While flying, I observed a pale rainbow in a perfect circle against the white cloud bank below the plane. Can you account for the phenomenon?
— Wliliam Stone, Crystal Lake
The circular rainbow you saw is called a glory. Glories are visible when sunlight interacts with small cloud droplets that reflect and refract the sun’s rays directly back toward the sun.
They are only visible around the shadow of an object in the direct path of both the sun’s incoming and reflected rays, in your case the plane’s shadow.
Before air travel, glories were only visible to people on sunny mountain peaks, viewing them around the shadow of their head on a cloud or fog bank below.
A glory’s colors are the same as a primary rainbow’s: red on the outside and violet on the inside.