The direction in which the Earth and the other solid planets—Mercury,

VeritasKarishma mam GMATNinja sir Please explain how to choose between D and E

(E) has redundancy.

"Determined by" is the same thing as "is a result of"

We can say:
The direction in which planets rotate was determined by collisions with giant bodies. (Depending on how the planets collided with giant bodies, they started rotating in one direction or the other)

or

The direction in which planets rotate was a result of collisions with giant bodies.

But you cannot use both i.e. you cannot say "determined as a result of"
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The most appropriate choice is option D) "spin was determined by" because it clearly indicates that the spin direction of the Earth and other solid planets was caused by the collisions with giant celestial bodies in the early Solar System. The word "by" is commonly used to indicate the cause or reason behind an event or action, which fits well in this context. Option E) is close in meaning to option D, but it is not as precise in conveying the idea that collisions were the cause of the spin direction.