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"within the orbit" is correct and usable in written English
You can use it when you want to say something is contained within a circular or elliptical range of motion. For example, "The satellite moves within the orbit of the planet."
Exact(60)
Within the orbit lies the orbital cone, which contains the eyeball and the rectus muscles surrounded by a fascia (Fig. 2).
Thus localized production of auto-antibodies could result from the high levels of IL-6 within the orbit, potentially driving their targeting of orbital antigens in TAO.
Anteriorly, the intraorbital fat and the other structures within the orbit are separated from the extraorbital structures by the orbital septum (Fig. 2).
Infections can also spread to the cranial cavity by way of the blood vessels that lie within the orbit.
One excellent solution is to shop Sancerre satellites, appellations within the orbit of Sancerre that also make sauvignon blanc wines.
In a country viewed as football crazy, almost no slice of life does not somehow fall within the orbit of the beautiful game.
Below are five examples, all within the orbit of Boston or Worcester, most established fairly recently in response to growing local support for the visual arts.
Because of her work at AllSafe, she's within the orbit of Evil Corp, even though it was responsible for the death of her mother.
Chamberlain saw no reason why Danzig should not come within the orbit of Nazi Germany and pressed Poland to open negotiations with Germany.
To account for this, the mass of the galaxy within the orbit of the stars must increase linearly with the distance of the stars from the galaxy's centre.
He and later astronomers spent decades looking for the missing planet within the orbit of Mercury which, they were convinced, explained what was going on.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com