Why do rockets launch in an arc, and not just go straight up?
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The thing about rocket is that going up is only a very small part of what they do.
We thing of things in orbit as being high above but the truth is that the added altitude is the least issue of getting there.
Space “begins” at 100 km high up according to some official designations. The International space station, a frequent target of rockets going into space, is about 400 km high up.
400 km may seem like a lot but if you consider that vertically, it is only about 4 hours worth of drive in a car. (2 to 3 hours in a fast car on a clear highway without any speed limits) it is maybe an hour and half on a good train, a fraction of an hour on a plane.
Distance wise there should be no issue getting there with a rocket. The 400 km up is the trivial part by comparison with the actual problem.
The ISS travel at speed of over 27,000 km per hour and so does anything else in a similar orbit. Those are speeds that would be over 22 times the speed of sound down here.
The main purpose of a rocket is not to go up, it is to go fast.
You don’t need to reach an altitude of 400 km above the ground, you need to be going insanely fast when when you reach there.
Rockets go up first to get out of the way of all the air we have down there. Once they reach an altitude where there is less air to get in the way they start to work on their true purpose of speeding up sideways to get as fast horizontally as they need to go.
There would be no need to go up all the way to orbital height, have your target zip by at speeds many many time faster than any speeding bullet and immediately fall back down again.
You need to accelerate enough that you stay up and can interact with stuff in orbit.
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