The correct option is B Discovered in 1884, the asteroid Ida, named for a mythological nymph who cared for the infant Jupiter, is in the middle of the belt of asteroids that orbit the Sun between Mars and Jupiter.
Here, option A has two errors (the same as that of the original sentence). The use of 'having been named' is wrong. This is so because 'having verb-ed' implies an action that was complete before another action. Since the main verb is 'was discovered', the meaning of the sentence becomes that the asteroid was named before it was discovered. Also, 'asteroid named Ida' seems superfluous when we can simply say 'asteroid Ida'. Since both 'discovered' and 'named' become verb-ed modifiers in option C, there is no verb left for the subject 'the asteroid'. The structure that D offers seems illogical. Here, 'discovered' seems parallel to 'cared' and even though this parallelism is not wrong, it is illogical. Additionally, the sentence is rendered illogical as 'to orbit' indicates purpose an implying that Ida is in the middle of the belt with a purpose to orbit the Sun between Mars and Jupiter. This same error occurs in E along with a lack of parallelism ('discovered in 1884', a verb-ed modifier, is not parallel to 'which was named..', a relative clause). Option B is the correct choice with no grammatical errors.