What’s black and white and red all over—and on a multimillion-year jaunt around the solar system? The answer is Elon Musk’s Tesla Roadster, launched earlier this month as the test payload for SpaceX’s inaugural flight of its Falcon Heavy rocket. Musk is CEO of both companies.
The car was originally intended to chase Mars around the sun. But the rocket’s upper stage delivered better performance than expected, boosting the roadster into an orbit beyond Mars and just shy of the Asteroid Belt. Although some may see the Tesla as just another piece of space junk, University of Toronto astrophysicist Hanno Rein and his colleagues consider it an opportunity to test science’s current models of how the orbits of small bodies in our solar system evolve.
Rein’s specialty is planetary dynamics—the study of orbits inside and outside our solar system, and how they change over time. Planets, for instance, can migrate closer in or farther out from their stars based on gravitational interactions with their neighboring worlds. Rein has created his own software, called REBOUND, which models the mutual gravitational interactions of multiple celestial bodies and can be applied to the complex dynamic problems of smaller orbiting objects. This includes the motion of dust and ice particles in Saturn’s rings—or, now, predicting the orbital evolution of the first car in space.
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“We saw that somebody had published orbital elements for the final orbit,” Rein says. “So we put them into the code that we already have and integrated forward in time to see what would happen, just out of curiosity.” Because the Tesla was launched from Earth, its orbit around the sun presently intersects with Earth’s—so car and planet will repeatedly undergo close encounters for the foreseeable future. “Close” in this case is more like one lunar distance (the distance from Earth to the moon, or approximately 240,000 miles), however. The authors initially predicted the next such encounter will occur in 2091, but subsequent tracking of the Tesla’s trajectory suggests this event will instead occur in 2088. Their results appear in a study recently posted online and submitted to Monthly Notices of the Royal Astronomical Society.
Despite this apparent precision in forecasting the motion of a small body some 70 years into the future, making such predictions over much longer periods of time is an unsolved problem in astrophysics. After a century or so a small body’s orbit tends to become chaotic due to the collective gravitational tugs of other, larger objects—chiefly planets. Therefore, at these longer timescales its actual path across the solar system comes to resemble a “random walk” with no discernible trend, forcing any long-term predictions to be relatively inexact. Rein and his co-authors looked at both the short-term millennial-scale and long-term million-year-scale evolution of the Tesla’s orbit. Despite the initial close encounter in 2088, they did not find any potential collisions with Earth in the next thousand years—although there appears to be a 6 percent chance of a collision within the next million years. Overall, the researchers conclude the Tesla’s likely orbital lifetime (before colliding with another body or being ejected from the solar system) is a few tens of millions of years. Assuming, that is, no far-future interplanetary archaeologists or artifact collectors remove it from orbit first. And the authors caution their calculations are very sensitive to initial conditions, namely the Tesla’s size, density and rotational period—the latter of which they sourced from Twitter (yes, really).
The point of most practical interest in this work is not the chance of the Tesla itself coming back to haunt us, however, but rather the opportunity it presents to test our capabilities in predicting the orbital evolution of near-Earth asteroids (NEAs). Some NEAs are potentially threatening to Earth, possessing a low but very real chance of nailing our planet. Most of these objects start as members of the Asteroid Belt, with orbits larger than Mars’s but smaller than Jupiter’s. Various gravitational perturbations, mostly from Jupiter, can sometimes kick NEAs down into the inner solar system where they wander among the small rocky planets—occasionally getting too close for comfort. Rein and his collaborators wondered if the Tesla might act like an NEA, but in reverse—starting from Earth and being slowly nudged outward by encounters with the inner rocky planets to eventually obtain an orbit more characteristic of an NEA.
In addition to gravitational influences, Rein and his colleagues had to consider other effects. Most asteroids have odd shapes that are far from spherical, and they rotate in periods of hours or days—meaning their surfaces are not uniformly exposed to the sun. This uneven heating can sometimes significantly change their orbits, behavior astronomers call the Yarkovsky effect. “The Yarkovsky effect is a nongravitational force,” Rein says. It comes into play “because the sun heats up one side of the asteroid, and then as the asteroid rotates away from the sun it starts to radiate that heat away. And because it’s radiating more on one side than another, you get a force.” The magnitude of that force depends on the thermal properties of the asteroid and how fastit is spinning.
In the case of the Tesla, Rein’s team made simple, back-of-the-envelope estimates for the thermal properties of the car’s various materials. No matter how they varied their assumptions, however, they found its relatively high rate of spin essentially nullified the Yarkovsky effect. Gravitational forces alone, it seems, will be the arbiter of the Tesla’s orbital fate.
Neither Rein nor his colleagues plan on making a career out of following the Tesla’s orbital evolution but they were excited to test their code on it. Cristina Thomas, an astronomer at Northern Arizona University, agrees the situation presents a unique opportunity. “Over the years we've gotten really good at understanding the many factors that contribute to an object's orbital evolution,” she says. “So having a Tesla Roadster as the newest near-Earth object is a fun way to test our current models.”
Those models, in turn, could someday be vital for more critical predictions of where and when an Earth-threatening NEA might strike. In the meantime, says Michele Bannister, an astronomer at Queen’s University Belfast, the Tesla “is a nice way to show people how good the tools are that we use to understand the evolution of the solar system…. It’s also dynamicists having fun.”