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Biggest Planet a Modern Rocket Can Launch From

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The question I have is what happens on a planet that's a lot bigger, say 2-4 times our mass? I don't know if even nuclear rockets would work.

The NASA article specifies a planet that is 50% larger diameter, which works out to about 3.375x the mass, assuming the same density. So chemical rockets would still barely work. With multi-stage rockets, you could probably escape a planet 4-5x our mass, though the payload fraction would be tiny, less than 1%. Beyond that, you'd certainly need nuclear or some other approach.
 
The 50% number is only from escape velocity. It doesn't consider atmosphere and gravity losses while trying to get out of atmosphere. If you plainly use the equation it assumes your rocket can be arbitrarily large. If you need rocket that's the mass of the moon to get off the planet, that's not a realistic scenario. Even if you could build it the shockwave would kill everything in a thousand mile radius.

50% larger would not cause enormously larger gravity loses. Gravity loses can be reduced with faster acceleration. If they live on bigger planet, they can tolerate higher acceleration. But then engines must be heavier. 50% larger seems reasonable limit. If atmosphere is very thick, then it is easier to lift rocket with balloon or winged first stage.

I cannot design nuclear socket, so I don't know what it could do. But 4 times Earth does not seem too large. Beaming energy to rocket with microwaves or laser would help. Again I don't know limits of this.
 
50% larger would not cause enormously larger gravity loses. Gravity loses can be reduced with faster acceleration. If they live on bigger planet, they can tolerate higher acceleration. But then engines must be heavier. 50% larger seems reasonable limit. If atmosphere is very thick, then it is easier to lift rocket with balloon or winged first stage.

I cannot design nuclear socket, so I don't know what it could do. But 4 times Earth does not seem too large. Beaming energy to rocket with microwaves or laser would help. Again I don't know limits of this.
But you can't get faster acceleration because you need even more fuel for more delta-V, but you also need more fuel to accelerate the additional fuel you took, and you need more mass for your rocket because your rocket not only is bigger, but it needs to be stronger. So we're talking at least single exponential here, probably more. The only way I see 50% more working is if there is NO atmosphere, and you basically have the minimum amount of gravity losses because you can almost immediately start moving horizontally.

Watch how slowly a falcon 9 accelerates in the first few hundred feet. It's quite a gentle acceleration, and we're still on earth.
 
Watch how slowly a falcon 9 accelerates in the first few hundred feet. It's quite a gentle acceleration, and we're still on earth.

A lot of that has to do with internal vehicle loads, not the least of which are the loads going into the payload. I'm a spacecraft guy (not a rocket guy) and like to remind people that the little thing bolted on the top of the rocket is the important part. ;)

A LOT of the technical dialogue between a LV provider and payload manufacturer centers around the CLA (coupled loads analysis) and then the subsequent single/random vibration testing of the payload is critical...many times with on-site reps from the LV. Often this results in 'notching' the vibe profile at critical frequencies/modes so the payload isn't over stressed, and sometimes that results in tailoring the LV mission profile (motor throttling, etc) to work around those critical notches.
 
A lot of that has to do with internal vehicle loads, not the least of which are the loads going into the payload. I'm a spacecraft guy (not a rocket guy) and like to remind people that the little thing bolted on the top of the rocket is the important part. ;)

A LOT of the technical dialogue between a LV provider and payload manufacturer centers around the CLA (coupled loads analysis) and then the subsequent single/random vibration testing of the payload is critical...many times with on-site reps from the LV. Often this results in 'notching' the vibe profile at critical frequencies/modes so the payload isn't over stressed, and sometimes that results in tailoring the LV mission profile (motor throttling, etc) to work around those critical notches.

While that's interesting I don't think that has anything to do with it. If you plot the acceleration curves of the Falcon 9 flight profile, clearly acceleration and fuel load are inversely proportional. First stage has highest thrust G force immediately before MECO, and second stage has highest thrust G force immediately before SECO, when fuel loads are the lightest. The first stage reduces thrust for MaxQ, which is has nothing to do with the payload. We're back to simple first principles of rocket operation here.
 
But you can't get faster acceleration because you need even more fuel for more delta-V, but you also need more fuel to accelerate the additional fuel you took, and you need more mass for your rocket because your rocket not only is bigger, but it needs to be stronger. So we're talking at least single exponential here, probably more. The only way I see 50% more working is if there is NO atmosphere, and you basically have the minimum amount of gravity losses because you can almost immediately start moving horizontally.

Watch how slowly a falcon 9 accelerates in the first few hundred feet. It's quite a gentle acceleration, and we're still on earth.

It looks gentle, but it does not take long to travel its own length. That is quite long distance. On earth acceleration is kept low to limit air resistance. If I remember correctly gravitation losses on Earth are much less than 2 km/s. Doubling it is still not impossible. Faster acceleration does not increase delta-v needed. It requires heavier engines and stronger rocket. Larger planet might have denser atmosphere, but that is not certain.