Have you read about groups and masks(http://www.defold.com/manuals/physics/#_group_and_mask)? If I understand correct, they are what sets the relationship between physics objects.
Edit:
I also think static is wrong for somehing that moves(your plane). From the manual -
Static objects These do not react in themselves, but any other object that collides with static objects will react. These are very useful (and cheap performance-wise) for building level geometry (i.e. ground and walls) that does not move. You cannot move or otherwise change static objects.
I would try to use kinematic on the plane, and handle the trigger response.