A ground-based cannon firing nearly horizontally could reach space by traveling 80 km through the dense lower atmosphere in about 10 seconds. Once past the thickest 5-10 km of air where drag matters, a projectile can enter orbit without needing to launch upward or achieve infinite velocity.
We're going to talk about how we can fire a cannon to get off the planet without pointing up. Now that is a sweet Earth, you might say. The classical boundary for where the atmosphere ends is about 100 kilometers. This is not to scale at all. We're going to fire our cannon right from here. Now, if we don't aim up, and we just fire straight across, that will be our sort of nominal trajectory. We're going to just fire straight up into space. We fire at infinite velocity, we're just going to fire straight up into space. We don't fire at quite infinite velocity. We fire pretty fast. So our actual trajectory is going to look kind of like that, and eventually it would come back around and, and hit in. The main thing to note is when we leave the atmosphere. So this distance here, from here to here, compared to the thickness of the atmosphere. So our atmosphere is like 100 kilometers thick. And this distance from our launch point to when we leave the atmosphere is about 800 kilometers. That's if we don't ramp off the atmosphere at all, if we just fire approximately straight. But the atmosphere is not uniform density. The atmosphere is much thicker close to the Earth's surface and much thinner as you go higher up. So we really only need to get through like the first 5 to 10 kilometers of the atmosphere before drag drops down to really small values. So we actually only need to go about 10 kilometers up, and that actually only takes us about 80 kilometers of distance. So if we didn't ramp off the atmosphere at all, we would be through the vast bulk of the atmosphere after traveling through the atmosphere after about 80 kilometers, which is about 10 seconds of flight time. So we just need to make sure that the area ahead of our cannon for about 80 kilometers is clear, and then we're— and then we're in orbit. Easy.
