Unlike the other major planets, Pluto has a highly eccentric

If the doubt is about how to identify what is being compared with what, then the following note may give some insight.
First of all, a comparison is always marked by a comparison marker such as unlike, like etc, or other things such as than, as, in comparison to, in comparison with et al. Secondly, because like or unlike is a preposition, it will always be followed by a noun or noun phrase and that is the one that is being compared with something similar.
That is how, in the given text, the planet Pluto is compared with similar other planets and we cannot assume any things other than planets as those compared, when it is part of the un-underlined part. You can see the same happening in the given examples below.

Like their male counterparts, women scientists are above average in terms of intelligence and creativity, but unlike men of science, their female counterparts have had to work against the grain of occupational stereotyping to enter a “man’s world.”
(A) their female counterparts have had to work
(B) their problem is working
(C) one thing they have had to do is work
(D) the handicap women of science have had is to work
(E) women of science have had to work

Here note the phrase, unlike men of science, which makes its clear that men of science is being compared to a similar women of science. Choice E exhibits that.

2. Like the government that came before it, which set new records for growth, laissez-faire capitalism is the cornerstone of the new government.
(A) laissez-faire capitalism is the cornerstone of the new government
(B) the cornerstone of the new government is laissez-faire capitalism
(C) laissez-faire capitalism is the new government’s cornerstone
(D) the new government has made laissez-faire capitalism its cornerstone
(E) the new government has a laissez-faire cornerstone of capitalism

Here the comparison is marked by the word like and what is compared is the government. Therefore, we should now compare it with a similar government, and therefore, choice D, which compares the old preceding government with a new government with the right intended meaning, is the right answer.

3. Like the color-discriminating apparatus of the human eye, insects’ eyes depend on recording and comparing light intensities in three regions of the electromagnetic spectrum.
(A) insects’ eyes depend on
(B) an insect eye depends on
(C) that of insects depend on the
(D) that of an insect’s eye depends on
(E) that of an insect’s is dependent on the

Here an apparatus of the human eyes -is standing next to the comparison marker like and it may be noted that it is un-underlined. Hence, we should now compare it with another apparatus of some other eye. Choice D correctly states that
Hope this elucidates a root principle of comparison. (In case it is irrelevant, just ignore this note please.)