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I was wondering what is the smallest possible rocket to get to LEO. I know that rocket fuel accounts for 90% the total mass of the rocket. Lets say I have 500g of payload and my rocket is made from an aluminium shell. How much fuel would I need to get to LEO and how tall and wide would the rocket need to be?

jack
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    From the little that I know about real rocket design, it is much more complicated than X kg of fuel (of a certain type) takes up Y m3 volume. Your best bet would be to look for details of current rockets (and sounding rockets) and use those as general characteristics. – hazzey May 05 '16 at 18:47
  • As this is on hold I can't answer - even though it is answerable usefully. I performed many such calculations some decades ago. As noted - there are many variables and assumptions but you can get a feel for it. There is a vital point to make - you say "TO LEO" not "To LEO orbit". Touching LEO and falling back is far far far (far ...) easier than achieving orbit. I'll assume you mean achieving orbit. Something in the order of 3 or 4 meters tall with 2 or 3 stages may be able to orbit and EXTREMELY low mass payload - 500g is too heavy for a minimal system. If you have all the technology ... – Russell McMahon May 06 '16 at 12:59
  • ... you want it's not too hard. The Atlas did it in 1.5 stages with two heavy booster motors dropping off and a sustainer plus tanks going to orbit. This takes cryo fuels and Isp of 300+. Cryo Hydrogen can give you ISPs of 400 + but that is very very high tech. Tiny turbo pumps that suit this are not really available but a pistonless pump system (invented by me long ago and Lockheed Martin longer again ago unknown to me :-) ) can do this much easier at this scale. | Hydrogen Peroxide at scarily strong concentration powered the British Black Arrow 3 stage rocket - 43 feet tall and 135 lb – Russell McMahon May 06 '16 at 13:11
  • ... satellite. Despite the squate leight:width ratio, toylike look and lack of the usual launch accoutrements this is a genuine photo of the only successful BA satellite launch. - Black Arrow liftoff - on the way to orbit . Probably a 3 stage all liquid HTP (peroxide) system OR a 2 stage liquid + solid 3rd would be workable. BUT making a say 20 foot version would probably be easier and no dearer. | MUCH more could be said. :-) – Russell McMahon May 06 '16 at 13:14
  • related discussions in Space SE: What is/was the smallest orbital launch system, by total mass? as well as Why isn't there a rocket to launch a single cubesat? and also If there “won't be” rockets to launch individual cubesats, then why did JAXA build exactly that? (SS-520-xx) – uhoh Aug 11 '19 at 08:09

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Keep in mind that most of the fuel is used to lift fuel, not payload. The amount of fuel required to lift a given payload is a complicated relationship involving many factors.

One aspect that limits how small a rocket can be is the cube-square relationship between fuel mass and drag: As the linear dimensions of the rocket scale down, fuel quantity goes down with the cube of the scale factor, but drag only goes down with the square of it. Eventually you get to a point where you can't carry enough fuel to even get out of the atmosphere.

Dave Tweed
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