Is the sentence right?

It’s incorrect basically because it’s an incomplete sentence.
It doesn’t say who did what in reference to the apartment.

One correct way of saying it would be ”...when I went back to the apartment.”

I saw a big white circle around the moon last night when I went back to the apartment, so it is going to be windy today.

It is going to be windy today; when I returned to the apartment last night, I saw a big white circle around the moon.

This is a good chance to use a semicolon to link two related sentences together.

I believe it will be windy today, since I saw a big, white circle around the moon as I was returning to my apartment last night.

It’s close to being correct. Aside from the suggestions above, it could also work if it were written as:

“It is going to be windy today, as I saw a big white circle around the moon last night when back at the apartment.” In this version, what is implied but not written is: “when [I was] back at the apartment”. That is, “I saw… circle… when [I was] at the apartment”.

English prepositions can give lots of trouble, because we use them in so many ways.

Missing a verb in between “when” and “back”. Could be ”...last night when I went back to the apartment” or maybe you meant “when I was back at the apartment”. Depends on what you were trying to say.

“Apartment” needs to have an article or another adjective in front of it, such as ”the apartment”, ”my apartment”, etc.

Also, saying “as I saw” to explain a reason is a bit awkward in English. It sounds better to say ”because I saw” or ”since I saw”.

Thanks for all your nice-answers. You just not merely correct the sentence, but taught me a lot.

“It is going to be windy today. I saw a big white circle around the moon last night when going back to my apartment.”

even better:

”...last night on my way back to my apartment.”

I would avoid any construction that suggests that seeing the circle is the cause of the windy weather. The windy weather is not the result of your seeing a circle around the moon. In other words, the sight of the white circle might be the (supposed) reason for your prediction, but it is not the reason for the wind.

You are talking about a halo around the moon (and not a “white ring”). And it usually predicts a storm rather than just strong wind. This has nothing to do with English grammar and usage, however. Photo

Moonlight is diffracted by ice crystals in the earth’s upper atmosphere.

whilst returning to my apartment.