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Comment by callumprentice | Hacker News Reader

Musk said at the start of his presentation that the magnitude of earth's gravity is such that we are right on the cusp of rocket flight possibility. If the magnitude were a little more, rocket flight would be impossible. If it were a bit less, it would all be a lot easier.

Can anyone expand on that, assuming it's the truth..

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I assume he's relating 1) the force of gravity, composition and distribution of our atmosphere, and incredible velocity required for orbit, to 2) the chemical potential of fuels and the limits of structural strength for materials to carry cargo to orbit.

I haven't run the numbers, but he's right: it's pretty hard to get something that can carry itself to orbit. It has to climb out of the atmosphere directly against gravitational force and atmospheric drag, and then as early as possible turn sideways and start accelerating to around 28000kph while making sure the rocket is pointed in the right direction and holding together. You need a lot of propellant to get to that state, which means you have to carry it around until you need it, which means the machine needs to be much bigger than just the cargo, which means that all of your challenges just magnified by many orders of magnitude.

Would it be possible for the numbers to be a bit more difficult to work with so maybe we could go to low earth orbit, but never be able to make it to the moon?

If you can make it to orbit, you can make it anywhere (it just may take multiple launches to assemble/fuel the spacecraft going elsewhere).

Wait, really? So what's the deal of first and second cosmic velocity?

I guess the idea is that if you can make it to orbit (even if you waste all of your fuel), then you could in principle refuel in-orbit (by getting another unmanned rocket with just fuel into orbit) and thus escape the orbit.

But yes, you still require more energy (exactly sqrt(2) times as much) to "escape" Earth's gravity entirely than to orbit it with a circular orbit.

Exactly twice as much energy. √2 as much velocity.

You're quite right -- that was a typo. ;)

Once you are in orbit, anything else is possible. Because if you can get something small to orbit, you can get a lot of small things (such as additional fuel) to orbit, to reach escape velocity. That is because once in orbit you no longer have a need to reach the next velocity stage as rapidly as possible, which is why ion engines are so efficient but can only be used after LEO.

Making orbit is a single hard step; raising orbit, which is all that making it to the moon requires, can be done more gradually (with low-thrust/high-efficiency engines, on-orbit resupply, etc).

So if you can get off the planet you can get anywhere... but that doesn't mean cost-effectively. If your planet is such that it takes a Saturn V to launch a cubesat, it may simply cost too much to make it to the Moon.

The don’t call it “The Tyranny of the Rocket Equation” for nothing.

More payload means more fuel. More fuel itself means more fuel.

That looks like an argument that you need more than twice as much fuel to get twice as much payload to orbit -- that fuel requirements go up more than linearly.

Maybe this is obvious, but two rockets can get twice as much payload to orbit using twice as much fuel. You can that up linearly all day long. (It holds for "twice as much", but the same argument doesn't work for "twice as fast" or other metrics.)

X fuel can get Y payload to Z speed. To get that payload to 2 * Z speed, you need 2 * X + (X * (X / Y)) fuel, because the fuel counts as part of your payload for the first Z of speed.

If X is 500t and Y is 5t, you now need 51,000t of fuel to achieve 2 * Z speed.

To augment what Duskstar said, "twice as fast" is what counts: to get something to orbit with a steeper gravity well, you need more of a velocity change.

It's also worth mentioning that once you are in space things are relatively easy. You only need around 20% more deltaV to get from Earth to Mars, as from Earth to the Moon (assuming a one way trip).

I highly recommend Kerbal Space Program for anyone interested in getting a feel for orbital mechanics. Please buy this game for any young people in your life.

It’s a great game, that will ruin your appreciation for basically all space movies.

It also made me enjoy seveneves

The rocket equation states that the amount of fuel that you need (to send a given payload into orbit) increases exponentially with the escape velocity of the planet:

mass of the rocket with fuel = mass of the payload * exp(escape velocity / engine exaust velocity)

That is because the faster you need to go, the more fuel you need to use, but now, you also need even more fuel to accelerate the fuel that you just added. So, it becomes exponential.

So, if the earth was bigger, its escape velocity would increase, and the amount of fuel needed to power a space rocket would increase (exponentially) so much that it would become unpractical. Vice versa, with a smaller planet it would require exponentially less fuel to reach orbit.

The only solution would be to have an engine with a higher exaust velocity. With the current technology, ion engines have very high exaust velocity but low thrust are very energy hungry. The thermal nuclear engines have both high exaust velocity and high thrust, working prototypes have been built, but all projects were boxed 60 years ago because of the fear of an accident.

Ok so doing super-approximate maths:

A fully fueled and loaded Saturn V weighs about 3,000,000 Kg, and has a payload of about 40,000 Kg to the moon.

So that means once you've put all the bits of the rocket together that collectively give you sufficient thrust to get you to the moon, you've only got about 1.3% left for actual payload.

S if earth's gravity had been ~1.3% stronger, then the weight of the "getting us there" bits of the rocket would have left no room for payload. Any more gravity, and we wouldn't even be getting to the moon.

Equally, if the earth's gravity had been 1.3% weaker, we could have doubled our payload to the moon (or done things way easier).

Contrast that with a Boeing 747 which has 50% of total mass as payload, and so is relatively insensitive to changes in gravity.

Some (funny) sources list Saturn-V payload as 140 tons on LEO :) so according to this logic to get to orbit one has plenty of margin. And as soon as the payload is in orbit it uses full value of accumulated speed, so it's used to get further and getting to the Moon is no harder than with Earth...

I recently realized that if we got in Jupiter's gravity well we could probably never escape it again. Someone correct me if I'm wrong. The thought made me feel really uneasy.

If that were true, it would be impossible to leave the solar system, since everything is currently in the Sun's gravity well, and the Sun is larger than Jupiter. But we have sent probes outside the solar system (did they fully leave the Sun's gravity well yet though? Not sure)

But we didn't send the probes from the Sun.

Plus I don't think it got its velocity from Earth, but by using gravity assists to steal momentum from other planets (which, if you don't know how that works, do yourself a favor and read the wikipedia page, it's pretty great).

Sure, we could orbit Jupiter and get back out. But if we ever descended to the "surface" we couldn't climb back out.

Voyager 1/2 and New Horizons are at escape velocity and leaving the solar system.

You have to have high thrust to get out of the dragging atmosphere.

The premise is about current chemical propellants and structural components. If you build a rocket out of nanotubes with nuclear propulsion you could go wherever you want from anywhere else. Except black holes.

Remember that we’re already orbiting the sun though. A lot of the hard work is already done.

Launching from the (nonexistent) surface of Jupiter would be the comparison. From a low orbit of Jupiter you need a lot of delta v to escape, but you don't need extremely high thrust as would be needed to get in to orbit in the first place from the surface of a body. You could use a very efficient thruster over a long period of time which is a lot easier to design for.

So along this same line the PSP Parker Solar Probe is exploring our gravity well in the other direction, and in some ways will be more gone forever than voyagers.

I think the Jovian Moon Io is very low, look up an eclipse photo from Juno; it would be key to exploring low Jovian orbit, just like Venus kicks PSP and Jupiter kicked Voyagers.

That's not really how it works. If Earth's gravity were 1.3% stronger, you'd need about 0.6% (√1.013) more delta-v to escape Earth, or about an extra 70m/s. That's not hard to achieve. Increasing the total mass to dry mass ratio by about 0.6% would do it (and the Saturn 5 was about 85% fuel) since ln(x*1.006) = ln(x) + ln(1.006) ≈ ln(x) + 0.006.

Someone else posted somewhere that if the Earth was about 3x heavier, we wouldn't be able to use chemical rockets to escape.

If the Earth were 3x heavier, birds wouldn't be able to fly, at least not the way they are now. Sparrows can barely get airborne when they're full, let alone at triple their weight.

Air density would be three times higher though. So they might still be able to fly.

Ooo, that's a good point!

> at least not the way they are now.

Yeah, but they wouldn't be, because the extra mass would have influenced their evolution.

Extra weight. If gravity is the only thing changed, mass would remain constant.

Since the discussion is about "earth's gravity", I'm assuming the change would be in its mass, not in the universal gravitational constant, which is not Earth-specific.

Did that take into account the possibility of an air breathing first stage?

Probably not. But, while an air-breather would be more useful on a larger planet, it would still be the case that almost all of the space launch system's work must be done outside the sensible atmosphere. Air breathing would only add the tiniest margin to "chemically escapable planets."

Why can't you aerodynamically fly up to high altitudes and then start rocketing?

You can, but it introduces its own set of complexities. The plane needs to carry a massive payload, and doesn't really get you much delta v.

The problem is not how do we get up high, but rather how do we get going really, really, really fast.

There is in fact a remarkably useful set of well developed air launch rockets that help provide a nice “benchmark” for comparison with air launching satellites/etc using rockets. Anti-SATellite (ASAT) weapons are making similar engineering trade offs but aiming at a different set of capabilities, optimising for smaller sizes, being “rack ready” in the event war breaks out, and so on.

Unlike the more modern ship launched SM3 that is part of the Ageis system, the older ASM-135 https://en.wikipedia.org/wiki/ASM-135_ASAT was designed to be air launched in a supersonic zoom climb to get maximum speed and altitude from the aircraft in order to maximise its capabilities.

For an even better comparison, you can compare air launches ASAT missiles with sounding rockets, they have a greater similarity in their trajectories/launch profiles, so it’s easier to see what the air launch “gains” over the ground launch.

There's always also e.g. Orbital Pegasus.

Rockets tend to throttle down at lower altitudes so they're not accelerating through thick atmosphere though? So Delta V isnt much of a loss.

When not burning sideways, you have the issue of gravity drag. Specifically, all the force spent firing downwards is wasted on fighting gravity rather than gaining speed. The reason rockets go up is to get above the atmosphere. Without an atmosphere, you'd launch rockets sideways.

It doesn't help much. Most of the work in achieving orbit is in gaining speed "sideways". Your average orbital launch achieves high airplane altitudes in the first 15-20 seconds out of a 500 second flight. It's easier to build a slightly bigger rocket than to add a giant airplane to the system.

It's not. That thing is called the rocket equation and the law is logarithmic. https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation

So basically in your example, if the Earth gravity was 1.3% stronger, payload would be ~37.8t instead of 40.

Or we'd have to use different lift technologies, e.g., https://en.wikipedia.org/wiki/Nuclear_pulse_propulsion .

https://www.nasa.gov/mission_pages/station/expeditions/exped...

Nice find! Near the end, the author directly addresses this question:

> If the radius of our planet were larger, there could be a point at which an Earth escaping rocket could not be built. Let us assume that building a rocket at 96% propellant (4% rocket), currently the limit for just the Shuttle External Tank, is the practical limit for launch vehicle engineering. Let us also choose hydrogen-oxygen, the most energetic chemical propellant known and currently capable of use in a human rated rocket engine. By plugging these numbers into the rocket equation, we can transform the calculated escape velocity into its equivalent planetary radius. That radius would be about 9680 kilometers (Earth is 6670 km). If our planet was 50% larger in diameter, we would not be able to venture into space, at least using rockets for transport.

Not using chemical rockets. Nuclear propulsion would be able to do it with the ~1000000x energy density advantage of nuclear fuel over chemical fuel.

The problem is that the super-dense energy of a nuclear blast also evaporates solids and rains gamma rays on everything around.

Imagine how hard space exploration would be if the only practical rocket were a Project Orion.

I remember seeing a simple demonstrator some years back of a laser pulsing against the backside of a spinning disc, the geometry of things causing the heat from the laser to provide thrust.

I can't find the video I saw, but here's a general link on the topic:

https://en.wikipedia.org/wiki/Laser_propulsion#Laser_energiz...

This comes with many problems, but it does bypass the rocket equation, while not requiring Project Orion levels of trouble.

I mean you still need to carry propellant: the stuff that is ablated away. It's just that the exhaust velocity is much higher.

Air from the atmosphere may be the propellant [1]. If sufficient velocity can be achieved before leaving the atmosphere, then no propellant is needed to be carried up on the way to orbit.

[1] https://www.youtube.com/watch?v=XhUasBcoj-Q

Nuclear would be better, but it's not quite as good as it seems. Nuclear engines are rather heavier than chemical.

There are more efficient propellants than hydrolox, but extremely toxic [1]. With a bigger planet, we would have been forced to use either those or nuclear propulsion to get to space.

1 - https://space.stackexchange.com/questions/19852/where-is-the...

He was talking about rocket reusability, specifically reusing orbital stage. Just reaching the orbit is possible in stronger gravity, but returning back whole stage is already very close to the limits of current material science

That is pretty much all there is: If earth was more massive, the chemical rockets we've been producing wouldn't have enough thrust-to-weight ratio to reach orbital velocity (about 25k km/h). We would have to load the rockets with so much fuel to break free of gravity that they would be too heavy to lift themselves.

This is all assuming yields and fuels we have now. If we lived on a more massive earth and we were trying to escape its gravity, I'm sure we'd be using more exotic and dangerous fuels (like all those fun fluorine and boron fuels Dr. Clark mentions in Ignition![0]) to do the job. We just happened to have the capability in the middle of the century to use a fuel we were already making (refined petroleum) for jet engines.

[0] https://www.amazon.com/Ignition-Informal-Propellants-Univers...

Well, it'd prevent rockets for sure, we'd only have nuclear pulse propulsion then to get into orbit and that's a lot harder to justify to people than a rocket.

There's a lot of alternatives, the main constraint is that it has to be built from the ground up, so space elevators are out.

I think a dynamic structure such as a launch loop https://en.wikipedia.org/wiki/Launch_loop would work.

Also inflatable towers for launch assist https://en.wikipedia.org/wiki/ThothX_Tower

For even kookier options we've got lasers! https://en.wikipedia.org/wiki/Laser_propulsion https://en.wikipedia.org/wiki/Beam-powered_propulsion

I wonder how much this could be mitigated by extra-rocket energy delivered while the rocket is still close to the ground - e.g. a cartoonishly large slingshot.

Or a comically large refueling hose hooked up until it hits orbit. I guess in that case you'd probably be fighting gravity even more trying to push fuel up the hose.

Ground laser propulsion has been considered. https://en.m.wikipedia.org/wiki/Laser_propulsion

There's also using chemical rockets for the first stage, then switching to nuclear for the second stage once clear enough of the ground to minimize fallout. Radiation pollution wouldn't be pleasant, but future advances could potentially minimize that also.

NERVA XE was damn near ready to fly during the Apollo era for Mars missions. Would've made a hell of 2nd stage engine.

https://en.wikipedia.org/wiki/NERVA

Unfortunately, drag force is proportional to the square of velocity... So the slingshot (or railgun or whatever) maybe gives you a nice acceleration at the start, but a LOT of that initial force will bleed off as drag early in the flight in the thick thick low atmosphere.

(Consider the difference in difficulty of riding a bike at 15mph vs 16mph and 25mph vs 26mph... 25->26 requires a hell of a lot more effort, all due to drag.)

Or you could just launch from a 12 mile tall tower: https://en.wikipedia.org/wiki/ThothX_Tower

Or a Lofstrom loop: https://en.wikipedia.org/wiki/Launch_loop

Or you could fly a high-altitude airplane into a skyhook: https://en.wikipedia.org/wiki/Skyhook_%28structure%29

> earth's gravity [..] right on the cusp of rocket flight possibility

He didn't actually say that. He was talking about "rapidly reusable orbital rockets" and "fully reusable orbital rocket[s]" being the "critical breakthrough" that's necessary, the "holy grail of space" and the "fundamental thing that's required".

So fully and rapidly reusable.

https://youtu.be/sOpMrVnjYeY?t=1234

Hmmm... That's actually really interesting to think about from the anthropic principle perspective.

Very interesting that the only intelligent species we are aware of is on a planet that we can leave.

I wonder to what extent higher gravitational planets could sustain love that couldn't leave it. An interesting answer to Fermi's paradox.

Nah, again - nuclear. I doubt the safety profile would factor much once it's the only available option.

Don’t forget ground based propulsion too.

if gravity were much more we'd be out of chemical reactions that produce the energy to beat the rocket equation.

This is a possible Fermi paradox answer, or at least factor. Maybe the vast majority of habitable worlds are larger than Earth. The inhabitants of those worlds might find space flight too hard or even impossible. They also might have less interest in it since they would make the natural anthropic assumption that worlds capable of supporting life are probably huge like theirs.

That really makes a lot of sense. Because planets smaller than Earth cool a lot faster, so they lose their molten core and plate tectonics (which keeps land mass rising and out of the water), and also a magnetic shield that keeps the atmosphere from stripping away (like Mars).

I'm going to be hopeful and optimistic and point out that the large planets in our solar system aren't rocky and suitable for life as we know it anyway. Earth is the biggest one and the rest are gas planets. Maybe planets that harbor life (rocky, liquid water, goldilocks zone closer to the sun) usually have low enough gravity for aliens to escape it.

This diagram has some exoplanets on it for size comparison- https://en.wikipedia.org/wiki/Circumstellar_habitable_zone#/...

Earth might be right at this threshold of small enough for space flight to be practical (still hard, but practical) but big enough to hang onto water and atmosphere.

I have another wild guess. Not only we have just right amount of fossil fuels to leave the planet, but also the sun has just right amount of energy to reach the stage when people can move to another solar system.

My guess is the Sun probably has more... it’s really big.

What if it’s just like fossil fuels and there’s enough energy there for us to smear ourselves out? Oh cool, kinda like fission then!

Gravity is taxing. It's possible that our galactic neighbors live on a larger planet with greater gravity which makes their escape from the planet next to impossible.

Can we swing by and drop them a ladder?

If we get sucked by the gravity, we are stuck as well.

Presumably we'd need to lower it from geostationary orbit. This is a unique solution though I suppose there is some dependency on the mass of the planet where you might be too deep in the well. But you'd be in orbit so presumably some low thrust low propellant engine powered by sunlight ought to be an option?