The similarities between Mars and Earth were enough to keep alive hopes of some form of Martian life.

1. 不定式的结构是：keep + 宾语 + 形容词（宾补）

2. 因宾语hopes of some form of Martian life 太长，为了照顾句子的匀称，把形容词alive 提前了。

3. keep hopes of some form of Martian life alive的含义是：使得......希望充满着的。alive不是“活着的”，而是表示“希望满满的，信心满满的”之意。

这种现象也叫作“词语分隔”或“成分分隔”现象。这属于谓语和宾语被宾补分隔。又如：

The discovery has made possible new techniques for brain surgery.

Finally, I dashed down the stairs, pushed open the front door.

He was told to speak briefly; accordingly he cut short his remarks.