How efficiently can you pack together disks?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
The observer's line of vision is along a tangent to the surface of the
earth at the far point she can see on the horizon. Imagine a right
angled triangle with the observer at one vertex, the far horizon point
at another vertex and the centre of the earth at the third vertex.
You have enough information to find the angles in this triangle and
hence the distance required.