Recent content by Puff Cube

I tried it: $$ \ddot{r} = a - \frac{GM}{r^2} $$ $$ \ddot{r} \dot{r} dt = ( a - \frac{GM}{r^2} )\dot{r} dt $$ $$ \frac{ d \dot{r} }{dt} \dot{r} dt = ( a - \frac{GM}{r^2} ) \frac{dr}{dt}dt $$ $$ \dot{r} d \dot{r} = ( a - \frac{GM}{r^2} ) dr $$ integrating, I get $$\frac{1}{2} \dot{r}^2 = ar +...

I saw it and fixed it before I even saw your post :cool:. As for energy, I'm afraid I'm not familiar enough with physics concepts to go down that route.

Never mind, I've tried it again and got this: $$ a_{net}(r) = a - g(r) $$ $$ a_{net}(r) = a - \frac{GM}{r^2} $$ So it looks like, if I'm not mistaken, I would need to find a solution to the following DE (which I won't): $$ \frac{ d^2 r(t)}{d t^2} = a - \frac{GM}{r(t)^2}. $$ I made...

Homework Statement Suppose there is an object that is a distance ##r_0## from the center of a planet that is nearby (the object is outside the surface of the planet). Let ## r ## represent the distance from the object to the planet's center. Let ## t ## represent time. The object, which is...