How would the Sun's gravity affect us if we weren't in orbit? So since we're in orbit around the sun, we are basically in free-fall. From what I understand, this means that we don't feel the gravity of the Sun like we do the Earth. Just like astronauts on the space station don't feel the gravity of the earth.
This got me wondering, how much would the Sun's gravity affect us if we weren't in free-fall. As if the Earth was being held by an invisible hand, and if that hand let go, we would fall straight into the Sun. Or if we had supports reaching to the Sun holding us in place, like a really really tall water tower.
Would the people on the side of the Earth facing the sun be lighter than the people on the opposing side? Would the difference be noticeable? Would people be pulled into the Sun, or would the distance make it's gravity be too weak compared to the Earth?
This has been bugging me for a while.
 A: That completely depends on the distance Earth-Sun. If the distance is high enough (currently no numbers, but I can add some later), then we can feel something, but the gravity difference is so low that only instruments can measure the difference. The nearer we get, the more we are going to feel the difference. First the people directing towards sun are getting lighter, if we move Earth further towards sun, gravity is going to start to influence earth directly, meaning that for example tectonics are going to depend partially on the gravity of the sun. The nearer we get, the more this effect is measurable and feelable, until we are near enough that the gravity of the sun can tear us apart.
Ok, let's add some numbers (if I did not make a mistake during calculation): If we are in our current position, the force between the side directed towards sun and the opposite site is at around $4\cdot10^{-8}\,{\rm N}$. Not so impressive? Ok, let's go further. If the distance is going down to $5\cdot10^8\,{\rm m}$, the difference force is going up to ~$1\,{\rm N}$. Still not impressive? Ok, let's narrow the distance down to $2\cdot10^7\,{\rm m}$. Then the resulting difference force is at around $17\cdot10^3\,{\rm N}$. Quite a lot and you are already worrying about that? Ok, then remember that Mercury is at a distance of $5.75\cdot10^{10}\,{\rm m}$, and there it is hot. So, I am sorry for the overweight ones who thought that moving themselves nearer towards sun would decrease the numbers on the scale: It would work, but only for a very short time.
A: If you weigh 200lbs, the force from the sun would be about 2 oz:

The difference in weight from one side of the earth to the other would be practically negligible (0.00033 oz).
If Earth was held in place, this would be too little force to pull people off the surface.
