Here is a related question that has bothered me for some time: in Jules Verne's "From the Earth to the Moon" (1865), he writes the travelers as only achieving weightlessness for a small moment, at just the point where the moon's gravity exactly cancels out the earths gravity.
This makes an intuitive kind of sense: you would gradually lose weight as you get farther from earth, then after a moment of weightlessness gradually 'gain' weight as you approach the moon.
(I'm not a physicist, so take the following with a grain of salt!)
It's not wrong, but it would never happen.
Let's say we've built a moon elevator. Like a space elevator, but tethered to the moon. You travel from the earth; there is a brief period of acceleration, then you settle down to a steady speed for your journey.
After you reach the steady state, you are going to experience normal Earth gravity. As you move further from the earth, however, you will experience less of it. As you approach the moon, its gravity will eventually be stronger - with this transition occurring at the Lagrange point L1 between the earth and the moon, where the gravitational pull from each is equal.
In practice, until we build a moon elevator, this isn't going to happen. Instead, we have to throw you at the moon using a rocket. Most of the energy we use for this is actually spent making you go sideways, instead of directly up. It's kind of cool actually - if you are orbiting the earth in, say, the ISS, you are actually experiencing nearly the same gravitational pull as if you were on the surface. You are just moving so ridiculously quickly in a circle around the earth that the centripetal force cancels out gravity - like someone is swinging you around on an invisible rope. Since this is happening to both you and the spaceship you are in, there is no relative acceleration - so you appear to be weightless.
If we fire some more rockets to accelerate you towards a lunar orbit, nothing else changes - you are still not accelerating relative to your spacecraft (assuming you are strapped in!) and so you continue to appear weightless. You transfer into orbit around the moon - and you are in the same situation you were in when orbiting earth. But if you drop a lunar lander, which slows itself down - it'll fall!
Orbital mechanics and gravity can certainly be counterintuitive, but it's thoroughly fascinating.
This makes an intuitive kind of sense: you would gradually lose weight as you get farther from earth, then after a moment of weightlessness gradually 'gain' weight as you approach the moon.
Obviously this is wrong, but why?