Is my sentence correct?

Or maybe I should say it dfferent as I actually wanted to take a picture of the moon not a plane. Is it okay to say it then: 'I captured the moon with unexpected plane flying against to it. '

anonymous I captured a flying plane on the background of the moon.

It is so unnatural that it is quite humorous.

I photographed a plane flying across the face of the moon.

If you are talking about being on the rear of the moon, as in the 'dark side', then you can't refer to it as the 'background'.

Grammatically, it is correct. But semantically, the context is not logical. What you probably meant was you shaw a picture or a video of the moon in which you spotted a flying object.

I caught the silhouette of a plane in flight against the face of the moon.

There are practically infinite ways to put that.