In the following sentence:
I don't think I can make it back to camp—you go on without me!
I would expect it to be "to the camp".
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For historical reasons, some words for places don't always require an article. "Camp" is one of those words. All of these are correct, for instance:
- My father is at church.
- Joe got sent back to jail.
- Sally's in hospital again.
There's a special rule that governs this usage though: the article is only optional if the place is being used for its intended purpose. This means that in sentence 1, my father is attending religious services at the church, not using the recreation facilities; in sentence 2 that Joe is a criminal, not a prison worker; and in sentence 3 that Sally is a patient of the hospital, not a visitor or a staff person.
In your example, it means the two people in the story are using the camp as a camp. And if it was, for example, an abandoned camp, and they were just meeting some people there, then they would have to say:
I don't think I can make it back to the camp
In such constructions, the determiner is optional. Sometimes it depends on the context and whether you are referring to a particular camp.
Back to camp/base/headquarters are all general descriptions rather than particular locations.
If you were referring to a particular camp or base, you would need the determiner.
Equally, you would need the determiner in phrases such as back to the office/factory/stadium/sports ground because you would be referring to particular locations.