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"The planet moves"

Inspired by this link in a comment from Gryphon here, I also see the concept in this question.

We've colonized the moons of Jupiter adjusted their orbits to our satisfaction (to avoid them being crisped by the BFR that comes next) & have suitable methods of adjusting them further if Jupiter's mass decreases sufficiently to require it & strapped our mighty rocket (a fusion candle) to Jupiter.

Gravity is our friend & as long as we don't accelerate too fast the moons will remain in orbit.

Now it's time to light the fuse.

My Question: how many light-years of fuel do we actually have in Jupiter, how far can we travel?

  • Using best guess approximations (if you can find any) of this theoretical engines fuel efficiency.
  • The fusion candle serves as a proxy sun so assuming we do want to stop somewhere we have constant acceleration to the mid-point followed by constant deceleration to journeys end, there will be no coasting with the engines off.
  • Consider the problem of keeping the moons in orbit as you burn away most of Jupiter's mass into energy a problem for another day.
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    $\begingroup$ To convert a mass into a traveled distance I think we would need the conversion efficiency of your proposed engine. A Ferrari travels way less km than a 500 using the same 10 liters of gasoline. $\endgroup$ – L.Dutch Feb 7 at 15:50
  • $\begingroup$ @L.Dutch : Damn! a piece of information I've not got :) any idea where I might find it? $\endgroup$ – Pelinore Feb 7 at 16:16
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    $\begingroup$ What timescale are we talking about?? If you leave it long enough then a well thrown baseball can travel across the galaxy, since it won’t stop unless something stops it. $\endgroup$ – Joe Bloggs Feb 7 at 16:45
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    $\begingroup$ @JoeBloggs : Dang! I didn't think the question through properly did I, the "fusion candle" will have to serve double duty as your proxy sun so assuming we want to stop somewhere & not just glide gloriously into the void assume constant acceleration to the mid-point followed by constant deceleration to journeys end, that should build the timescale into the answer, I'll edit the question $\endgroup$ – Pelinore Feb 7 at 17:04
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Not very far at all, I'm afraid. The problem is that while Jupiter supplies a huge amount of fuel, it also has a huge amount of mass, which neatly uses up the advantage of having all the fuel. Basically, it's just an expanded version of a fusion rocket and to a first approximation gets the same performance.

Take a look at the Rocket Equation: The delta V you get from a rocket is the product of the exhaust velocity (which is the same for all fusion engines) times the log of the ratio of the initial mass to the final mass. (The initial mass is the mass of the rocket plus fuel. The final mass is the mass of the rocket after the fuel has been exhausted.)

Note that this doesn't depend at all on how big the rocket is, just on the ratio of its initial to final mass. Big rockets don't fly faster than small ones or go further than small ones unless they have a higher exhaust velocity or a bigger mass ratio.

Because you're talking about a low thrust for a long time, the engines can be very low mass compared with Jupiter, and that improves the efficiency of the system. (Also, Jupiter's mass supplies its own fuel containment for the start of the voyage, so tankage may be ignored. Maybe.) Rockets are very sensitive to the non-fuel mass they have to carry along, so based on this fact, the Jupiter plus fusion candle would be somewhat more efficient than a "conventional" fusion rocket and would be able to go further.

But, when we think about parasitic mass, Jupiter is about 25% parasitic mass: By mass, it's 70-75% Hydrogen, 20-25% Helium and roughly 5% heavier stuff. The bulk composition of Jupiter is about (See the Wikipedia article on Jupiter for a bit more detail.) Jupiter's fuel is terrible for rocket efficiency! (It's like trying to fly a chemical rocket where a third of the fuel tank is accidentally filled with water.)

This second "minor" effect completely dominates the first, so Jupiter would be significantly less effective than a "conventional" fusion rocket.

So, bottom line: Don't buy a ticket on Jupiter Interstellar Spaceways.

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    $\begingroup$ @Pelinore The problem with the question "How far?" is that it depends on the answer to "How long?" Any plausible "conventional" fusion-powered ship would easily achieve escape velocity from the Solar System -- depending on what you imagine the engine to be like, it could potentially get to a decent fraction of lightspeed -- and it would be able to coast at that speed for any distance you like, given enough time. Regarding Saturn, it wouldn't make a significant difference -- less mass, but also less fuel. $\endgroup$ – Mark Olson Feb 7 at 17:30
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    $\begingroup$ @Eth: Sure, but only if you're willing to entirely disassemble Jupiter. The OP wants to even keep the moons in orbit. Also, I think you'll find that winds up lowering the exhaust velocity enough that the gain is less that you'd hope. (The "real" optimal approach is to disassemble Jupiter right at the beginning to get rid of all the parasitic mass. But that seems well outside the OP's question.) $\endgroup$ – Mark Olson Feb 7 at 17:35
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    $\begingroup$ With energy of fusion and hydrogen/helium mix, we should be able to calculate an upper delta-V limit, though. $\endgroup$ – Eth Feb 7 at 17:49
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    $\begingroup$ Sure. What's the engine design? What is the exhaust velocity? Assume a magic engine so that 100% of the energy release in fusion is converted to kinetic energy of the resulting helium atoms. Fusion turns about 0.7% of the rest-mass of the hydrogen it consumes into energy. If that goes 100% into kinetic energy, it will given you an exhaust velocity of around 0.7% of c. Multiply that by the log of the mass ratio -- five would be a very aggressive value for that -- and you get no more than 5% of lightspeed. (Lots of assumptions there, all focused on getting highest possible speed.) $\endgroup$ – Mark Olson Feb 7 at 18:07
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    $\begingroup$ Realistic engines are much, much less effective. See en.wikipedia.org/wiki/Fusion_rocket for example, (or nasa.gov/directorates/spacetech/niac/…) where somewhat plausible schemes predict exhaust velocities on the rough order of 300 kps. (Still plenty of delta-V to go anywhere in the galaxy if you're willing to wait a bit.) $\endgroup$ – Mark Olson Feb 7 at 18:20
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You misunderstand the fundamentals of space travel! You don't want or need to run engines in space constantly to move. You don't need to push 24/7 till Jupiter runs out. You just need to give Jupiter enough of a heavy kick to get out of the solar system, then Newton does the rest.

In space, there is no friction to break you downTV-Tropes Warning. There is no Arbitrary Maximum Range on weapons or shipsTV-Tropes Warning. Newton's first law of motion tells us that "an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force". As soon as the escape velocity of the solar system is reached, you can shut down the engine and enjoy the ride on the generation ship and have Jupiter supply all the heat needed from its ginormous radiation and gravity well. It will be a dark journey, and a cold one, but not too cold.

"I dare to assume you ignorant jackasses know that space is empty. Once you fire this hunk of metal, it keeps going till it hits something. That can be a ship, or the planet behind that ship. It might go off into deep space and hit somebody else in ten thousand years. If you pull the trigger on this, you are ruining someone's day, somewhere and sometime. That is why you check your damn targets! That is why you wait for the computer to give you a damn firing solution! That is why, Serviceman Chung, we do not 'eyeball it!' This is a weapon of mass destruction! You are not a cowboy shooting from the hip!" - The Gunnery Chief from Mass Effect 2

On long timeframes, it doesn't actually matter if you ride Jupiter spiraling out of the solar system within 1 swing or 10-million swings around the sun, but the change in velocity and this spent fuel is vastly different. You might ride much longer the Jupiter train than if you spent all of the gas giant in one huge push, but you really want to preserve some to actually slow down into an orbit at the destination or correct the course mid-flight to get to the star system you desire... Note that the spent fuel is measured in $\Delta \text V$ as in change of velocity, not in reach as in space. Reach in space is infinite till you hit something. Calculate the delta-V from the rocket equitation as Mark did show in his answer.

But you still don't want to ride the Jupiter express, especially not burning away Jupiter: As Jupiter gets spent on exhaust, Jupiter gets lighter and lighter. As his mass decreases, so does his gravity well weaken, changing the carefully balanced out orbits of the moons circulating him. They spiral outwards and might get lost, together with the colony on them, shot out of the solar system. Without the sun and Jupiter to provide at least some heat, the moon soon turns into an iceball and within an astronomically short timeframe has frozen down to the roughly 3 Kelvin of interstellar space, destroying all chance of life.

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