I think you're used to things losing inertia due to wind resistance, friction or ground collision. Relative to the ground increases in speed increase the amount of loss of inertia, but relative to the sun that's not always the case.
We can look at UA521 as a real world example. It leaves JFK at 8am EST, travels at about 500mph, and arrives SFO 6h later at around 11am PST. Despite the 6 hour trip, the local time didn't change very much, because while traveling faster compared to the ground, it's traveling slower compared to the sun.
For even clearer numbers, imagine the plane traveling twice as fast. It would leave JFK at 8am, and land in SFO at 8am. For the entire 3 hour trip the plane would have been traveling 1000mph, but it's speed relative to the sun in this case is 0mph.
If the same plane traveling "0mph" turned off its engines, it would immediately begin to speed up relative to the sun, all the while slowing down relative to the air and eventually begin to fall
(post is archived)