StephenHawking believes that the earth is unlikely to be the only planet _____ lifehas developed gradually.

which 吧！

StephenHawking believes that the earth is unlikely to be the only planet _____ lifehas developed gradually.

where,或者 on which
where 前面的介词会省略
在地球上演化出的生命，需要介词on

that需要做成分 可以看到空格前后的表达都是完整的 不缺成分

where 或者on which，lifehas developed gradually on the planet，所以 on which

StephenHawking believes that the earth is unlikely to be the only planet on which life has developed gradually.

'That' is not appropriate here as it is referring to a specific planet and not a general one, also it is not clear which one is referred to by 'that'. So it's better to use 'on which' to specify the planet.

因为后面的从句不全成分，只能用关系副词，不能用关系代词，若要用关系代词，则必须在关系代词之前加介词

此题为定语从句，先行词为planet，从句里为主谓结构，符合五大基本句式，故不填写关系代词。先行词是以地点状语的身份带回去，所以应该填where，或 on which

这里应该是where，因为earth是生命逐渐发展起来的地方。

如果一定硬要用that，也应该是that has developed life gradually。