This beautiful woman is holding an armilar sphere. In National Gallery web site we can read:
This richly clad girl, her clothes sewn with hundreds of pearls, is probably the exiled Dorothea, eldest daughter of King Christian II of Denmark, who was deposed in 1523.
In her left hand she holds, upside down, a small armillary sphere. The hoops indicate the motions of the heavenly bodies. The latitude the girl is indicating is very close to that of Copenhagen: the sphere may be upside down in allusion to her father’s lost kingdoms.
She is placed in front of a painted frame, a device Gossaert often used in his portraits to give the illusion that his subjects are real rather than painted.
So the armilar sphere can be a propagandistic object which was put in her hands to claim for the political troubles of her family.