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

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

• Clearing its orbit of other objects does not require pushing them away. A small object may just crash into the planet. It happened many times on Earth during the last billions of years. – Uwe May 4 '20 at 7:36
• Ideally they crash into other planets. We got to see Jupiter do its job with the impact of Shoemaker–Levy 9. (my answer at WB for, minimum set of physical characteristics to define an Earth like planet) – Mazura May 4 '20 at 22:10
• @Uwe The Moon is witness to one such event. – Peter - Reinstate Monica May 5 '20 at 8:08
• @eagle275: And of course that artificial (and false: no planet has actually "cleared its orbit") was made up entirely so some people would have reason to claim that Pluto was not a planet. – jamesqf May 5 '20 at 16:43
• @AtmosphericPrisonEscape It's not that hard to hit a planet, just have half your team work in metric :) – Harper - Reinstate Monica May 5 '20 at 19:51

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|, 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.

• In the case of v << v_esc, isn't it more likely that the captured satellite will end up in an unstable orbit, which eventually will decay until the satellite impacts the planet? On planet-formation timescales this should happen most of the time, right? – KutuluMike May 5 '20 at 23:55
• @KutuluMike: No, the probabilities are ordered according to Miss > Hit > Unstable orbit. The capture into an unstable orbit is would require even more fine-tuned velocities, because you would need to end up in a orbit that grazes a thin atmospheric ring of several scale-heights thickness, which has still smaller geometric cross-section than the Earth. – AtmosphericPrisonEscape May 6 '20 at 9:38
• This is simply a more sophisticated way of saying that whilst frame-dragging might result in a collision, it usually accelerates the object out of orbit instead, if the object's approach velocity is greater than the planet's escape velocity. Assuming that the angle of approach is greater than zero. – Ed999 May 6 '20 at 13:16
• @Ed999 This has nothing to do with frame-draggin. This is pure Newtonian gravity. – AtmosphericPrisonEscape May 6 '20 at 13:27
• @KutuluMike: If you check en.wikipedia.org/wiki/Orbital_decay, then there is a document linked at the end that lists orbital decay rates for various satellites as function of altitude. There, I took the 'fast decay' curve, which is an exponential, fitted it, and checked at which altitude the decay time would be the age of the solar system (5.67 Gyrs). The result is an altitude of ~1200 km, which is about the altitude of the exobase, i.e. space space. Your chance encounter with small velocity must therefore get a perigee of < 1200km altitude for it to ever decay. This still has a small – AtmosphericPrisonEscape May 13 '20 at 19:41

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.)

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.

*) 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.)

• +1 Nice illustration of the fly-by physics in the limit of similar velocities. Do you know what orbital integrator KSP uses? Is it a simple leapfrog? – AtmosphericPrisonEscape May 5 '20 at 8:16
• @AtmosphericPrisonEscape: Even simpler, in a way; KSP splits the orbit into a series of conic (elliptic / parabolic / hyperbolic) segments and solves those analytically, gluing the results together. Hence the term "patched conic approximation". (I'm not sure how it's solving for orbital encounters to find the patch points; there might be some clever math involved there.) – Ilmari Karonen May 5 '20 at 8:23
• @AtmosphericPrisonEscape: see wiki.kerbalspaceprogram.com/wiki/Sphere_of_influence for an explanation. There is a mod for the game, Principia, that does implement n-body physics (github.com/mockingbirdnest/Principia/blob/master/README.md). – Roel Schroeven May 5 '20 at 12:26
• @RoelSchroeven: Thank you. So do I understand this correctly, that KSP never solves the n-body problem, but instead, when a satellite leaves the SOI of Earth, then it orbits on a 1-body solution in the SOI of the sun? – AtmosphericPrisonEscape May 5 '20 at 16:51
• @AtmosphericPrisonEscape: Yes, until it comes close enough to the Earth or some other planet to cross into its SOI. – Ilmari Karonen May 5 '20 at 16:53

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
• Isn't giving a small body a slingshot with a close encounter and ejecting it from the solar system also "clearing its orbit"? Some theories suggest Jupiter or Saturn might have ejected another planet. – Polygnome May 4 '20 at 8:13
• Good point, see my edit @Polygnome – GdD May 4 '20 at 8:23
• Yeah, and that's by far the more important mechanism. Collisions are really unlikely because “space is big”™ and frictionless. It's true that planets originally accreted lots of material, but that was in the protoplanetary disk, which had so much stuff flying around in it that inelastic collisions in between the smaller objects created effectively a sink for kinetic energy. When an object does collide with a planet, like Shoemaker-Levy 9, it's typically not a direct collision but first getting below the Roche limit, “inelastically disintegrating”, and the parts then crashing down. – leftaroundabout May 5 '20 at 15:38
• Ilmari Karonen appears to have given a convincing explanation of how gravity does push objects away, at least in cases in which the object pushed away has a trivial mass in comparison to that of the body causing the gravity. The "push" is accounted for by the acceleration imparted to the smaller object by the rotation-dragging principle. – Ed999 May 6 '20 at 12:57
• Sorry @Ed999, gravity does not push. There are mechanisms which end up with smaller body moving away from larger body after their interaction, but gravity does not push. – GdD May 6 '20 at 13:43

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.

• This is unclear. Can you give it another shot, perhaps with diagrams? BTW, no such animal as "kinetical" – Carl Witthoft May 4 '20 at 14:15
• @CarlWitthoft Kinetic fixed, sorry. What is not clear? If there is a random elastic collision between a big and a small body in the gravitational field of an object far more massive than both of them, then the small one will go away. This is what I tried to explain. – peterh May 4 '20 at 14:33

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.

• I very much wanted to up-vote, but there was a snag: if two objects share the same orbit (All intruders sharing the planet's orbit), they must, by definition, have identical velocity. Therefore, on the most obvious level, one will not catch-up with the other. There may be infinite complexities introduced by the mass of external objects: but the basic principle has to be that a body in a stable orbit has a stable velocity. – Ed999 May 6 '20 at 13:06
• "the same orbit" is used in the context of "a body must clear its orbit to be a planet". This refers to a general orbital volume (much larger in cross-section than the cross-section of the body), not a perfect line defined by the body's center of mass – johnDanger May 6 '20 at 15:37
• If you are modifying your explanation in that manner, then it seems that objects with a smaller orbital radius than the planet will be travelling faster than it, so will catch up to it, whereas those with a greater orbital radius will be travelling more slowly, so the planet will do the catching-up. How does this explain the more fundamental point: the gravity of any body having mass (i.e. Pluto) will tend to disrupt the orbital path of a body it encounters which has less mass. How does this equate to Pluto not clearing its orbit? It seems to be doing just what any planet does. – Ed999 May 6 '20 at 16:05
• It's not a modification, an answer is always in the context of the question. As to the rest of your question, yes any body with mass will have this effect on any body it encounters (whether it is larger or not) but only a planet is considered to have a dominant enough presence that it (and its satellites) will end up as the only significantly large body in that orbit (again with the orbit being a general volume) – johnDanger May 6 '20 at 16:23