Why is the gravitational potential against distance graph a curve?

F=GMm/(r^2)

Rewriting this a little u get

F=GMm*(1/r^2)

Comparing this to y=mx c u get he gradient as GMm, the intercept is the origin and the x axis must be 1/r^2.

For a graph as in c, consider

R^2=0.5, F=2GMm
R^2=1, F=GMm
R^2=2, F=GMm/2

As r^2 approaches zero F approaches infinity therefore the graph is not linear. In other words for a double in r^2, F halves.

Try plotting the above values on a graph and u should see it is non linear.

For ur first question u will get a straight line graph, try rearranging for urself as i have done above and comparing to equation of straight line.

The equation is V =-GM/r so wouldn't this mean that the relationship is V ∝ 1/r which is a straight line not a curve.

Also, I need an explanation for this question:

Which one of the following graphs correctly shows the relationship between the gravitational force, F, between two masses and their separation r.


The answer is D but I don't understand why C can't be the answer as well. All help is appreciated thanks!

Consider a graph of y=1/x let v=y and x=r and then -G and M are transformations

you wrote v a 1/r so v=k/r k is -GM

I honestly don't understand what you mean. Sorry

Do you do A level maths/ do you know what the graph of 1/x is?

Also At GCSE Maths you might have learned that if something is proportional to something else you can write an = if you add a k

i.e x ppt y so x=ky
or x ppt 1/y so x=k/y

Okay actually I do get what you mean. Having a graph of V against r and plotting V=1/r would be a curve. Holy crap lol I can't believe that I missed this.

So for the graph question. F against r^2 should be a curve so it is incorrect.
Thanks!