GPE
figure 5.2 shows how the Ep of an object changes with distance either side from planet X.
such a graph is called a gravitational potential energy well or, more simply a gravity
well.
a) add to it a gravity well for a planet which is much more massive.
b) account fro the shape of the graph you have drawn
the new graph would have a well with more depth because the mass would mean
more GPE according to the absolute GPE formula
but wouldn't it also be skinnier and its curve approach zero GPE more quickly
because of its larger mass?
Hey! So if we have our function of GPE with respect to distance as:
That's really just a graph of the form \(y=\frac{k}{x}\). By increasing the mass of our planet, we are just increasing our value of \(k\). Let's say we take something 10 times greater, so \(10k\). Then compare the graphs (the
green graph is the larger planet):
So based on that, I'd actually say that the well is wider! I don't like this question though, because it doesn't specify that the mass is larger specifically, it just says "more massive." Also, I'm not sure whether you are drawing gravity wells that don't tend to negative infinity in the middle, that would alter this slightly and definitely result in a
deeper well as you've described
Welcome to the forums Katniss!