Question on Planet Hi: Why is the Answer B?

[jack1234]

Hi, I have a question here:
http://tinyurl.com/2v9vp7

I expect the answer to be c, but it ends up to be b, what is the reason?

 

[dynamicsolo]

Hi, I have a question here:
http://tinyurl.com/2v9vp7

I expect the answer to be c, but it ends up to be b, what is the reason?

What a lousy diagram! No wonder people can get this wrong! I think the intention is that the F vector is pointing from the planet right to the Sun. You are apparently intended to read this drawing as meaning that the planet is moving farther away from the Sun. Alternatively, you are supposed to see that the included angle between the force vector F and the velocity vector v is obtuse (> 90º), so that their dot product is negative, giving a negative gravitational power applied to the planet. But it doesn't look enough different from a right angle... (And what's with this lopping off of about a third of the ellipse?)

Frankly, though, particularly with that shading rendered on the planet, I was trying to read the image as a perspective drawing of a circular orbit or something near to one. I think the choices made in preparing this drawing are so poor that more than one ambiguity in interpretation is possible. (I sometimes think some of these drawings are deliberately made badly to trip up people taking the tests...)