The earth rotates once every 24 hours and moon every 29 days. But there are bigger problems to take care of.

- The length of the wire at minimum would be 384000 km. now this is a huge length. Let’s assume we have a steel rope of radius 1 cm. This entails a volume of 3 x 10^-4 × 4 × 10^8 cu.m. Our 12 x 10 ^4 cu.m. This will entail a mass of 96 × 10^7 kg or roughly 1 billion kilogram. This means a force of 10 billion Newton. I don’t think we have any rocket which can carry this weight into earth’s orbit let alone to moon.
- Let’s say somehow someone does this. Then comes the next problem. The weight is so high that the rope will snap under its own weight.
- Let’s say somehow it survives then comes the next problem. At the fastest the rockets will take at least two days to reach moon. In these two days earth would have spun twice. so the rope will simply get whirled around earth.
- Let’s say somehow that problem is also overcome then comes the Most severe problem. The rotation rates are so different that the stretching force on the rope will simply shred it into two.

So final verdict. It’s not possible to ties a rope between moon and earth.

via quara/shubham chakraborty