Naked Science Forum
General Science => Question of the Week => Topic started by: Adam Murphy on 19/01/2021 16:02:47
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Stephen got in touch to ask:
"Is it true that if the mass of the Earth were greater, it would render our chemical rockets incapable of reaching orbit?"
Any astronomical insights?
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Stephen got in touch to ask:
"Is it true that if the mass of the Earth were greater, it would render our chemical rockets incapable of reaching orbit?"
Any astronomical insights?
'Our rockets' are designed for getting off Earth, so no, they'd not work as designed for getting off a significantly more massive planet. If Earth's mass were greater, we'd need better rockets to do the job. It becomes an engineering question.
Is there a theoretical limit to the power or delta-V of a chemical rocket? I imagine there must be but I don't know those limits. If atmospheric friction was not a problem, then any low power rocket (say one with an Ion engine) could get into orbit given enough time, and that is true of a planet of any mass.
Imagine trying to escape Uranus. It has lower gravity than does Earth, but still requires about twice the delta-V to get an object into orbit. More depending on how far down you start since there may be more atmosphere to slow your ascent.
Yes, I think a chemical rocket could do that, but there are definitely limits.
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If it was big enough, it would turn into a black hole.
That would stop any rocket.
The question is, whether the other problems of gravity would stop us before spaceflight did.
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If it's gravity was too strong, we would have never evolved in Earth on the first place.
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One of the critical parameters of a rocket engine is specific impulse.
- This describes the efficiency with which it uses fuel.
- A less efficient rocket means you need more fuel, which needs a bigger rocket, which needs more fuel... Eventually, you get to the situation where you can't get into orbit with a specific rocket engine
- You can improve specific impulse by having a higher exhaust velocity, which for a chemical rocket normally means a higher reaction temperature. This runs into problems with materials that can stand these high temperatures, and how to keep them cool.
Jet engines can get their oxygen from the atmosphere, and so have a higher specific impulse than space rockets that need to carry their oxidizer.
- So hybrid systems like Virgin Galactic use a jet aeroplane to get above most of the atmosphere, and then a conventional rocket
See: https://en.wikipedia.org/wiki/Specific_impulse
Hypothetical alternatives like a space elevator avoid this specific impulse problem - but it is hard to imagine how you would construct a space elevator if you didn't have any rockets that could escape from the atmosphere...
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but it is hard to imagine how you would construct a space elevator if you didn't have any rockets that could escape from the atmosphere...
A very long ladder.
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Could Earth get so big
It is hard to imagine any process that would increase Earth's mass significantly and still leave the planet habitable.
Even a dinosaur-killer asteroid hitting Earth every year wouldn't affect Earth's mass very much (on human timescales).
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As mentioned by evan_au, ISP is an important factor for rockets. Another is the thrust to weight ratio, especially when dealing with launch vehicles.
ION engines have very high ISPs, but because they have thrust to weight ratios of less than 1, are useless as launch vehicles.
The RS-68A, which is an engine used for the Delta rocket, has an ISP of 360.5 sec (3.5 km/s exhaust V)*, and a thrust to weight ratio of 47.4
Thus, if we consider an "ideal" rocket which just consists of rocket engine and fuel (zero mass allotment for fuel tanks, superstructure, etc.) then if the fuel massed 46.4 times the rocket engine, the rocket would just be able to hover above the ground.
With the given ISP, it requires a mass ratio of ~24.4 for our ideal rocket to reach escape velocity. In other words, you need 23.4 times the engine mass in fuel. This is well below the 47.4 thrust to mass ratio.
So what kind of increase in the Earth's mass would it take in order for the mass ratio to approach or exceed the thrust to mass ratio?
First off, we'll assume this mass increase occurs without increasing the Earth's size*
Increasing the Earth's mass has two effects:
It increases the value of g at the surface, thus decreasing the effective thrust to mass ratio.
it increases the escape velocity, which increases the required mass ratio.
With a 25% increase in Earth mass, the mass ratio increases to 35.6 and the effective thrust to mass ratio decreases to 27.92.
While the thrust to weight ratio still is larger, it is just barely so. A rocket under these conditions trying to launch vertically would still be using most of its thrust just to hold up it own weight and likely wouldn't get very far before exhausting its fuel and falling back.
So, we could safely say that a 25% increase in Earth mass would effectively prevent a Delta rocket from achieving escape velocity**
Real life practical issues would drive this maximum mass increase down.
*At sea level conditions
** This assumes a single stage rocket, and the Delta is a multistage launch system. However, our single stage "ideal" rocket would out perform a practical multistage rocket.
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Stephen got in touch to ask:
"Is it true that if the mass of the Earth were greater, it would render our chemical rockets incapable of reaching orbit?"
Any astronomical insights?
With a stronger gravity you would need a slightly different rocket to compensate, more fuel more thrust. So no.
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more fuel more thrust.
More weight; more failure.
Did you somehow miss the point of the thread?
Incidentally...
https://what-if.xkcd.com/24/
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Stephen got in touch to ask:
"Is it true that if the mass of the Earth were greater, it would render our chemical rockets incapable of reaching orbit?"
Any astronomical insights?
With a stronger gravity you would need a slightly different rocket to compensate, more fuel more thrust. So no.
More fuel = greater Delta V, but thrust is dependent on the type of fuel and the design of the rocket engine. And the ability of a rocket to reach orbit relies on the thrust to weight ratio. This, in turn, is dependent on the energy that can be extracted per mass unit of fuel.
Since the original post specifically asked about chemical rockets, and there are limits on the amount of energy that can be extracted via chemical reaction, and thus a limit to the possible thrust to weight ration with chemical rockets, then yes, there is a maximum mass the Earth could have before chemical rockets would not be up to the task.
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Answered (in much simpler form) on the Question of the Week podcast: https://www.thenakedscientists.com/podcasts/question-week/if-earth-were-heavier-would-rockets-work
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I have to agree with @Halc that ultimately this becomes an engineering problem.
If one was living at the bottom of the Marianas Trench, one wouldn't necessarily blast a rocket from 10km below the surface of the sea, and use rocket propulsion to get to the surface through 10km of water before continuing into space.
So, around Jupiter or Saturn, one would likely have some kind of a floating launch platform, then use some kind of conventional wing structure to fly higher and faster before discarding the wings and going to pure rocket propulsion/lift.
Jet propulsion, of course, involves carrying a fuel and scavenging atmospheric oxidizer. Thus, the actual atmosphere makeup would be critical.
There have been early proposals to use fission rocket propulsion, but ultimately we have chosen not to go that route due to difficulties in containment and atmospheric contamination. Yet, more rocket fuels might be possible, or even some kind of a hybrid fuel system.
A complex ring and/or moon structure might make navigation more difficult, but if one could reach the rings/moons, it may provide an opportunity to refuel, and use gravity assist to achieve escape velocity.
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No one much mentioned staging. All practical orbital rockets stage, because, while a single stage rocket could just about reach orbit, it would have only a very small payload. If the Earth was significantly bigger the rocket would need another stage. Each stage multiplies the mass of the rocket by about 5 for the same payload. That would make the rocket much more expensive. Although you can ALWAYS add more stages in principle to make the rocket get more oomph (technical term is greater 'delta-v'), in practice you run out money at some point, the rockets get too expensive to build.
Roughly if I've done my sums right, if the Earth was twice as massive you'd need an extra stage. If it was twice as much again, I'm not sure anyone would have ever have been launched to orbit due to cost.
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If the earth had much more mass = gravity yes the rocket would need to be considerably larger and more powerful. Take the Saturn v rocket for example it was 3000 tons at liftoff if the earth had 10% greater gravity we would need a much larger rocket to hold the extra fuel we would need more powerful engines to provide the power and burn the extra fuel. So to cap bigger rocket bigger engines moor fuel in total this would be a rocket approaching 5000 tons a structure that most likely would collapse under its weight on take off. so no rocket of this size will ever be built to tackle such a payload. If it was feasible a rocket of this size would be usful now to lift a graiter payload into space but no such rock egsists I wonder why.