(a) and (d) both make conceptual sense. (a) probably makes more sense than does (d), but both are at least somewhat reasonable.
they have slightly differing meanings:
(a) [participial -ing modifier] implies that "analyzing..." was just something that the satellites did while they were orbiting
while
(d) [infinitive] suggests that this is the PURPOSE - the reason WHY the satellites were orbiting.
(d) seems less likely to me, since it's a bit weird to orbit for the PURPOSE of analyzing echoes (as opposed to collecting or intercepting such echoes, which would make a lot more sense).
HOWEVER,
(d) is incorrect because this sort of infinitive construction CANNOT be preceded by a comma.
it just can't.
that's really the only reason why (d) is wrong.
Ron has been teaching various standardized tests for 20 years.
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Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
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Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
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