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How much thrust is necessary to launch a regulation size FIFA soccer ball into orbit around the Earth? Let us assume a size 5 which weighs between 420g and 450g. Remember, we will need thrust to ensure the ball will continue until the minimum altitude and orbital velocity have been attained otherwise it will fall back to the Earth. Minimum altitude is rarely desirable, therefore thrust must continue to be generated to gain additional orbital altitude.

Also, would the ball explode from the air pressure?

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    $\begingroup$ Hi Quant7, welcome to Space Exploration. There are many ways this questions could be interpreted. You need to be more specific about what you want to know. I have a feeling it would be helpful for you to look at the basics of how this works to better define the nature of your question. Thrust occurs over time and varies during different stages of a launch, and the launch vehicle is the main determinant of how much energy is consumed. Try looking at this nasa.gov/pdf/153415main_Rockets_How_Rockets_Work.pdf $\endgroup$ – kim holder Jun 17 '15 at 4:01
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    $\begingroup$ Given the answer provided, I am voting to reopen the question. I think it is clear what the OP is asking. If the question is in scope would be a different close vote. $\endgroup$ – James Jenkins Jun 17 '15 at 16:05
  • $\begingroup$ Related: How small could an orbital rocket be? $\endgroup$ – Peter Cordes Dec 29 '19 at 2:58
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What's your engineering budget?

This is a hideously impractical undertaking. Most of the mass of an orbital rocket is fuel and the tanks to hold it; even though your payload is tiny, all the rest of that stuff is big. The smaller a rocket is, the harder it is to design it with the high fuel-mass-to-dry-mass ratio that is required to attain high speeds, because some elements (like electronics) don't scale with the size of the rocket.

Depending on what design assumptions you make, you will get wildly different results. Some arbitrary examples:

Scenario 1: two stage solid rocket, 90% propellant fraction. Stage 1: 700kN thrust, 240s sea level Isp, 40 tons propellant. Contributes 3886 m/s ∆v. Stage 2: 80kN thrust, 280s vacuum Isp, 5 tons propellant. Contributes 6581 m/s ∆v.

Scenario 2: single stage kerosene/LOX rocket using the SpaceX Kestrel engine, fuel tanks whittled by hand from carbon fiber by a team of elves on Adderall, total dry mass 100kg, of which the rocket motor is half. 96% propellant fraction, 2.4 tons of propellant, 31kN thrust, 317s vac Isp, total ~9600 m/s ∆v. (At the end of the burn for the Kestrel option, the rocket would be accelerating at better than 30g, so I hope those elves know what they're doing!) I don't think this is actually plausible, but it's theoretically possible.

And a real world example.

Scenario 3: Vanguard 1/TV-4 was a 3-stage rocket that put a satellite into orbit that weighed only about 3 soccer balls. First stage thrust 135kN. From my brief research, Vanguard and the Japanese 4-stage solid-rocket Lambda 4S seem to be the two smallest orbital launchers in history.

So depending on how you tweak the other variables, the needed thrust could be anywhere from 31kN to 700kN.

As for the ball, FIFA regulations say the air pressure in a soccer ball needs to be between 8.5 psi and 15.6 psi (above ambient), so presumably it can handle somewhat more pressure than that without exploding. Sea level ambient air pressure is about 15 psi, so if you deflated the ball before launch (to ambient air pressure), then took it into vacuum, it would then be at 15 psi overpressure - the high end of regulation inflation, so a very taut ball, but not exploded.

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    $\begingroup$ A very interesting take... I really wasn't sure what to do with this question and would be interested to know what the asker gets out of your answer. Good relevant info that just swallows the whole big scope of it and tries to play with it enough to get something across. $\endgroup$ – kim holder Jun 17 '15 at 4:07
  • $\begingroup$ There are a lot of questions on here where my initial response is really, "well, why do you ask?" Any excuse to bust out my delta-v spreadsheet, though... $\endgroup$ – Russell Borogove Jun 17 '15 at 4:08
  • $\begingroup$ For such a small rocket, the fuel cost should be almost negligible; it may make sense to use Syntin and get extra performance for just a few thousand dollars per rocket (if it's not significantly more expensive to produce on these small scales). $\endgroup$ – lirtosiast Jun 22 '15 at 0:08
  • $\begingroup$ Also, have you considered air drag? space.stackexchange.com/a/750/10547 suggests it would cost on the order of 23.7*cbrt(333 t/2.5 t) = ~125 m/s, assuming the same shape as the Falcon 9, which is small but significant. It would really be more, since the Falcon 9 shape probably can't be achieved with that absurd propellant fraction. $\endgroup$ – lirtosiast Jun 22 '15 at 0:15
  • $\begingroup$ Syntin has only about a 3% ISP advantage over kerosene. This is all very gross back-of-the-envelope analysis, using a target total ∆v of roughly 10,000 m/s. Note that drag cost is higher for smaller rockets given the same shape -- Saturn V/Apollo lost only about 50m/s to drag despite being a less streamlined shape than F9 -- so our little soccer ball lofter will probably lose quite a bit more. $\endgroup$ – Russell Borogove Jun 22 '15 at 0:23
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Taking the question literary; If you have a "thrust" pushing the ball, the only limiting factor is to manage to get off the ground. g ($9.81 m/s^2$) times 420-450grams is 4.16 to 4.46 Newtons. Why there is such a force acting on the ball in the first place seems to be outside the scope of the question.

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