|MadSci Network: Physics|
The short answer to your question is "no", 100 mph is just not enough and straight up doesn't lead to an orbit. The reason is that orbital speeds for near-Earth orbits are very high. The shuttle, for example, typically orbits at about 17,000 mph. So 100 mph, while fast by our everyday standards, is slow for something in orbit! (By the way, here is a useful website on orbits. In particular, the Orbital Velocity and Period Calculator is fun.) Also (and I apologize if you knew this), straight up isn't the direction to head if you want to get into orbit. Orbit is, to borrow one from the late Douglas Adams, falling and missing the ground. So you need a sideways motion to be in orbit. At some point you need to turn to get to orbit and not just fly off into space. (However, if you kept traveling straight up at 100 mph, you would eventually just leave Earth altogether and head out into the solar system. Alas, at that speed it would take you 100 years just to reach the Sun or 50 years to reach Mars.)
More basically, the problem of orbiting isn't really about speed as much as it's about energy. To put something in the right location at the right speed to orbit as you want it to, you need to expend a certain amount of energy. (Usually, you get this from your rockets' chemical energy.) The speed that you use to get there doesn't really affect the energy needed much. So 100 mph isn't really any easier than 1,000 mph or 10,000 mph in these terms. Getting the thrusted need to reach these speeds is not particularly difficult once you have all of that fuel. So fast seems to be the way to go.
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