In Chinese, people say "看书“ when they read quietly content of the book, instead of looking at its cover. It's a common and simple way to describe the action. While "读书“ has multiple meanings. 1. it means reading as "看书“；2. it means "read out" a book, because "读" initially means "read out". In ancient times, students used to read out loud poems in class to study and recite. "看天“ is okay. For astrologist, we could say "观察天“（observe the sky). If you were astrologer, you could also say "观察天相“ when reading its signs. ;) Hope it would help.

看书 means to read a book - like sit down and read a book in your spare time. 读书 also means to read a book but not in the casual sense, it is used for studying and can even refer to attending school. 我看天 would be more like saying "See what heaven does" "Wait on heaven". 天 means heaven, 天空 means the sky. You could say 我看天空 but it isn't natural because 天空 is a large expanse of the sky. It's easy to take 看 to mean "wait and see“, ”look for an outcome". If you say 《看你。》It would usually mean - "Whatever you think/like". To say "I look at the sky" it may be best to use the verb 观看 or 望 - 我望天看。我望着天。If you add another verb at the end of the sentence it makes it clearer that you are looking at the sky. 我看着天唱歌。(I looked at the sky and sang.) Your question tricky and brings up quite a unique situation that is affected by the Chinese cultural-linguistic mindset around 天, which is much different from that of Western languages.

In both Mandarin and Cantonese, 看书 means read a book. While 读书 is more likely in Cantonese. It means "general study" and for sure it including 看书 this short term action. 读书 is more likely a long term thing last for several years. Normal people looking at the sky we say "看着天", while astrologist looking at the sky we say "观天." Feels a bit hard.

The answer is no. This is cultural biases. I watch the sky = 我視着天空 I look at the sky = 我望着天 I observe the sky = 我觀着天 astrologer = 占星家 imperial astrologer = 鑒天官

不能说 “我读天”，也不要说 “我看天”，应该说 “我看着天空” 或 “我往天上看”。