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A secretive space catapault is said to be in progress. For the sake of mathematical simplicity, assume the launch vehicle is one kilogram point-mass and to be placed in geosynchronous orbit.

What quantitative forces (impulse?) and energy necessary to accelerate said vehicle into geosynchronous orbit? Feel free to make any assumptions necessary to facilitate an answer.

gatorback
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    This would probably be a better fit for space.stackexchange.com. – Tanner Swett Jan 17 '20 at 05:43
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    Maybe read about escape velocity – PerlDuck Jan 17 '20 at 07:18
  • Notice how time lapse photos of orbital rocket shots go up to gain altitude before arcing over to gain speed. As with aircraft, atmospheric drag is a huge issue. Good link and very interesting projectile design. Similar concept to "space cannon" tested around 50 years ago. Geosynchronous orbit? That's around 22,000 miles up. – Robert DiGiovanni Jan 17 '20 at 10:17
  • @TerranSwett I have tried to delete the question & copy it to space.stackexchange.com , however, the system prevents deletion. Do moderators have the ability to move migrate the question? If so, please to migrate – gatorback Jan 17 '20 at 22:40

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I won't be displaying mathematics or even a guesstimate here because this subject is somewhat beyond my scope of competency. However:

To shoot something into orbit with a catapult from ground level is not feasible, as the object would immediately burn to ashes, no matter what the material would be. The required velocity to reach orbit is about 40 000km/h, and to make things worse, you'd have to reach that speed at basically zero altitude, with a very dense atmosphere creating friction.

See this question and answers from physics stack exchange for further information.

Jpe61
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    See also Operation Plumbbob https://en.wikipedia.org/wiki/Operation_Plumbbob#Propulsion_of_steel_plate_cap - which may or may not have launched a 900kg steel plate into space, but definitely isn't practical for a useful payload. – Robin Bennett Jan 17 '20 at 13:51