I understand that when one is orbiting the earth in say the Shuttle the feeling of weightlessness is due to you "falling" with the curvature of the earth, however if you are say half way to the Moon and traveling in a "straight line" the force of gravity due to the earth is about 1.3 (if I've worked it out correctly) so would you be floating around in your space capsule? 1.3 is only slightly less than the acceleration due to gravity on the Moon which you can walk on?

The feeling of weightlessness is not to an astronaut falling with the curvature of the Earth. It arises from falling, period. After the Apollo vehicle performed its trans-lunar injection burn, the Apollo astronauts "fell" all the way from low Earth orbit to the Moon.

 

The feeling of weightlessness arises whenever gravity is, for all practical purposes, the only force acting on a person.

Sorry but I don't understand that.

 

I always thought from the "firing a canon ball fast enough off a mountain" experiment that if you were going fast enough you would always fall at the same rate as the curvature of the earth.

 

I'm not too sure about falling to the Moon either.

You cannot feel gravity. Whether you are moving toward the Earth, around the Earth, away from the Earth is irrelevant. If the only force acting on you is gravity, you feel weightless.

another example is skydiving or bungee jumping, for a short while after you jump out you are weightless as there isn't much air resistance acting on you but once you reach terminal velocity (or the bungee rope starts stretching) you feel your weight again.

Sorry but I don't understand that.

 

I always thought from the "firing a canon ball fast enough off a mountain" experiment that if you were going fast enough you would always fall at the same rate as the curvature of the earth.

 

I'm not too sure about falling to the Moon either.

 

That's because you need to get the ball into orbit — if you don't follow that circular path, you can run into the earth. That part's not about weightlessness.