How Do Orbits Change Over Time?

by Carson
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You might think that orbits are very stable; they work independently and do not change. However, the opposite is true; orbits change over time, and the orbits of different objects, such as asteroids and planets, affect each other. Find out how orbits change over time in this article.

1. Close Approaches

Close approaches are carried out to achieve a drastic change in the orbit. Basically, one object is near a massive body in a close approach. This means that the object gets a strong gravitational pull from the more massive object very close to it, and thus the velocity vectors of the objects are changed. Note that the plural form of object is used here, because the more massive body also gets a slight tug from the other object, changing its orbit by a smaller amount.

In fact, space probes have used close approaches to gain or lose heliocentric velocity to change their trajectories. For example, the Voyager 1 spacecraft had very close approaches to Jupiter and Saturn in 1979 and 1981, respectively. As it followed a hyperbolic trajectory relative to the planet, the space probe entered and exited the planet’s gravitational pull at the same speed. It passed the planets from behind, so the planet steers the probe in its direction of motion. This transfers some angular momentum from the planet to the spacecraft, thus increasing its velocity relative to the Sun. This technique is called a gravity assist and has also been employed on many other space missions.

Asteroids and comets also get these close approaches occasionally, changing their orbits in the same way that space probes get boosts from planets. For instance, comet 81P/Wild 2 resided in the territory of the outer Solar System in the past, with its perihelion being close to Jupiter’s orbit. However, in 1973, it had a close approach with Jupiter. The comet passed in front of Jupiter, losing momentum relative to the Sun, and falling further in. This shortened its orbital period and turned it into a short-period comet.

The orbit of 81P/Wild 2 from 1920 to 1985 projected on the plane of the ecliptic, showing how it changed due to a close approach of Jupiter.
Note that 81P did not have a hyperbolic orbit to begin with, but its closed orbit before the Jupiter approach was so large that the graph could not plot its entirety without risking losing details on the post-approach orbit.
Data source: JPL Horizons
Blue: Earth; Red: Mars; Brown: Jupiter; Magenta; 81P/Wild 2; Yellow: Saturn

In fact, most of the chaos from the orbits of the small bodies comes from these close approaches. The other perturbations (mentioned below) have a relatively small effect. But once a close encounter comes, these uncertainties inflate dramatically. Even a tiny change in the initial position could mean a significant change after a close approach, as it could mean the difference between passing ahead of or behind the planet, or passing closer or farther away.

2. Constant Planetary Perturbations

Other than the major close approaches, the small perturbations from distant planets play a role in changing the orbits of objects as well. Remember that gravitational forces do not decrease to zero if the objects are a finite distance away. Therefore, planets could still exert slight forces to nudge the orbits of the asteroids and the comets, even if they are a few astronomical units away.

In the Solar System, this effect is best seen in the Kirkwood gaps in the asteroid belt. They are the main orbital resonances with Jupiter (specifically, the main gaps are the 2:1, 3:1, 5:1, and 7:3 resonances). Objects there receive periodic perturbations from the massive planet. Eventually, the eccentricity of the asteroids increases, and their orbits begin to cross that of the inner planets. Close approaches with a terrestrial planet then cause a sudden change in the semi-major axis and kick the asteroid out of the region, explaining the gaps.

Distribution of 20000 randomly selected numbered asteroids with semi-major axes between 2.0 to 3.5 AU and eccentricities < 0.6
The red lines mark the Kirkwood gaps, and the text above them marks the resonances in each of these gaps.
Data source: JPL Small-Body Database

Apart from mean-motion resonances described above, secular resonances can also magnify the effect of planetary perturbations. This means the precession rate of an object’s orbit is the same as that of a massive body. For instance, in a specific range of semi-major axes and inclinations, the object’s orbit precesses in sync with Saturn. The distant perturbations from the planet then push the eccentricity and inclination of the orbit, taking it toward a close encounter with the planets and ejecting them out of the configuration.

3. Non-gravitational forces

Apart from the gravitational perturbations from the planets, non-gravitational forces can also alter the orbit of asteroids and comets significantly. For example, comets undergo outgassing during their close approaches to the Sun, as it vents out gases from its gas vents. These gas jets act like a rocket engine and accelerates the comet in one direction (due to the inherent asymmetry of the comet), pushing the comet in any arbitrary direction.

Moreover, as the asteroid rotates, the asteroid is unevenly heated. The places in the afternoon are hotter than those in the morning, and thus one side of the asteroid emits more heat than the other. The heat leads to the emission of photons due to blackbody radiation, and remember that photons themselves carry energy. Therefore, the asymmetry preferentially accelerates the asteroid in one direction. Again, this changes the asteroid’s orbit by modifying the velocity vectors.

An illustration of the Yarkovsky effect
An illustration of the Yarkovsky effect
The red waves are of lower energy levels and the blue ones are of higher energy levels.
The direction of the push is illustrated in white.

The unpredictable thing about this is that the push produced by the Yarkovsky effect depends on the shape of the asteroid. Suppose there are two asteroids, one shaped slightly differently from the other but with the same orbit and location. These two objects will go on slightly different paths at first. But when they inevitably come close to a planet, the uncertainties inflate, and the two copies go on completely different paths. That’s why it’s essential to map the asteroid’s shape and rotation precisely if you want to make predictions about the impact risk of the asteroid. For more information, see this article about how an asteroid’s rotation makes its orbit hard to predict.

Conclusion

In this article, we’ve mentioned the events that can cause an object’s orbit to change over time. This includes close approaches with planets, planetary perturbations, and non-gravitational forces. These forces act together chaotically so that small changes, even minor uncertainties, can cause huge differences later down the line. Thus, if you’re exploring the long-term dynamical behavior of an object, it’s essential to use a Monte Carlo method. This means running multiple simulations based on the uncertainty space and then exploring the statistical properties of the outputs.

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