1. Working outside is very hard for the people in Antarctica.

2. Working outside is very hard for the people of Antarctica.
[Can we use both prepositions, 'in' and 'of'?]

3. They study sea animals in Antarctica.
4. They study sea animals of Antarctica.
[Can we use both prepositions, 'in' and 'of'?]

Yes, you can use both prepositions, but they don't mean exactly the same thing. Do you understand the differences?

What differences do they have?

The differences are very slight. I'll vary the sentences a bit so you can tell the difference easily. (These differences don't matter when referring to Antarctica since there have never been indigenous human populations there.)

1. Working outside is very hard for the people in Alaska.
2. Working outside is very hard for the people of Alaska.

#1 refers to people who are in Alaska, working hard, no matter where those people came from.
#2 refers to people who are indigenous to Alaska.

3. They study sea animals in Australia.
4. They study sea animals of Australia.

#3 refers to people who study sea animals, no matter where those animals came from.
#4 refers to people who study only species that are native to Australia.

In referring to Antarctica, the differences between these two prepositions in these particular sentences is practically non-existent. But if you put other geographical areas in place of "Antarctica," the differences are clearer.

1. Both "in" and "of" can be used in these sentences, but they convey slightly different meanings.

Using "in" in the sentence "Working outside is very hard for the people in Antarctica" suggests that the people being referred to are currently located inside the continent of Antarctica. It implies that they are part of the population residing and working in Antarctica.

On the other hand, using "of" in the sentence "Working outside is very hard for the people of Antarctica" refers to people who are from or associated with Antarctica. It could refer to people who are natives of Antarctica or those who have a strong affiliation with the continent.

So, while both prepositions are grammatically correct, they carry different connotations.

2. Regarding the sentences "They study sea animals in Antarctica" and "They study sea animals of Antarctica," again, both prepositions can be used, but they convey different meanings.

Using "in" in the sentence "They study sea animals in Antarctica" means that the study of sea animals takes place within the boundaries of Antarctica. It implies that researchers and scientists are conducting their studies physically in Antarctica.

Using "of" in the sentence "They study sea animals of Antarctica" suggests that the focus of their study is specifically on sea animals that are native to or associated with Antarctica. It implies that researchers are studying the unique sea life found in the waters surrounding Antarctica.

So, both prepositions can be used, but they convey different aspects of the research being done.