Project Amaze!

While in orbit around Adrian, Ryland assesses the remaining Astrophage fuel reserves to determine the Hail Mary’s possible course of action. He tells Rocky, “The ship would get less than 800 meters per second velocity. We can’t escape Adrian’s gravity with that, let alone cross 150 million kilometers of the Tau Ceti system.” 22.132

We are never given the size or mass of the planet Adrian, but the fact that 800 m/s is not enough to escape its gravity does provide a clue.

Escape velocity refers to the speed an object must reach in order to break free of a planet or other celestial body’s gravity. It depends upon the mass and radius of the (in this case) planet, as seen in the escape velocity equation.

The escape velocity of the Earth is about 11,200 m/s. Jupiter has the highest escape velocity of any planet in our solar system, at ~60,000 m/s. Of course, both of these planets’ values pale in comparison to the Sun, which has an escape velocity closer to 600 km/s (note the unit change there; this is 600,000 m/s, or ten times that of Jupiter). Of course, this would be the value for a spacecraft with a beginning position close to the Sun’s surface, so our hypothetical spacefarers might be too toasty to escape under such conditions.

Clearly the Hail Mary wouldn’t stand a chance of breaking free from the gravitational influence of any of these larger bodies, with a maximum speed of 800 m/s as given in the passage above. Even Pluto would require a speed of ~1,200 m/s to escape! Let’s consider some even smaller bodies.

The dwarf planet Ceres, located in the asteroid belt, has an escape velocity of around 500 m/s, so the Hail Mary could safely break away with a maximum speed of 800 m/s. The ship could also zoom away from Phobos, the Martian moon with a required escape speed of only ~11 m/s. Comet 67P, visited in 2014 by the Rosetta mission, is estimated to have an even tinier escape velocity of 1 m/s.

While we still lack enough information to arrive at a true estimate of Adrian’s size and mass, the fact that 800 m/s is insufficient does at least suggest that Ryland and Rocky are in orbit around something larger than an asteroid!