I am trying to find a velocity for an object that would launch it into space from earth (straight up, NOT into orbit) and return exactly 8 days later. I cannot use x = v0t + 1/2at^2 (x=0 t=691200 a=9.8 [seconds in 8 days]) because the distance from the Earth changes in such a great way that acceleration is not realistically constant any more. I know this would require calculus, but I cannot find a formula or a method. I believe some reworking of escape velocity would do, but there is no reference to time. I know this is a very specific question, but any guidance would be a great help.