# The Speed of Constant-Thrust Space Travel ![[images/The Speed of Constant-Thrust Space Travel.webp]] **Channel:** The Overview Effekt (@OverviewEffekt) | **Published:** Mar 7, 2025 | **Length:** 11:44 | [Watch on YouTube](https://www.youtube.com/watch?v=AojKy1iDloQ) Playlist: Stellar Cartography > Screenshots are from YouTube's storyboard preview frames (low resolution), since the full video download was blocked. The outline is from the creator's English captions and chapters. ## Outline ### 0:00 Introduction to sci-fi travel - Star Trek and The Expanse are both set about 300 years from now (around 2350), but they're very different futures: warp drives versus physics-based travel. - Goal: visualize how fast constant thrust gets you around the solar system, then test whether the Epstein drive could handle interstellar trips. ### 0:41 How space travel works - The breakthrough that lets humanity colonize the system in The Expanse is **efficiency**. - Today's rockets burn briefly to reach orbit, circularize, then coast. A **Hohmann transfer** (burn to widen the orbit, then coast) is the most efficient route now: about 9 months to Mars, years to the outer planets with gravity assists. Europa Clipper won't reach Jupiter for about 5 more years. ![[images/The Speed of Constant-Thrust Space Travel-t0119.webp]] - The fictional **Epstein fusion drive** is efficient enough to burn for days, weeks, even months, so ships can fly in a near-straight line. ### 2:13 The brachistochrone trajectory - Aim where the planet will be and burn; at these speeds gravity barely bends the path. - Burn the whole way and you overshoot, so accelerate for half the trip, **flip**, and decelerate for the other half. The show calls it "flip and burn"; physics calls it a **brachistochrone trajectory**, the fastest route possible under known physics. ![[images/The Speed of Constant-Thrust Space Travel-t0213.webp]] ![[images/The Speed of Constant-Thrust Space Travel-t0243.webp]] ### 2:58 Sponsor message - World of Warships (code IMPACTFORCE). ### 4:15 Travel times in the solar system - Human tolerance is the limit: Expanse ships usually run 1/3 g to 1 g. The video uses **1/3 g** throughout. - Planet positions set a minimum and maximum trip time. Maximums assume planets on opposite sides of the sun (the line passes through a scaled-up sun; a small detour fixes that). - **Earth to Mars:** 3 to 8 days (versus about 9 months today). ![[images/The Speed of Constant-Thrust Space Travel-t0452.webp]] - The asteroid belt is easy to cross: NASA puts the odds of hitting something at about 1 in a billion. - **Earth to Ceres:** 6 to 10 days. Tycho Station has its own engines and moves around; Eros passes close to Mars on an eccentric, inclined orbit. ![[images/The Speed of Constant-Thrust Space Travel-t0542.webp]] - **Earth to Jupiter:** 10 to 13 days. **Jupiter to Saturn:** about 10 days nearest, up to 20 days at opposition. - **Earth to Saturn:** 14 to 16.5 days; **Mars to Saturn:** 13.5 to 17 days. From the inner system, orbital position matters less. ![[images/The Speed of Constant-Thrust Space Travel-t0626.webp]] - Uranus and Neptune get "no respect"; only Voyager 2 has visited (1986). The longest planet-to-planet trip, Uranus to Neptune on opposite sides, takes about **36 days**. ![[images/The Speed of Constant-Thrust Space Travel-t0651.webp]] ### 7:11 Delta-v and efficiency - Velocity change (**delta-v**) is a better measure than time, and lets you work backward without knowing the drive's specs. - Epstein's yacht, the first Epstein drive, ran dry at about **15,000 km/s**, so its delta-v was 15,000 km/s. - Context: Earth escape needs about 13 km/s; **Dawn** had the highest onboard delta-v ever, 11 km/s (about 24 km/s with the booster); **Parker Solar Probe** had only 0.3 km/s onboard but reached 190 km/s (heading past 200) through gravity assists. - Lowest estimate for the **Rocinante:** about 4,000 km/s. ![[images/The Speed of Constant-Thrust Space Travel-t0840.webp]] - The Neptune-to-Uranus trip needs about 10,000 km/s. In a flip-and-burn, delta-v is exactly double peak velocity, because braking spends as much as accelerating. ![[images/The Speed of Constant-Thrust Space Travel-t0910.webp]] - So every planet is within reach, which is how Expanse-era humans colonized and exploited the solar system. Travel-time and delta-v calculators are on the creator's website. ### 9:53 Interstellar travel possibilities - In canon, the **Nauvoo** generation ship is built to reach **Tau Ceti** in about 100 years: accelerate about 100 days to about 12% of light speed (36,000 km/s), coast nearly a century, then brake 100 days. Total delta-v: **72,000 km/s**. ![[images/The Speed of Constant-Thrust Space Travel-t1019.webp]] - With that same 72,000 km/s, **Alpha Centauri** would take about **36 years 9 months**, within a lifetime. ![[images/The Speed of Constant-Thrust Space Travel-t1044.webp]] - His reading: the Nauvoo shows The Expanse's theme of religion's power to organize people and give them purpose, which can also be irrational and deadly. The show made the point and backed it with the science. - Calculator source code is on the site; he asks for feedback on the math. ## Things Mentioned ### Fiction and Franchises - The Expanse (Epstein drive, Rocinante, MCRN Donnager, MCRN Tachi, Tycho Station, Nauvoo, Epstein's yacht) - Star Trek (warp drive) - Mass Effect (music credit) ### Real Spacecraft and Missions - Europa Clipper - Dawn (ion drive) - Parker Solar Probe - Voyager 2 - SpaceX Starship (Ship 24 and Booster 7 model) ### Physics Concepts - Hohmann transfer - Brachistochrone trajectory / flip and burn - Delta-v - Gravity assist - Constant acceleration (1/3 g) ### Places - Earth, Mars, Ceres, Eros, Jupiter, Saturn, Uranus, Neptune - Tau Ceti (11.91 ly), Alpha Centauri (4.37 ly) ### Tools and Resources - Brachistochrone rocket calculator and Interstellar Delta-v Calculator: https://www.overvieweffekt.com/tools/brachistochrone-rocket-calculator - Project Rho, engine list (Epstein drive): https://www.projectrho.com/public_html/rocket/enginelist3.php - Project Rho, torchships / brachistochrone: https://www.projectrho.com/public_html/rocket/torchships.php - 3D models from Sketchfab (Clarence365, Jakub.Vildomec, NestaEric, Chris Kun), CC BY ### Sponsors - World of Warships (code IMPACTFORCE) ## Bios ### The Overview Effekt YouTube channel (@OverviewEffekt) making 3D visualizations of space: where sci-fi stars and settings really are (Stellar Cartography playlist), sci-fi megastructures, and spaceflight history. Runs overvieweffekt.com, which hosts the travel calculators from this video. ### Solomon Epstein (fictional) In The Expanse, the Martian inventor of the efficient fusion drive that made solar-system colonization possible. He died aboard his own modified yacht when he couldn't stop accelerating.