Escape velocity question & planet sizes

Sorry if the question seems naive, rocket science isn’t my strong suit.

So I got to wondering about what an enormous problem escaping earths gravitational pull was initially, and still is WRT fuel payload. All other civilizations that have earths mass will have this same problem.

But what about larger planets? What’s the break over size for a planet that would effectively limit space travel? And how common might those planets be?

I’m thinking about our current technology.

I’d argue that Earth is already over that limit–space travel is obscenely difficult and expensive.

I don’t think that you really need to power a ship to escape velocity to travel elsewhere in the solar system, as you can do various sorts of lower-energy transfer orbits to get you there.

FWIW, most space travel has been just in orbit, which doesn’t have anything to do with escape velocity (the speed needed to escape a body’s gravity well), but rather with the speed necessary to orbit the earth at the altitude of your choosing. Both however, are related to the mass of whatever body you’re orbiting or escaping from.

Assume density stays constant, then escape velocity (EV) is proportional to the radius of the planet.
EV = sqrt(2MG/R) where G is the gravitational constant, M is the mass of the planet and R is the radius of the planet. We can rewrite this as sqrt(2G) * sqrt(M/R). Let’s call the density P* and the volume V. M = P*(4/3)piR[sup]3[/sup]. Let’s reduce all of the constants to the single constant k[sup]2[/sup]. This means sqrt(M/V) = k * sqrt(R[sup]3[/sup]/R) = k * sqrt(R[sup]2[/sup]) = k * R
So escape velocity is proportional to the radius if two bodies have the same density. In this case smaller is better.

If mass is the same, it can similarly be shown that EV is inversely related to the radius so larger is better. So clearly there is an interplay of size and mass which mean we could try to put P = density* into the equation. If we do we get
EV = sqrt(8piG/3) * R * sqrt§ meaning escape velocity is proportional to the radius and to the square root of the density. For a given EV you should now be able to come up with a relationship between R and P.

*To stand for rho
** Specific gravity might be an easier way to normalize this so let’s say specific gravity of 5.5 for the Earth

It’s a nasty cycle. The heavier the rocket, the more fuel needed. More fuel means an even heavier rocket.

The ultimate solution is a form of propulsion that is much more powerful and efficient. With the present technology, the “solution” is to build ships designed for interplanetary travel out in space itself, so no escape velocity is needed. The necessary supplies would be sent into orbit in the standard manner, and construction crews rotated via shuttle. True “space ships” would never leave outer space. They would simple leave one orbit, travel to their destination, and enter orbit there, sending smaller shuttles to the surface.

Could it be that whatever planet intelligent life developed on, it’s just a matter of time before a propulsion method is developed for said planet? Are we at the end of the cycle with chemical rockets? Or can we look forward to more powerful propulsion systems?

While it’s true that you only need orbital speed, not escape speed, it’s not true that the two have nothing to do with each other. Orbital speed is 0.707 (1/sqrt(2)) times escape speed.

And for any escape speed and any fuel, there is some fuel-to-payload ratio that suffices to get you into orbit. But that ratio can get really big. How big is too big? As Darren Garrison says, for any practical standard, we’re already past that point.

It’s not simply a function of escape speed (or orbital speed). The thicker & denser the atmosphere, the more work is needed to get past it and into orbit.

I’d guess getting to orbit from Jupiter is impossible with current technology, even if you are starting at the top of the liquid hydrogen layer, not the rocky core.

It’s just not a problem we are used to overcoming due to our sparse atmosphere. see Rockoon - Wikipedia for a simple solution for very thick atmospheres.

First you would need basically a submarine that could withstand such pressures and temperatures, but it would be easy to lift it once those are overcome into the high pressure atmosphere using buoyancy, not fuel. So you wouldn’t launch from that layer, but much much higher. However escaping Jupiter - yeah you may as well just come to terms that your not leaving.

Escape velocity from the top of Jupiter’s atmosphere is about 215,000 km/hr. You get a benefit from the planet’s high rotational speed if you launch near the equator, but that only gives you 45,000 km/hr, so your rocket still needs to achieve 170,000 km/hr to escape. From what I can see, the fastest rocket ever launched was the New Horizons launch, at 58,000 km/s, so we need a rocket that will launch 3 times faster than that. I don’t know if it’s possible with today’s technology but it’s far beyond what we’ve done so far.

Ugh, I just noticed that I used an ambiguous phrasing that I HATE hearing other people use. I will correct that to “we need a rocket that will launch 3 times as fast as that.”

Not sure what the ambiguity is. The rocket needs to go faster by a factor of 3. Thus 3x faster. It seems crystal clear - at least communication wise.

But if you say something needs to go 5% faster, clearly you mean 1.05x as fast, not 0.05x. That would imply that 3x faster means 4x as fast.

Most of the time you can figure it out from the context, but it isn’t great phrasing.

Much depends upon how much mass you want to get off of the planet. A Saturn 5 could launch a kilogram from Jupiter without any problem, but could not launch a space shuttle. from there. So far, we have only been able to detect very large planets in orbit around other suns, so we don’t really know what the typical size planet is.

58,000 km/s is about a thousand times faster than 170,000 km/hr. Watch your units.

That is profoundly incorrect.

Indeed. There are two main methods for detecting planets. The wobble method can only detect very large planets very close to their star (“hot superJupiters”). But the transit method, while it’s biased towards planets that are large and/or close, can detect any of them. And I think the number detected by the transit method is currently actually larger than by the wobble method.

Whoops, the New Horizons launch was 58,000 km/hr of course, not 20% of the speed of light.

Launching from Jupiter or another large planet with a similar escape velocity could probably be achieved using fusion-powered rockets. Certainly we don’t have this sort of technology today, but we might have had fusion rockets several decades ago if Freeman Dyson’s Project Orion had been completed.
https://en.wikipedia.org/wiki/Project_Orion_(nuclear_propulsion)
This method has the advantage that it relies on hydrogen isotopes that could potentially be extracted from Jupiter’s atmosphere.
Jupiter has several moons which could be used for slingshot manoeuvres, so you can gain some delta vee that way, saving fuel if you are reaching for escape velocity.

Not even close. Low Jovian orbit is about 42 km/s. With no payload, a Saturn V could reach maybe 17.9 km/s (linking to the answer since I’m lazy).

You could sorta do it if you added stages. The first three stages of a Saturn V can put 41 t at 10.8 km/s. Suppose we stack ever smaller hydrogen stages, each with a 25% payload and 8% stage mass fraction. With an Isp of 460 (a good expander cycle engine), you can get 5 km/s with each extra stage. That means you need 6 additional stages:
stage 4: 41,000 kg -> 10,252 kg
stage 5: 10,252 kg -> 2,563 kg
stage 6: 2,563 kg -> 641 kg
stage 7: 641 kg -> 160 kg
stage 8: 160 kg -> 40 kg
stage 9: 40 kg -> 10 kg

So you could just about do it, if you can build each stage with the same mass and engine efficiency. You did still end up with a 10 kg payload, so there is some margin, if 1 kg was your target… but this is going to be difficult.

More problematic is the high surface acceleration; about 2.5 g. So really the rocket isn’t going to lift off in the first place. You would need to add more engines, but that cuts into your payload.