed (relative to the planet) but in a different direction.

However, the planet is also in orbit around the sun, and thus moving relative to it. If the new direction in which the small object leaves the planet's vicinity after the encounter happens to point the same way as the planet is moving in its orbit, the object will end up moving in the same direction as the planet but faster, and will thus be flung outwards from the sun.

(Conversely, if the object leaves the planet's vicinity in the opposite direction to the way the planet is moving in its orbit relative to the sun, then the opposite velocities will (partially) cancel out and the object will end up losing speed and thus falling inwards towards the sun — possibly even into the sun, if it manages to lose enough velocity.)

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To illustrate this visually — a picture often being worth a thousand words — here's a couple of screenshots from Kerbal Space Program. (Because why the heck not? KSP's orbital mechanics model is a bit simplified compared to real life — it basically follows the patched conic approximation — but it's quite sufficient for modeling gravitational slingshots.)

The first screenshot below shows a small asteroid — mysteriously labelled as "Unknown Object" on the map — that has fortuitously (or, rather, via shameless use of KSP's cheat menu) been captured into a temporary orbit around the planet Kerbin, KSP's Earth-analogue (shown as the dark blue sphere in the exact center of the map). The reason why the asteroid's current orbit (blue-green line) is only temporary*** is that it's quite close to the orbit of the larger of Kerbin's two moons, creatively named "The Mun", soon resulting in a near pass:

As the asteroid passes by the Mun (orange line), it ends up getting flung in (more or less) the same direction as the Mun is orbiting Kerbin, gaining a bunch of extra speed relative to Kerbin and, in fact, getting ejected from the Kerbin system entirely (purple line).

(In real life, the extra momentum gained by the asteroid would be balanced by a corresponding loss of momentum by the Mun, slowing it down very, very slightly. Since the Mun is much bigger than the asteroid, however, the slowdown is so negligible that KSP doesn't even try to model it.)

Meanwhile, here's the same close pass as seen from the Mun's viewpoint:

As you can see, in this reference frame the fly-by trajectory looks quite symmetric: the asteroid falls towards the Mun (but not so directly that it would crash into it), accelerating as it's pulled closer by the Mun's gravity, and then starts slowing down again after passing the closest point of approach (marked as "periapsis" on the map). But the end result is that the asteroid leaves the Mun's vicinity in a different direction, and that change in direction is enough to put it into a completely different orbit around Kerbin — in this case, one that ends up taking it out of Kerbin's vicinity entirely. Thus the Mun has once again cleared its orbit of such pesky intruders.

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^{*) There's a kind of a third way, too, where the planet and the smaller object end up in an orbital resonance that gradually transfers momentum from the planet to the small object without them ever getting very close to each other. You can sort of think of such a resonance like a series of very slight gravitational slingshots, each of which nudges the smaller object's orbit further and further in the same direction.}

^{**) Obviously, the converse happens too, but if the smaller object is much smaller than the planet, then its effect on the planet's motion will be negligible.}

^{***) It's actually quite natural for a captured asteroid to end up in such an unstable orbit: since orbital mechanics is time-symmetric, both in KSP and in real life, if we traced the asteroid's orbit backwards in time we'd presumably find another, earlier encounter with the Mun that would've caused it to be captured into its current temporary orbit in the first place. In real life, the Earth every once in a while also captures such temporary satellites, but their orbits are also basically never stable, since the same gravitational interactions that allowed them to be captured will also, by time symmetry, eventually allow them to escape again. (Of course, in this case I was actually lazy and just cheated the asteroid into that orbit, rather than waiting for one to be "naturally" captured.)}

Answer 3

Gravity does not push away, it only attracts. What clearing means in this case is that a planetary body attracts smaller objects to it. This will end up with one of the following effects:

1. The object will impact the surface larger object or burn up in its atmosphere, presuming it has one. This is how many planets gain mass earlier on in their development, i.e. they get hit a lot for a long time until the orbit is cleared of debris, then things settle down
2. The smaller object will go into orbit of the larger object, and become a moon. This is infrequent
3. The small object will be thrown into a radically different orbit by the larger object's gravity, which clears it out of the larger object's path in the future

Answer 4

We can assume as if they would exchange kinetic energy randomly. I.e. in the general case, depending on the circumstances, both bodies can gain and lose kinetical energy.

However, for the smaller body, gaining or losing the same kinetic energy means a larger change in its velocity. The orbits depend on the velocities and not on the energy (remember, both are in the gravitational field of a body being much larger than both of them).

The result is that the orbit of the smaller body will be affected more by the same change, thus it will go away from the orbit of the larger body and not vice versa.

Answer 5

Put simply, the planet (P) doesn't push away an intruder (i) like so:

Rather it pulls the intruder like so:

All intruders sharing the planet's orbit will generally be traveling parallel to the planet previous to the encounter. Therefore, assuming the intruder is not heading perfectly for the planet's center of mass (whereby it would impact the planet anyway), the pull of the planet's gravity will add momentum that is pointed in a direction other than that of the original orbit (in addition to momentum in the original orbital direction but this is irrelevant).

No matter which way the intruder passes the planet (or the planet passes it), it will end up with additional momentum that is perpendicular to the planet's orbit, yanking it out of that orbit.