A satellite at about 400km altitude needs to move at 7.8km/s to stat in a circular orbit.
At 11km/s it will enter an elliptical orbit that stretches beyond the moon and gets *just* too high to fall back down again.
Anything between 7.8 and 11 km/s is just going to determine how elliptical the orbit is.
If you are in a higher orbit the speeds drop, so at 35,786km you need to go only 3km/s to stay in a circular orbit. You do some maths and you realise that orbit takes exactly a day, so the satellite can be geostationary.
Look up newton’s cannonball to start understanding. Play Kerbal space program to really understand.
It sounds like you fell into the trap of thinking that there is no gravity in Space. There is, everything near earth still falls down to earth, nothing just “drifts away”. So how do satellites stay up? By flying sideways so insanely fast that they are falling but are literally missing the earth. That’s what being in orbit means. We’re talking about kilometers per second fast here.
With that in mind: Drifting into space would be impossible for a satellite, as it would take a lot more energy (speed) to do so. As for falling back down, there is still a tiny bit of air drag that would get a satellite down eventually, but satellites have a small booster with some fuel that they use to boost back up. It doesn’t need much, so it can keep this up for years without a problem.
It’s a lot simpler than one might think. It drifting off into space won’t happen unintentionally. It’s constantly pulled towards earth. It can only drift off if you cancel that pull, and using an engine is the only practical way to do that. I.e. you’d have to actively thrust away from earth quite intently for a long time to get away.
Not having it drop down on earth just requires it to have sufficient speed perpendicular to earth. As long as nothing is slowing it down, like atmosphere, it’ll just keep going round and round. If you accidentally make it move too fast, it’ll just get a slightly higher orbit, and if it’s too slow it’ll just be lower. The only disastrous scenario is if it’s so slow that the orbit gets low enough to start interacting with the atmosphere, which will slow it down even more.
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