Planets sit at their real positions for the simulated date (JPL orbital elements) and spin at their IAU rotation rates. Voyager-class trips inside the Solar System fly real two-body transfer orbits with a launch-window search.
Fast ships follow exact special-relativistic motion: constant acceleration, coasting, flip-and-burn braking. Ship clocks run slow.
The warp drive follows Alcubierre's 1994 metric: space contracts ahead of the bubble and expands behind it, so the ship can outrun light while sitting at rest inside, with no acceleration felt and no time dilation. From outside, the bubble bends the view through it like a lens: squeezed and bluer through the front, stretched and redder through the back. From inside, the sky crowds toward the front. These views are illustrative (the exact image depends on the bubble wall, which the theory leaves open), and the drive needs negative energy, which may not exist.
What you see at high speed is physical. Starlight crowds toward the direction of travel and stars ahead turn bluer and brighter. At extreme speed the Big Bang's afterglow ahead shifts into visible light.
Stars: 109,000 real stars at their 3-D positions. Gaia BH1 bends light by exact Schwarzschild ray tracing. The real Gaia BH1 is dormant; its glowing disk is an optional "what if it were feeding" view.
Credits
Planet textures: Solar System Scope (CC BY 4.0). Milky Way: NASA/Goddard SVS Deep Star Maps 2020; glowing hydrogen: Finkbeiner 2003 all-sky H-alpha map (ApJS 146, 407), via NASA LAMBDA. Voyager & Parker models: NASA 3D Resources. Star catalogue: HYG Database v4.1 (CC BY-SA 4.0). Andromeda photo: Adam Evans (CC BY 2.0), foreground stars removed and mounted at M31's true position, size and orientation. The Milky Way is built from published structural measurements; seen from outside it is NASA/JPL-Caltech/ESO/R. Hurt's illustration (eso1339g, CC BY 4.0), as no one has photographed it from outside. Black hole disk modelled after SkyWalkerPS/kerr-black-hole. Orion, Daedalus, Starshot and the antimatter ship are reconstructions from their design studies. Proxima Centauri photo: ESA/Hubble & NASA (CC BY 4.0); Proxima b impression: ESO/M. Kornmesser (CC BY 4.0). Neptune: Voyager 2, NASA/JPL; VLT view, ESO/P. Weilbacher (AIP) (CC BY 4.0). Ship pictures: NASA, NASA/JPL and NASA/JHUAPL (public domain); Daedalus render by Diego bf109 (CC BY-SA 4.0), via Wikimedia Commons.