I first want to say that this isn't a problem from school or anything, I just thought of it one day and when I tried to do it, I couldn't! 1. The problem statement, all variables and given/known data If the earth suddenly stopped orbiting the sun in its circular path, it would immediately begin the accelerate toward the sun in a straight path. From a classical kinematic point of view, how long will it take the earth to reach the sun if r(0)=ri (distance from earth to sun), v(0)=0, and a(0)=0. I understand classical kinematics (a=dv/dt=d^2x/t^2), but in a macroscopic case like this, acceleration isn't constant; its a function of position, according to Newtons Law of gravitation a=G*m/r(t)^2. 2. Relevant equations Newton's law of gravitation: A smaller object will accelerate towards a larger object with an acceleration = G*m/r(t)^2, where G is the gravitational constant, m is the mass of the bigger object, r(t) is the distance between the two objects. 3. The attempt at a solution The first thing I thought to do was integrate a=G*m/r(t)^2 twice with time to get s as a function of t. => v=G*m*t/r^2 => s=G*m*t^2/(2*r^2) and s(ti)=r and s(tf)=0. I don't know where to go from there because of I have position as a function of time and position (if that makes sense?) So r(t)=ri - s. => s=ri - r(t) => ri - r(t) = G*m*t^2/(2*r^2). Can anyone help me out with this one? Thanks!