# How Does Asteroids’ Shapes Make Their Orbits Unpredictable?

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Modeling an asteroid’s orbit is challenging. There is the chaotic nature of the n-body problem, in which complex perturbations can greatly magnify even the tiniest uncertainties. But even if we have a perfect model of the asteroid’s orbital vectors and a flawless n-body model, the prediction will still be flawed. Why? It’s because you must also consider the asteroid’s rotation and shape. Let’s dive into that in this article.

An asteroid in orbit around the Sun consists of the sunlit and shaded regions. During the day, the object heats up in sunlight, and during the night, it cools down. That’s why the day is always hotter than the night. That’s going to be the key to the radiation pressure, but we’ll talk about something more physical first.

To explain this, we first need to talk about blackbody radiation. Everything above absolute zero emits light, and the hotter the temperature, the more light it emits and the shorter the wavelength. This increases the energy level of the light according to the Stefan-Boltzmann law, which states that it is proportional to the temperature to the fourth power. Basically, it means that the hotter the temperature, the more light the system emits.

Let’s get back to the asteroid. As you can see, the sunlit side emits more light than the shaded region. Thus, there is an asymmetry of the blackbody radiation being emitted. Although photons (the carriers of light) are massless, they still carry momentum. This means that the asymmetry, like a rocket engine, can push the asteroid off its orbit. Although the tiny thrust of this engine is almost negligible, it can still cause significant changes to the asteroid’s orbit in timescales of millions of years.

#### The Yarkovsky Effect

After talking about all of this, you should understand the Yarkovsky effect. This effect dictates the force applied to the asteroid based on its rotation, size, and shape. We’ll explore each one of these factors in this section.

First, the peak temperature of the asteroid is not exactly at noon. After noon, the region still receives sunlight, so it takes a while before the ground cools down at the same rate as sunlight heats it up, and the region reaches its peak temperature in the afternoon. The faster the rotation, the farther the peak temperature is away from noon. Apart from that, the rotation can also affect the temperature distribution in other ways. For example, a rapidly rotating asteroid has an almost uniform temperature since there is not enough time to heat up or cool down.

Secondly, the size of the object also affects the phenomenon. The mechanism is simple — the bigger the asteroid, the more surface there is to exert the Yarkovsky effect, and the more force is applied to push the asteroid. However, the mass of these asteroids is also large. In fact, the smaller the object, the larger the ratio between the surface area and the volume. Therefore, the effect exerts a smaller force per unit of mass in more massive objects; thus, the overall push is smaller.

Thirdly, the shape of the asteroid can also act on the situation. If an asteroid is asymmetric, different surface area sizes are exposed to sunlight in different rotation phases. This is best exemplified by producing the fluctuations in the lightcurve of the asteroids, in which the data can actually be used to predict the object’s shape. Similarly, the shape of the asteroid also changes how the Yarkovsky effect affects an asteroid over a rotation. This makes the effect chaotic, enabling it to push the asteroid in whichever direction you can imagine.

#### The YORP Effect

Other than influencing the heat distribution of the object, there is another factor about the shape that can change the asteroid’s orbit. Other than the intrinsic thermal emission, it also affects how sunlight reflects on the asteroid. Again, this also acts as a rocket engine, speeding up or slowing down the rotation it decides to based on the asteroid’s shape. In fact, this is the main reason asteroids break up. They start spinning quickly enough that they cannot overcome the centrifugal forces along their equator so that they shed material and ultimately break apart.

However, there is one thing that the YORP effect makes things even more unpredictable. It’s the albedo variation on the asteroid’s surface. The larger the geometric albedo, the more light the object reflects. This means these changes, often caused by subtle differences in chemical composition, can affect how sunlight pushes the asteroid around. This makes long-term predictions even more challenging unless we map and characterize the asteroid completely.

#### Why They Matter

The Yarkovsky and YORP effects are highly nonlinear and do little to an asteroid’s orbit. Why don’t we exclude them for simplicity? Doing so might still give a decent estimate of how the asteroid might behave in the future, but these effects are still essential to explain the dynamical evolution of these objects.

For example, near-Earth asteroids are highly unstable, and objects there leave the region in a relatively short time. This means an active dynamical pathway from the main belt is necessary to explain the abundance of this population. What is pushing these asteroids from there to here? The Yarkovsky effect is the main driver for most of that migration. As small asteroids orbit the Sun in the main belt, it is constantly getting pushed by their own temperature, sometimes bringing them close to an orbital resonance. It bumps up the eccentricity of the orbit as the planets periodically perturb the object, eventually bringing it to the near-Earth population.

Moreover, we must consider these effects to predict impact risks accurately. Take Bennu, for example. Owing to the Yarkovsky effect, this near-Earth asteroid wandered 100 miles off where it would have been in just 12 years. Likewise, over long periods of time (like hundreds of years), the deviations are large enough that the asteroid could hit the Earth instead of missing (and vice versa)! Even if that time frame is shorter, it could still substantially affect the probability of an impact.

#### Tackling the Uncertainties

After reading all of this, you might throw in the towel and think there are simply too many uncertainties and that accurate orbital prediction is impossible. However, this isn’t the case. There is one solution — explore the asteroid up close. By doing so, we can get excellent models of the asteroid’s shape, rotation, and chemical composition, which are the major uncertainties the algorithms face. Although a mission to an asteroid might seem overwhelming (and it is), space agencies have already done it many times. They have even returned samples of them to Earth, specifically from 25143 Itokawa, 162173 Ryugu, and (coming soon) 101955 Bennu.

Sending an orbiter to an asteroid might be necessary if the object is a possible threat to Earth. However, there are still less costly ways to do this task from the ground. When an asteroid flies close to Earth, just millions of kilometers away, we can use radio telescopes to image them. The telescope first uses its transmitter to send a powerful signal to the object. Then, it waits for the signals to bounce back, and when they do, it takes an image. They might appear pixelated since the distances involved are large, but they can still provide decent models of an asteroid’s shape.

#### Conclusion

In this article, we have described how an asteroid’s shape and rotation make its orbit very chaotic. There is the YORP effect, which messes up with rotation periods, and the Yarkovsky effect, which exerts small forces on the asteroid to change their orbits. Thus, if you want to make highly accurate predictions of an asteroid’s future position, you must take them into account. This makes missions to asteroids valuable for orbit determination and planetary defense.