1. The problem statement, all variables and given/known data A broken spaceship is located 10 km above the center of a large circular thin sheet of unknown dust. The sheet has a radius of 106km and a density of 7×1011kg/m2. The spaceship and the dust attract each other due to the gravitational force. a) Find the initial acceleration of the spaceship. b) Find the acceleration of the spaceship right before the spaceship hits the dust. c) What will the astronauts in the spaceship experience right before the spaceship hits the dust? 2. Relevant equations F=(GMm)/r2 3. The attempt at a solution I realized that the distance from the spaceship to any point on the sheet (except the center) would constantly be changing as the spaceship moves close and closer. This prompted me to set up an integral of the form F=∫(Gm*(2Mr/R2)*h)/(r2+h2)3/2 dr with integrating factors from h2 to( R2 + h2) using U-sub and moving the constants out I obtained the answer ((1/2)*GMm)/R2)(1-h)/(r2+h2) then use F=ma and solving for a a=F/m I obtained a=(((1/2)GM/r2)(1-(h/sqrt(r2+h2) this seems right, but does not make any sense for the acceleration right before the spaceship hits the cloud. I would assume this value would be zero.