This is an article about goofs and inconsistencies in The Expanse books and the TV series.
Accelerations in both the book and TV series are exaggerated by approximately a factor 10. That is: At one tenth of the stated acceleration (e.g. 0.1g rather than 1g for cruising) the travel times would be roughly correct.
The authors use extended high g burns for dramatic effect throughout the books. Probably an innocent calculation error when starting to write the books, the authors choose to "keep it consistently wrong" by reporting the relative travel times and distances correctly, but the acceleration consistently too high.
For simplicity we approximate 1g as 10.0 m/s^2 and c as 3*10^8. Unless otherwise noted, we will also assume initial velocities as zero.
Earth to Saturn travel: ~20 light minutes (lm) Edit
Consider transit between the orbits of Earth and Saturn. For this calculation, we will use the planets' semi-major axes as their orbital radii: and , for Earth and Saturn, respectively. To determine the transit time, , we may use
from basic kinematics, where distance to travel is . Doing so, we find that at trip between Earth and Saturn would take about 506 thousand seconds or 5.89 days. In The Expanse travel time is given as several weeks.
High g burn for a few hours Edit
When the Rocinante escapes from the Donnager, Alex does a high g burn of 5g or more for 10-11 hours. This would leave the ship flying at 1800 km/s or more. 0.6% of the speed of light or 50-100 times the escape velocity for the solar system at this point in space.
In "practical" terms this would mean: Should the engine fail, the ship would leave the solar system within a matter of days with little chance of rescue. Micro debris the size of a grain of sand would impact with the energy of a 100g TNT detonation.