The most common and most likely answer to this crossword clue is the 10 letter word EQUATORIAL
I've seen this crossword clue in Independent
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More clues leading to the result EQUATORIAL
Buddy explains!
The straight part
We know that "on a great circle" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case on a great circle = equatorial.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does EQUATORIAL mean?
EQUATORIAL noun- A kind of telescope mounted so as to have two axes of motion at right angles to each other, one of them parallel to the axis of the Earth, and each carrying a graduated circle, one for measuring declination, and the other right ascension, or the hour angle, so that the telescope may be directed, even in the daytime, to any star or other object whose right ascension and declination are known.
- Of, near, or relating to the equator
- Perpendicular to the plane of a ring