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Comment by inigyou | Hacker News Reader

√(G × mass÷radius) [escape velocity] = v_e × ln(m_0 ÷ m_f) [Tsiolkovsky]

Impossible to tell how much extra mass you need but it's exponential. Adding a unit of v_e [effective exhaust velocity] to escape velocity means you need 2.717 times as much fuel in an ideal rocket.

Earth escape velocity is 11000m/s ignoring atmosphere (which is not ignorable). If the new planet is 6x mass and 2x radius then √3 times escape velocity (about 1.73) would be about 8000m/s extra velocity which is about 3 times a random v_e which means you need about a 25 times bigger rocket. Ignoring the denser atmosphere which makes it even worse.

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From the archives ... How much bigger could Earth be before rockets wouldn't work? https://space.stackexchange.com/q/14383 Feb 3, 2024 https://news.ycombinator.com/item?id=39243303

https://physics.stackexchange.com/questions/117347/when-a-pl...

Man I love this.

> Up above 10g, something really interesting happens that is kind of a theoretical limit. The mass of the rocket reaches a measurable fraction of the mass of the entire planet it's launching from.

one thing about physics, particularly astro-physics, is it's NEVER boring

been diving into PBS-Space-Time and DrBecky past few years as distraction from the endless nightmare of the world we are living in

this has been a great educational thread on HN too, I knew rockets would have to be bigger but didn't realize exponential and the 10g upper-limit

also puts the "Mars sample return" mission into perspective, very difficult

Playing with the trajectory browser at NASA is kind of neat.

https://trajbrowser.arc.nasa.gov/traj_browser.php?NEAs=on&NE...

The "view" at the bottom has an animation of the various routes. They're all EM-ME though...

If you pick some other interesting targets you can get EVJS or something like that (launch from Earth, Gravity assist at Venus, Gravity assist at Jupiter, rendezvous with Saturn)... and then the trajectory animations are much more interesting.

Don't these estimates assume launching from the surface, fully via rocket? On Earth, having air breathing stages to gradually build up speed, or using other launch mechanisms, isn't worthwhile because rockets are more cost effective here, but those tradeoffs change if you're on a planet with higher gravity and a denser atmosphere.

You still need to get to escape velocity that doesn’t change the delta v required does but not by that much you are looking at 5-10%. Maybe a bit more if the atmosphere is really really thick.

Unless you skip chemical rockets altogether there is a pretty hard cap on how much bigger a planet can be than earth before a space capable civilization becomes almost impossible.

Perhaps that's why they're attempting to build a starship out of helium.

or it's all the "pollution" leaking from their fusion reactors ;-)

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