Titanium-Devouring Aliens-Gravitational Field,Potential Energy (Titanium-Devouring Aliens) A spaceship of titanium- devouring little green people has found a perfectly spherical asteroid that they confirm is made of homogeneous titanium. A narrow shaft was bored from some point on the surface to the center of the asteroid. But then, an accident occurs when one of them falls into the hole at the surface, down the shaft, and dies upon impact. However, these aliens being devoid of human sympathy, continue working until out of the narrow shaft they have excavated an entire sphere with a diameter equal to the asteroid's radius. Then again, at this point, another accident occurs. From the same hole at the surface, another green person falls, and again dies upon impact. Now the Supreme Commander of the little green people is alarmed by these events and sends an expert to investigate. In particular, the expert is asked which of the two accidents had a larger impact speed. The expert does more though; she sends the exact ratio between these speeds. What is this ratio that she sends? (Hint: It may help to consider a sphere of "negative mass density".) Ok so this is a question that was created out of thin air obviously by my teacher but whatever. The only thing I can think of is that the gravitational field in the asteroid must be equal everywhere, despite the shape of the shaft in which the alien falls. If this is the case wouldn't the ration be zero? Please help!!!!