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• 10-11-2016 12:01am
Registered Users Posts: 13,942 ✭✭✭✭

Please excuse the terminology but the recent announcement about the Chinese Long March got me wondering about how much effort it takes to get something off the planet, up to LEO or beyond.

Looking at the Delta Heavy, the mass at launch is 730,000 kg and all it can get to LEO is 29,000 kg or 15,000kg to Geosync Transfer Orbit.
So 2% of the launch mass is all it can get Geo Sync.

Does that mean that if the Earth was 2.1% more dense (excuse the approximation but I can't do all the rocket launch maths) we would not be able to launch an interplanetary probe with our current chemical technology?

Or if Earth was 4% more dense we couldn't launch any satellites?
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#2
Registered Users Posts: 1,608 ✭✭✭

I happened to come across this relevant article by a NASA flight engineer recently: The Tyranny of the Rocket Equation. It's long but well worth the read for the matter-of-factness of the arguments. It points out that the majority of the effort in going anywhere off planet is in getting to LEO. When you're there you've already expended half the energy needed to get to Mars. Different chemical fuels deliver different levels of efficiency, but the most energetic -- hydrogen-oxygen -- requires 83% of the launch mass to be fuel under absolutely ideal conditions. Add in a rigid rocket body and various other non-negotiable requirements, and 4% payload mass fraction to orbit is about the best you can hope for.

Just as an aside, it is interesting to compare orbital velocity with escape velocity. They are both easy enough to derive, but just using the final formulae:

$v_o=\sqrt{\frac{GM}{r}}\ ,\ \ v_e=\sqrt{\frac{2GM}{r}}=\sqrt{2}v_o$

This, of course, means that escape energy is twice the orbital energy:

$\tfrac{1}{2}mv_e^2=mv_o^2$

No matter what orbit you are in, you have already expended half the energy required to achieve escape at that height. And that's even before you worry about the rocket equation and the exponentially increasing fuel requirement for a given payload mass fraction.

As they say, gravity sucks! :pac:

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#3
Registered Users Posts: 13,942 ✭✭✭✭

From that article
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.

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#4
Registered Users Posts: 1,608 ✭✭✭

I scribbled some notes about the gravitational aspect of the problem, here.

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#5
Moderators, Recreation & Hobbies Moderators, Science, Health & Environment Moderators, Technology & Internet Moderators Posts: 91,636 Mod ✭✭✭✭

ps200306 wrote: »
This, of course, means that escape energy is twice the orbital energy:
qft.

The only good news is that once you are in Leo gravity isn't a constant drag. So you can use things like solar powered Hall effect thrusters. These have much higher specific impulse and so the Rocket Equation doesn't hurt quite as much.

Gravity drag means a rocket that only generates 1g of acceleration doesn't even get off the ground, it's fine later on though.

And yes you could lift off from a bigger planet. Saturn has a surface gravity about 2.5 times ours so you'd need something generating at least 3g to get anywhere. No a problem as a many rockets can do this and more, and anyway you could just use more rocket motors but that would screw up your mass fraction. The only big change is that you'd need more stages. LOTS more of them.

If you had a planet with the same surface gravity as ours but just twice the escape velocity, like a gas giant, then you'd need twice as many stages. So you'd launch a Saturn V, with an Atlas - Mercury on top. The Saturn V could put an Atlas into LEO here but there it would only get half way. And the Mercury capsule is so small you practically wear the thing. Of course you'd need a lot more heat shielding on the way done ...