Psyche

For an orbital mechanics HW I was looking at Psyche and the effects of different perturbations. Psyche, an M-type asteroid, is one of the largest objects in the asteroid belt and contains about 1% of the belt’s entire mass. As an M-Type asteroid, Psyche is expected to be a reddish world mostly made up of metal. NASA’s launching a mission to Psyche in 2022 in order to study it as it represents an unexplored area of planetary formation, the iron cores found at the center of most planets. Although we have not yet gone to Psyche, here’s an artist’s impression.

One question in the HW asked about the perturbations caused by the Sun, Earth, Mars, and Jupiter if all the bodies were co-linear. This produced the following visualization, which shows were psyche is located (Note the planets are not to scale):

In addition to every body being co-linear, I assume that everything is co-planar as well as in circular orbits. In reality, Mars and Psyche both have significant eccentricities to their orbits and each planet has some inclination. This led me to the question, is the configuration I used stable? So I coded up a 5-body simulator and integrated it forward for about 150 years. Not a long time on astrophysical time-scales, but a long time on astrodynamical time-scales. At that scale, I plotted the Psyche-Sun distance, and while you can see the various interactions with other objects it’s mostly stable.

Increasing the runtime to about 1500 years, did nothing to destabilize the system. I played around with both speeding up and slowing down Psyche, but I couldn’t find a configuration that would destabilize the entire system. This outcome should be expected, as any object in an orbit near Psyche will already be in the asteroid belt, which is a mostly stable configuration.

Psyche the Mission

The spacecraft set to visit Psyche is also named Psyche and will arrive at the asteroid in 2026, after a 4-year journey that includes a gravity assist from Mars.

Psyche will have hall-effect thrusters that can only put out around .2 Newtons of thrust, which I find fascinating as an aerodynamicist who does low-thrust trajectory design, it also has one of the coolest badges.

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