Several science fiction writers have proposed a simple “skyhook” satellite. This would consist of a (very) long rope placed in a geostationary orbit at a point directly above the equator, and aligned along the radial direction from the centre of the earth. The bottom end of the rope would thus remain just above a fixed point on the equator and the rope would extend vertically upwards. Find the length of rope which would be needed for such a device. Express your answer in units of the earth’s radius RE You can assume that the rope would have a uniform mass density and be strong enough not to break. You can also ignore the mass of any actual satellite at the end of the rope. So i assumed straight away that this question is all about infinitesimals. I thought the approach was, if you worked out what forces were acting on the rope, these could be summed over the entire length of the rope, as if they are broken small enough, these forces would essentially be constant. From this it would then be possible to solve for 'L', which is the length of the rope. Firstly i equated the forces; Gravity acting towards earth and 'centrifugal' force acting out due to the rotation of the earth. => mg = (mv^2)/r => mGM/r^2 = mw^2r These i thought would be integrated from RE to RE+L (where L is the length of the rope). However, i couldn't actually get to the point where you would solve for L so have became a bit lost. Any help would be appreciated. Thanks.