If orbital mechanics were this unstable, we wouldn't ever manage to have any sattellites up in orbit around the Earth (or have the Earth orbit the Sun, and the

If orbital mechanics were this unstable, we wouldn't ever manage to have any sattellites up in orbit around the Earth (or have the Earth orbit the Sun, and the Sun orbit the centre of the galaxy..). The important part of your orbit is the sideways velocity (For example, the International Space Station orbits at around 27,600 km/h). Let's say you're launched from the ISS (and that the ISS's orbit is perfectly circular), straight down towards the Earth at about 30km/s. Initially, you'll get closer to the Earth, but at the same time your orbital velocity will increase as you're going down, which eventually ends up sending you back up to the same orbit as the ISS (although I'm not sure if you'll end up ahead of the ISS, behind it or right back at it). You'll have an upwards speed of 30km/s, and will keep going up at a decreasing speed until you hit some maximum point, and start coming back down to repeat the cycle. Your orbital path will end up tracing out an ellipse, and at no point will you spiral in or away. Ultimately, to actually come back down to Earth you have to burn off a lot of sideways speed (especially if you don't want to be going too fast when you enter the atmosphere). And, to leave Earth's gravity, it takes quite a lot of acceleration too.