Yup. As I said in another comment, you are not a point mass. The amount of your and her flesh that’s atom-width close is an astronomically small fraction of the total weight, no matter how close you cuddle, and this fraction gets squared because there are 2 bodies. (It’s an integral over two volumes – in layman’s terms, an atom in your hand feels strong (for an atom) attraction to an atom on her hand, but not her head even if your heads also touch.)
I know you realize this but for others: For atoms, point masses at the nuclei are a good simplification, but not for larger non-spherical objects unless they are really far away. The center of mass can be outside your body when you bend over and two people can therefore reduce the distance of their centers of masses to 0. However, this will not result in infinite attractive force (that could get Cirque de Soleil performers stuck bent over each other), similarly: pouring a liquid without adhesion or surface tension on a giant donut-shaped object in space would not result in it accumulating in a sphere in the center, the donut would get covered in it.
But if you are holding hands then r² becomes zero and the force of attraction is infinite.
Take the center of mass at that point. Can’t be 0 because atoms have widths.
Well we need to dive in quantum physics if we are going that deep, no?
Quantum gravity time! (Or each of you could be charged)
If clothing can have 00 sizes then so can anything.
Yup. As I said in another comment, you are not a point mass. The amount of your and her flesh that’s atom-width close is an astronomically small fraction of the total weight, no matter how close you cuddle, and this fraction gets squared because there are 2 bodies. (It’s an integral over two volumes – in layman’s terms, an atom in your hand feels strong (for an atom) attraction to an atom on her hand, but not her head even if your heads also touch.)
I know you realize this but for others: For atoms, point masses at the nuclei are a good simplification, but not for larger non-spherical objects unless they are really far away. The center of mass can be outside your body when you bend over and two people can therefore reduce the distance of their centers of masses to 0. However, this will not result in infinite attractive force (that could get Cirque de Soleil performers stuck bent over each other), similarly: pouring a liquid without adhesion or surface tension on a giant donut-shaped object in space would not result in it accumulating in a sphere in the center, the donut would get covered in it.
First assume that it is a spherical cow traveling through a vacuum…
Reading that was fun. Thanks.
If you’re holding hands tight enough that you can feel it at all, you’re already exerting more than 2 milliNewtons of force.